FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK

FIBEROPTIC SENSOR
TECHNOLOGY HANDBOOK
by
Charles M. Davis
Edward F. Carome
Martin H. Weik
Shaoul Ezekiel
Robert E. Einzig
Publisher and Distributor
Optical Technologies (OPTECH)
A Division of Dynamic Systems, Inc.
360 Herndon Parkway, Suite 1200
Herndon, VA 22070-5225
Tel: (703) 478-0844 Fax: (703) 478-0649

Copyright Optical Technologies, Inc., 1982; 1986
Registration Number TX 1-094-758
All rights reserved.
No part of this publication may be
reproduced, copied or transmitted, in any
form or by any means - graphic, electronic,
or mechanical, including photocopying,
taping or information storage and retrieval
systems - without the prior written
permission of Optical Technologies (OpTECH).

FOREWORD
THE FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK
The FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK reflects
the latest technology concerning the field of
fiberoptic in general and fiberoptic sensors in
particular. The fiberoptic sensor technology principles
and practices laid down in this HANDBOOK will give the
reader a solid basis for mastering a relatively new
technology. Only a nominal general technical background
is needed to fully comprehend its contents. The
contributing authors have been as explicit and rigorous
in their presentation as time and space constraints in
this HANDBOOK would permit. All the material has been
edited to ensure coherency and consistency.
OPTICAL TECHNOLOGIES, INC.
Optical Technologies, Inc. (OPTECH) is a young and
rapidly growing corporation devoted to the research and
development of useful fiberoptic sensor applications and
to the advancement of fiberoptic sensor technology.
OPTECH is recognized as a leader in this field. The cofounders
of OPTECH, Dr. Charles M. Davis and Mr. Robert
E. Einzig, who are also authors of this HANDBOOK, are
pioneers in the field of fiberoptic sensor technology.
Dr. Davis headed the branch at the Naval Research
Laboratory that designed and produced the first
fiberoptic hydrophore. He has since collaborated in the
design of numerous other fiberoptic sensor systems. Mr.
Einzig has also designed fiberoptic sensor systems for
private research laboratories, industry and government.
Finally, both men were the key contributors to the
development of the Navy’s Fiber Optic Sensor System
(FOSS) Program in 1977. Presently, their experience and
talents are being applied at OPTECH where, together with
other physicists and engineers specializing in
fiberoptic sensing, advances in the field are continuing
to be made. To date, OPTECH’S experience with
fiberoptic sensors includes development of sensors for
the measurement of temperature, pressure, acoustic
signals, acceleration, magnetic fields, and seismic
disturbances.
AUTHORS
Charles M. Davis, PhD. Currently Dr. Davis is Vice
President of Optical Technologies, Inc. He has over 30
years of experience in acoustooptics and physical
acoustics. As head of the Physical Acoustics Branch at
the Naval Research Laboratory, he was instrumental in
the development of the fiberoptic hydrophore and the
establishment of the FOSS Program.
Edward F. Carome, PhD. Currently Dr. Carome is a
Professor of Physics at John Carroll University. He
participated in the initial research at the Naval
Research Laboratory that led to the development of the
fiberoptic hydrophore.
Martin H. Weik, D.SC. Currently Dr. Weik is a
senior systems analyst at Dynamic Systems, Inc. Dr.
Weik has written several comprehensive dictionaries in
the fields of computers, information processing systems,
fiberoptic, lightwave propagation, and general
communications.
Shaoul Ezekiel, D.SC. Currently Dr. Ezekiel is a
Professor at MIT. He has conducted research concerned
with ultraprecision measurements using optical
techniques. More recently, he has investigated the use
of passive resonators and fiberoptic interferometers for
rotation measurements.
Robert E. EinziR, MSEE. Currently Mr. Einzig
serves as President of Optical Technologies, Inc. He
has extensive applications experience in fiberoptic
sensors and data transmission systems, which adds to his
broad underwater acoustic sensor background.
ACKNOWLEDGEMENT
Appreciation is extended to Dynamic Systems,Inc.
and specifically to Mickey Hedrick, Sandee M. Boyer, and
Sue M. Gift, and their supporting staff for their
secretarial, word-processing, and graphics support in
the preparation of this Handbook.
Robert E. Einzig
President
Optical Technologies, Inc.

TABLE OF CONTENTS
FOREWORD
CHAPTER
1.0
1.1
1.2
INTRODUCTION
Background .
Purpose . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . .1-1
. . . . . . . . . . . . . . . . . . . . . . . . . . . .1-1
. . . . . . . . . . . . . . . . . . . . . . . . . . . .1-1
1.3
Contents by Chapter . . . . . . . . . . . . . . . . . . . . . . . .1-1
2.0
2.1
2.2
FIBEROPTIC SENSOR COMPONENTS . . . . . . . . . . . . . . . . . . . .2-1
Optical Fiber Properties . . . . . . . . . . . . . . . . . . . . . .2-1
2.1.1 Design Objectives . . . . . . . . . . . . . . . . . . . . . .2-1
2.1.2 Lightwave Propagation . . . . . . . . . . . . . . . . . . . .2-4
2.1.3 Propagation Modes . . . . . . . . . . . . . . . . . . . . . .2-5
Optical Fiber Fabrication . . . . . . . . . . . . . . . . . . . . .2-12
2:2.1
2.2.2
Refractive Index Profile Control . . . . . . . . . . . . . .2-12
Fiber Fabrication Processes . . . . . . . . . . . . . . . . .2-13
2.2.2.1 The Double-Crucible Process. . . . . . . . . . . . .2-13
2.2.2.2 The Inside Vapor-Phase Oxidation (IVPD) Process . .2-14
2.2.2.3 The Outside Vapor-Phase Oxidation (OVPD) Process . .2-15
2.2.2.4 The Vapor Axial Deposition (VAD) Process . . . . . .2-15
2.2.3 Fiber Strength . . . . . . . . . . . . . . . . . . . . . . .2-16
2.3
2.4
Solid State Fiberoptic Light Sources . . . . . . . . . . . . . . .
2.3.1 Energy Levels in Semiconductors . . . . . . . . . . . . . .
2.3.2 Light Emitting Diodes (LEDs) and Diode Laaers . . . . . . .
Photodetector . . . . . . . . . . . . . . . . . . . . . . . . . .
.2-17
.2-17
.2-19
.2-22
3.0
3.1
3.2
3.3
4.0
FIBEROPTIC COMPONENT INTERCONNECTION . . . . . . . . . . . . . . .
Fiberoptic Connectors and Splices . . . . . . . . . . . . . . . .
3.1.1 References. . . . . . . . . . . . . . . . . . . . . . . . .
Fiberoptic Couplers . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 References . . . . . . . . . . . . . . . . . . . . . . . .
Fiberoptic Cables . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Commercial Fiberoptic Cables. . . . . . . . . . . . . . . .
3.3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . .
LICRTWAVES IN FIBEROPTIC SENSORS . . . . . . . . . . . . . . . . .
.3-1
.3-1
.3-5
.3-5
.3-7
.3-7
.3-7
.3-8
.3-8
.4-1
4.1
Interferometric Fiberoptic Sensors . . . . . . . . . . . . . . . .
4.1.1 Intensity Interferometry . . . . . . . . . . . . . . . . .
4.1.1.1 Basic Principles . . . . . . . . . . . . . . . . .
4.1.1.2 The Michelsen Interferometer . . . . . . . . . . .
4.1.1.3 The Mach-Zehnder Interferometer . . . . . . . . .
4.1.1.4 The Sagnac Interferometer . . . . . . . . . . . .
4.1.1.5 The Fabry-Perot Interferometer . . . . . . . . . .
4.1.1.6 Interferometer Sensitivity . . . . . . . . . . . .
4.1.2 Fiberoptic Intensity Interferometers . . . . . . . . . . .
4.1.3 Polarization in Fiberoptic Sensors . . . . . . . . . . . .
.4-1
.4-1
.4-1
.4-1
.4-1
.4-2
.4-2
.4-2
.4-3
.4-3

4.2 Phase
4.2.1
4.2.2
4.2.3
4.2.4
4.2.5
4.2.6
4.2.7
4.2.8
and Intensity Detection . . . . . . . .
Phase Detection . . . . . . . . . . . .
Homodyne Detection Applications . . . .
Phase Noise . . . . . . . . . . . . . .
Amplitude Noise . . . . . . . . . . . .
Satellite Modes and Multimode Operation
Phase-Locked-Loop Operation . . . . . .
Heterodyne Detection . . . . . . . . .
References . . . . . . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
. . . . . . . . . .
.4-5
.4-5
.4-8
.4-8
.4-9
.4-9
.4-1o
.4-1o
.4-11
4.3 Integrated Optical Circuits (IOCS) . . . . . . . . . . . . . . . . .4-12
5.0 FIBEROPTIC SENSORS AND COMPONENTS . . . . . . . . . . . . . . . . .5-1
5.1 Phase Modulated Fiberoptic Sensors . . . . . . . . . . . . . . . . .5-1
5.1.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . .5-1
5.1.2 Fiberoptic Acoustic Sensors . . . . . . . . . . . . . . . . .5-2
5.1.2.1 Acoustic Pressure Sensors . . . . . . . . . . . . .5-2
5.1.2.2 Pressure Gradient Sensors . . . . . . . . . . . . .5-3
5.1.3 Fiberoptic Magnetic Sensors . . . . . . . . . . . . . . . . .5-5
5.1.4 Fiberoptic Electric Current Senaors . . . . . . . . . . . . .5-6
5.1.5 Fiberoptic Spectrophones . . . . . . . . . . . . . . . . . .5-6
5.1.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . .5-7
5.1.7 Reference . . . . . . . . . . . . . . . . . . . . . . . . .5-7
5.2 Intensity Modulated Fiberoptic Sensors . . . . . . . . . . . . . . .5-7
5.2.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . .5-7
5.2.2 Evanescent-Field Fiberoptic Sensor . . . . . . . . . . . . .5-8
5.2.3 Reflection Coefficient Fiberoptic Sensor . . . . . . . . . .5-8
5.2.4 Moving Grating Fiberoptic Sensor . . . . . . . . . . . . . .5-8
5.2.5 Microbend Fiberoptic Sensor . . . . . . . . . . . . . . . . .5-9
5.2.6 References . . . . . . . . . . . . . . . . . . . . . . . . .5-12
5.3 Fiberoptic Linear Accelerometers . . . . . . . . . . . . . . . . . .5-12
5.3.1 References. . . . . . . . . . . . . . . . . . . . . . . . . .5-14
5.4 Fiberoptic Rotation-Rate Sensors . . . . . . . . . . . .
5.4.1 Introduction. . . . . . . . . . . . . . . . . . .
5.4.2 Methods of Rotation Sensing . . . . . . . . . . .
5.4.3 Interest in Optical Rotation Sensors. . . . . . .
5.4.4 Sagnac Effect in a Vacuum . . . . . . . . . . . .
5.4.5 Sagnac Effect in a Medium . . . . . . . . . . . .
5.4.6 The Magnitude of the Sagnac Effect. . . . . . . .
5.4.7 Methods of Optical Rotation Sensing . . . . . . .
5.4.8 Fundamental Limits in Optical Rotation Sensors. .
5.4.9 Fiberoptic Rotation-Rate Sensors. . . . . . . . .
5.4.10 Photon Shot-Noise Limit . . . . . . . . . . . . .
5.4.11 Ideal Performance . . . . . . . . . . . . . . . .
5.4.12 Measurement of Nonreciprocal Phase Shift. . . . .
5.4.13 Methods of Nonreciprocal Phase Modulation . . . .
5.4.14 Open Loop and Closed Loop Operation . . . . . . .
5.4.15 Problems in Fiberoptic Rotation Sensors . . . . .
5.4.16 Integrated Fiber “Gyros”. . . . . . . . . . . . .
5.4.17 Fiber Gyro Performance. . . . . . . . . . . . . .
5.4.18 Summary of Rotation-Rate Sensors. . . . . . . . .
5.4.19 General Conclusions Regarding Fiberoptic Sensors.
5.4.20References. . . . . . . . . . . . . . . . . . . .
. . . . . .5-14
. . . . . .5-14
. . . . . .5-14
. . . . . .5-15
. . . . . .5-15
. . . . . .5-16
. . . . . .5-16
. . . . . .5-16
. . . . . .5-17
. . . . . .5-18
. . . . . .5-18
. . . . . .5-19
. . . . . .5-19
. . . . . .5-20
. . . . . .5-21
. . . . . .5-21
. . . . . .5-22
. . . . . .5-23
. . . . . .5-23
. . . . . .5-23
. . . . . .5-23
6.0 FIBEROPTIC SENSOR ARRAYS AND TELEMETRY SYSTBMS . . . . . . . . . . .6-1
6.1 Fiberoptic Sensor ArraYs . . . . . . . . . ● . . . . . . . . . . . .6-1
6.1.1 Fiberoptic Senaor Array Design Considerations . . . . . . . .6-1
6.1.1.1 General Design Considerations . . . . . . . . . . .6-1
6.1.1.2 Specific Design Considerations . . . . . . . . . . .6-1
6.1.2 Fiberoptic Sensor Array Basic Configurations . . . . . . . .6-1
6.1.3 Fiberoptic Sensor Array Budgets . . . . . . . . . . . . . . .6-5

6.2 Fiberoptic Telemetry Systems . . . . . . . . . . . . . . .
6.2.1 Fiberoptic Telemetry System Design Options . . . .
6.2.2 Fiberoptic Telemetry System Basic Configurations .
6.2.3 Telemetry System Budgets . . . . . . . . . . . . .
6.2.3.1 Risetime Budget Analysis . . . . . . . . .
6.2.3.2 Optical Power Budget Analysis . . . . . .
6.2.3.3 Cost Budget Analysis . . . . . . . . . . .
6.2.4 Fiberoptic Telemetry System Specific Configurations
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
. . . .
.6-5
.6-6
.6-6
.6-7
.6-7
.6-9
.6-9
.6-9
6.3 Fiberoptic Sensor Array Telemetry Transmission Line Parameters . . .6-11
6.3.1 Transmission Line General Parameters . . . . . . . . . . . .6-11
6.3.2 Transmission Line Specific Parameters . . . . . . . . . . . .6-11
6.3.3 Multiplexing with Optical Fibers . . . . . . . . . . . . . .6-12
6.3.4 Connector Parameters . . . . . . . . . . . . . . . . . . . .6-13
6.4 End-Terminal (Receiver) Consideration . . . . . . . . . . . . . . .6-13
6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6-13
APPENDIX - Fiberoptic Sensors Glossary. . . . . . . . . . . . . . . . . .A-l

CHAPTER 1
INTRODUCTION
1.1 BACKGROUND
The ever-present need for increased communication
aystem capacity and reduced cost per message
unit has spurred the development and installation of
hundreds of operating lightwave communication ayatems
around the world. Compared to wire aystems, optical
fiber transmission syatems operate with less energy per
message unit-mile, lower signal attenuation per unit
distance, higher bandwidth for increased channel capacity,
lower electromagnetic interference, lower crosstalk,
higher resistance to clandestine tapping, lower
shock hazard, amaller size, less weight, reduced consumption
of critical metals, and many others. These
advantages have encouraged improvements in light
sources; optical fibers, cables, and connectors; and
photodetectors. Optical fiber data links are off-theshelf
ready-to-install items. Hundreds of millions of
dollars are being spent annually for improving optical
communication system component.
Capitalizing on the availability of optical
components, there haa been significant progress during
the past few years toward the development of a new
claaa of sensors employing fiberoptic. These sensors
are capable of detecting acoustic fields, linear and
rotational acceleration, electric and magnetic fielda,
and many other physical parameters. In effect, the
senaor modulates some feature of the lightwave in an
optical fiber such as the intenaity OT the phase.
Usually phase modulation must be converted to an intensity
modulation prior to detection. This may be accomplished
by means of an optical interferometer. The resulting
signals (intensity or phase) can be telemetered
to places other than the location of the sensor (transducer,
modulator) by means of a fiberoptic signal transmission
(telemetry) system. The optical signal may be
in analog or discrete form and the system may operate
with or without optical-to-electrical or electrical-tooptical
signal conversion. The fiberoptic aensors described
in this manual may use fiberoptic transmission
systems as well as electrical or electromagnetic transmission
systems. Even for the simplest case, one in
which a visual field or image is to be transmitted in
a coherent-fiber cable, the fiber bundle itself must
serve as the sensor and all the aspects of achieving
lightwave acceptance by optical fibers must be considered.
1.2 PURPOSE
This manual on fiberoptic sensors is designed
to be a stand-alone document intended to serve many purposes.
It provides a basic background for understanding
the concepts that make up the field of fiberoptic,
particularly as they apply to fiberoptic sensors. It
describea the propertied of optical fibers, then fabrication,
and the properties of light sources and detectors
associated with fiberoptic sensora. Specific
emphasis is placed on design considerations for these
major components and for associated connector,
splices, couplers, and cables.
Different schemes may be used for controlling
lightwaves in order to sense a physical parameter. Many
of these control schemes are discussed in this manual,
including interferometry, polarization, and modulation.
Intensity and phase modulation are discussed in terms
of homodyne and heterodyne detection. Integrated optical
circuits are introduced with emphasis on their fabrication
and operating principles.
Many different types of fiberoptic sensors
are described in terms of their design and operation.
Some of these include intensity and phase modulation
sensora, rotation sensors, and accelerometers. Devices
discussed include the fiberoptic sensora (transducers,
modulators) used in hydrophores, magnetometera and geophones.
In most fiberoptic sensor and sensor array
applications there will be a requirement to telemeter
sensed data over the full range of distances. Various
fiberoptic aensor arrays and telemetry schemes are discussed.
Information is given concerning risetime and
power budgeting. Overall design considerations for telemetry
systems are also briefly discussed.
1.3 CONTENTS BY CHAPTER
Following thia brief Introduction, (Chapter
1), Chapter 2 is devoted to the properties of the baaic
component of the fiberoptic sensor: the optical fiber
itself. Electromagnetic wave (lightwave) propagation
in optical fibera in terms of the wave equation; the
coupling of lightwaves in and out of fibers; power loss
by absorption, leakage, and scattering; are all discussed
in some detail. Various properties of fibers, their
basic construction and limitations are discussed, including
basic concepts of total internal reflection,
critical entrance angles, and numerical aperture. The
concepts of mode propagation, refractive index profiles,
and polarization are introduced. Various methods of
fiber fabrication are covered, including several methods
of drawing fibers. Obtaining deaired refractive
indices and the size, strength, and level of purity of
fibers are also described. Finally, in Chapter 2, the
characteristics of various types of light sources are
discusaed in sufficient detail to understand their use
in connection with fiberoptic sensors. The chapter
closes with a discussion of the characteristics and
limitations of photodetectors with apecial emphasis on
their importance and use in connection with the output
signal from a fiberoptic sensor.
Chapter 3 follows with a diacuasion of the
various means for connecting fiberoptic aenaor inputs
to electrical or optical sources and outputs to photo-
1-1

detectors or display devices. The sensor may be connected
to optical fibers and cables by various types
of connectors, splices, couplers, mixers, and cables,
the connector and splice being used primarily to join
fibers and cables, the couplers being used to connect
one source to many fibers (divergence), the mixer being
used to couple many fibers to one photodetector (convergence).
The operation of fiberoptic sensors cannot be
well understood without an understanding of the varioua
actions and interactions that can take place by and
among lightwaves. Many of these interactions are the
basis for sensing physical parameters. The lightwave
characteristics discussed in Chapter 4 include interferometrics,
polarization, and intensity and phase modulation
in relation to homodyne and heterodyne detection.
Chapter 4 ends with lightwave control technique
used in integrated optical circuits.
Chapter 5 turns primary attention from general
principles and techniques used in the operation of
fiberoptic aensora to a description of the sensors
themselves and their components. Intensity modulation
sensors; phase modulation devices, such aa those used
in hydrophores and magnetometera; rotation sensors, accelerometers,
and geophones are discuased as examplea
of fiberoptic sensor applications.
The grouping of fiberoptic aensors into senaor
arrays and the telemetering of their outputs to
other locations are covered in Chapter 6. Design options;
basic configuration; riaetime, power, and coat
budgeta; and specific configurations of fiberoptic
arrays and telemetry aystema are diacuased in depth,
along with light sourcea, transmission lines and endterminals
as they relate to fiberoptic senaors.
Bibliographies pertinent to the subject are
included at the end of each chapter. The appendix contains
an authoritative glossary of terms and definitiona
in the field of fiberoptic with emphasia on the terms
used to describe the design, fabrication, and operation
of fiberoptic aenaors. Particular attention in the
gloasary is devoted to the terms used in this manual.
Many topics and concepta related to fiberoptic senaors,
their operating principles, and supporting theory are
included in the glosaary ao aa not to overburden the
reader with too many detaila while the main topics are
being discussed. For example, concepta concerning diaperaion,
Msxwell’a equations , modulation, polarization,
reflection and transmission coefficient, and various
tvpes of fiberoptic sensors and interferometers are
described in the glosaary.
1-2

CHAPTER 2
FIBEROPTIC SENSOR COMPONENTS
2.1 OPTICAL FIBER PROPERTIES
In this section the basic properties of optical
fibers are discussed in some detail with emphasis
placed on concepts that are important in optical fiber
sensor technology. The structure of optical fibers is
quite simple, as shown in Fig. 2.1. Basically they
consist of layered cylinders of glass or plastic with
small diameters. There is a central cylinder called
the core, which is made up of one type of glass or
plastic. Surrounding the core is a cylindrical shell
called the cladding that is made of a slightly different
type of glass or plastic. The difference between
the core and cladding materials will be discussed later.
Finally, this layered cylinder is usually surrounded by
a Protective jacket. The light-guiding capability of
the fiber is dependent upon the properties of the core
and cladding while the mechanical strength of the fiber
is maintained by the jacket that is usually made of
plastic.
CL’
‘A’!” A
INPUT
Fig. 2.2
MODULATING SIGNAL
LIGHT PULSES
OPTICAL
DET&CT- .
A basic optical fiber link.
OUTPUT
Four major optical fiber design objectives
will be discussed. The first major objective is the
desirability of maximizing the amount of available light
that is transferred (coupled) into the core of the
fiber. It is only the light in the core that is propagated
along the length of the fiber with relatively low
optical power loss. In order to maximize the amount of
light transferred (coupled) into the core, it is necessary
to maximize the numerical aperture (NA) of the
fiber. This is one of four important fiber parameters
that strongly affect the behavior of the simple system
shown in Fig. 2.2. After introducing the other three
important parameters, each will be discussed in some
detail.
The second fiber design objective is the de-
1/ L sizability of minimizing the light lost from a beam as
it travels through the core from the input end to the
output end of the fiber. This light loss is described
as the attenuation (power leas) rate, usually expressed
in dB (decibel) per kilometer of fiber.
CORE
Fig. 2.1 The basic structure of an optical fiber.
2.1.1 Design Objectives
Some of the design objectives considered in
the development of a good optical fiber are illustrated
by the simple system shown in Fig. 2.2. The system consists
of a pulse-modulated optical source. The input
signal at the left represents the intelligence (information)
that is impressed on (modulates) the light beam
that, after emerging from the source, is focused with
a lens into one end of an optical fiber. The light
travels through the fiber and emerges from the opposite
end, where it is directed into an optical detector
(photodetector), possibly focused again with a second
lens.
The third optical fiber design objective is
the desirability of maximizing the information carrying
capacity of the fiber. The input to the fiber may be
a light beam of continuously-varying intensity or a
group of well defined pulses of light as shown in Fig.
2.2. As the light pulses propagate through the fiber,
their amplitude will decrease due to attenuation. In
addition, due to a number of other effects to be discussed,
the individual pulses also may broaden (spread).
If they become too broad they will overlap or coincide
with one another in both time and space. If this OCcurs,
the intelligence (information) originally impressed
on the light beam would be lost. Pulse broadening
that occurs in the fiber is called dispersion. This
parameter places a limit on a fiber’s information carrying
capacity (signaling rate).
The fourth design objective is the desirability
of maximizing the strength of fibers when they are
Initially drawn and maintaining this strength when the
fibers are formed into cables or are used in sensors
and other applications.
Before considering these and other fiber design
objectives in some detail, the basic theory of
light propagation in optical fibers will be discussed,
beginning with light-ray propagation in layered media.
2-1

1
The light-ray concept is a convenient approximate approach
that may be used to introduce other important
concepts such as total internal reflection and ray trapping.
To extend the theory of light propagation farther,
however, it is necesaary to take into account the
notions that light is an electromagnetic wave phenomenon
and that optical fibers are cylindrical dielectric
waveguides. With these in mind it is possible to
develop concepts regarding the allowed electromagnetic
propagation modes of a cylindrical waveguide and to
introduce the frequently encountered optical fiber waveguide
V-Parameter (V-value) that must be considered
when selecting a suitable fiber for a particular application.
In accordance with the ray theory of light
propagation, a light beam incident from below on the
interface surface between two transparent media, at an
angle e 1 with the interface surface behaves as shown in
Fig. 2.3. When fll ia large, part of the incident beam
Fig. 2.3
MEDIUM2 ! .-”’”
X6;
n2
k
n1>n2
Reflection and refraction at the interface
when a lightwave travels from a higher to
a lower refractive index medium.
is transmitted into the upper medium and vart is reflected.
Their relative intensities depend upon the
refractive indices of the two media. The refractive
index of a medium is defined as the ratio of the velocity
of light in a vacuum to the velocity of light in
the medium. The higher the refractive index of a medium
the slower light will travel in it. The refractive
index of medium 1 is designated as nl and that
for medium 2 as n2 as shown in Fig. 2.3.
These indices alao determine the direction
of the beam transmitted into medium 2, i.e., @2 in
Fig. 2.3 is determined by the indexes of both media.
Snell’s law of refraction of light at an interface predicts
that the ratio of the cosine of the angle 131 to
the cosine of the angle of t12 is equal to the ratio
n2/nl which is equal to the velocity ratio v1/v2. Thus,
as shown in Fig. 2.3, if light propagates in medium 1
at a lower velocity than in medium 2, the angle 01 will
be greater than the angle 02 and the ray will be bent
toward the interface when entering medium 2. The angle
of the reflected beam is equal to the angle of the incident
beam. These are an application of the well known
laws (Snell’s laws) of refraction and reflection that
aPPIY in ray treatments of wave phenomena.
nl > n2
+’*NG)
v,< V2
I \ MEOIUMI’(CORE)
CASEI 01>0, CASE2 e)=ec CASE3: 01 n2. There is both a refracted and a reflected
beam and, from the conservation of energy, the sum of
their energies must equal the energy in the incident
beam.
2-2
Fig. 2.5
A step-index optical fiber showing the
critical angle, 6C for total internal reflection.

fleeted each time it is incident on the core-cladding
interface so that it remains ““trapped”” in the core.
This, and any other ray with f31

”’’-” [--::=
----
\
.! (
ACCEPTANCE
&
CONE
J-’’”
Fig. 2.8
The acceptance cone for a ~tep~i~~$x optical
fiber. (N. A.=sinec=(nl ‘n2 )
end surface, where the refractive index of air, no7 IS
equal to unity, there is another critical angle,3c ,
such that all ,the light contained within the cone of
half angle Clc , will be trapped within the fiber. Applying
Snell’s Law, this time in the sine form because
ec ‘ is the angle between the cone edge (elements) and
the normal to the surface of incidence (end face of fiber),
the ratip of the sine of ec within the core to
the sine of ec in air is equal to the refractive index
n. of air divided by the refractive index nl of the
core. Thus, since n. = 1:
(sinoc)/no = sinec = (sin9c’)/nl (2.8)
At the core-cladding interface within the fiber it was
shown that Cosoc = n2/nl Eq. (2.3). Combining Eqs.
(2.3) and (2.8) and using the Pythagorean theorem:
sin28c + c0s20c=l=(sin20c’ )/n12 + n22/n12 (2.9)
Transposing:
(5in2ec’ )/n12=l-n22/n12=(n12-n22)n12 (2.10)
Thus, from the defini~ion that the numerical aperture
is equal to the sin ec” :
As
2 1/2
N.A. = sinoc’ = (n12 - n2 ) (2.11)
defined in Eq. (2.2) above:
Solving for n2:
A = (nl - n2)/nl (2.12)
n2 =
nl (1 - A) (2.13)
Substituting Eq. (2.13) in Eq. (2.11) and simplifying:
N.A. = nl(2A - A2)1/2 (2.14)
If A2 !9’
~
A
Light rays in a step-index fiber core.
Two rays are ,showo in Fig. 2.9. One enters
from air at an angle, 0 , such that on intersecting the
core-cladding interface, it makes an angle less than
the critical angle, 13c, with the interface. This ray
will be totally internally reflected and will be trapped
in the core, so that it propagates with minimal
loss through the fiber core. A second ray, incident
from air at a larger angle, intersects the core-cladding
interface at an angle greater than tic. At each
reflection part is reflected back into the core and
part is transmitted into the cladding. Such a ray is
strongly attenuated, rapidly decreasing in intensity
as it propagates along the core of the fiber.
The Eqs. (2.8), (2.11) and (2.15) show that
the critical angle at the core-cladding interface for
total internal reflection in radian measure for the
trappin of light in the core is approximately equal
to (ti) f 12 when A2

6=0
REFERENCE PLANE
that propagate along the axis of the guide each with a
discrete velocity.
,> = (J
REFERENCE LI
z
In order to characterize light propagation in
a step-index optical fiber it is convenient to use a
parameter, usually referred to as the waveguide V-parameter
(V-value). It is defined by the equation:
V = 2ma(nl
and therefore from Eq. (2.11):
2- 2 112/i
n2 ) o (2.18)
V = 2~a(N.A.)/& (2.19)
Fig. 2.10 The cylindrical coordinate system for expressing
lightwave propagation in an optical
fiber. The point P is designated as p,
0, z.
The Z-axis of this coordinate system is taken
to be the central axis of symmetry of the waveguide.
The z-coordinate is the distance from a reference plane
designated as Z. (zEO). A spatial point in a fiber is
located by defining a radius coordinate, p, as the distance
radially from the Z-axis; an azimuthal (angular)
coordinate, $, measured from an arbitrary reference
plane ($=0); and a value of z. This coordinate system
is commonly known as the cylindrical coordinate system.
In the simple case where the refractive index
depends only on the radial coordinate, the solution to
the wave equation, derived from Maxwell’s equations for
the electric fields, can be expressed as the product
of two functions as follows:
where a is the core radius; N.A. is the fiber numerical
aperture, a function of the refractive indices of the
core and cladding; and i. is the wavelength of the incident
light in a vacuum. (The wavelength of a lightwave
in a vacuum is nearly equal to its wavelength in
air.) These are the main parameters needed to describe
light propagation in a step-index optical fiber. The
V-parameter may be designated as the light propagation
characteristic of an optical fiber. The larger the V-
value the larger the number of modes (different discrete
waves) the fiber can support, i.e., allow to propagate.
The predictions or conclusions that may be
drawn from the wave theory of light propagation in
fibers may be summarized in graphical form. As already
mentioned, only particular (discrete) solutions of the
wave equation exist. These correspond to discrete waves
propagating along the axis of the guide with particular
velocities. Some of the characteristics of these particular
(allowed) modes are shown in Fig. 2.11. The
kn,
E(p, $,z,t) = E(p, $)e-j(~t-W) (2.16)
= E(p, $)sin(ut-&) (2.17)
The variable t is the time measured from a time reference
of to. The first is an amplitude factor E(P ,$)
that depends on the radius vector P and the azimuthal
(angular) coordinate $. The second, which can be expressed
as complex exponential or sinusoidal function,
indicates that the electric fields are sinusoidal waves
in time and in space. The angular frequency is u= 2nf
where f is the optical frequency. The B is the propagation
constant, defined as the refractive index, n,
times the z component of the wave vector k, where kn=
2h/io, and i. is the optical wavelength in a vacuum at
frequency f. Thus, optical energy transfer in dielectric
media takes place in the form of wave propagation
along the axis of the guide. The absolute value of k
is also called the wave number.
2.1.3 Propagation Modes
When the geometric boundary conditions at the
core-cladding interface are introduced only particular
(discrete) solutions of the wave equations are permitted.
Only these values can exist, each designated by a
value for i, for the amplitude factor Ei(P,$) and cor -
responding discrete values for the propagation constant
~. The velocity of propagation of each allowed wave,
i.e. mode, along the axis of the waveguide is given
by the ratio of the angular frequency divided by the
propagation constant Bi, of a particular wave designated
by the subscript. Thus, the various allowed solutions
represent discrete waves with discrete amplitudes
2-5
kn2
V=? G
wAVEGUIDE PARAMETER
Fig. 2.11 The propagation constant, i3, and the velocity
of various modes as a function of the
V-parameter of an optical fiber.
curves show the allowed values of the propagation constant
& as a function of the V-parameter (V-value).
Each curve corresponds to a particular allowed solution
of the wave equation. This graph indicates that the
allowed values of %for the various solutions are in
between knl and kn2, corresponding to the wave numbers
in the core and in the cladding, respectively. Since
the wave (phase) velocity in the Z-direction is given
by the quantity m/6 the curves in Fig. 2.11 also show
the phase velocity versus the waveguide V-parameter (Vvalue).
Thus, the velocity of the allowed waves (modes)
represented by the different curves is seen to range
from the higher velocity in the cladding (lower ordinate,
higher value) to the lower velocity in the core
(upper ordinate, lower value) as the waveguide V-parameter
increases. Thus each curve in Fig. 2.11 corresponds
to an allowed solution of the wave equation applied
to dielectric waveguides. The waveguide V-para-

1
meter varies directly with the core radius and numerical
aperture and inversely with the wavelength of light.
As the V-parameter increases, the number of allowed
modea increasea. For V less than 2.40, only one wave
or mode, designated in Fig. 2.12 as the HE1l mode,
ia permitted. For V in the range of 2.4 to 3.8, four
modes are allowed, these being the HE1l, TEOl, TMol,
and HE21 modes. These particular alphanumeric designations
are standard for electromagnetic waveguides.
They have been chosen because of the specific forms
of the spatial variations for the electric and magnetic
fields associated with the particular solutions for the
wave equation. As V increases, more and more modes are
permitted (supported).
Consider the specific case in which V is less
than 2.40 as shown in Fig. 2.12. This is especially
k“,
pattern is circularly symmetric and shows no fine structure.
Horizontally polarized light could also have
been introduced into the same fiber at the same time.
Such light would remain horizontally polarized in an
ideal fiber. In fact this same type of behavior applies
to any direction of polarization and gives rise
to one scheme for multiplexing.
In an ideal singlemode fiber with perfect cylindrical
symmetry the direction of light polarization
once introduced remains constant and there is no energy
transfer among the waves with different polarization
directions. However, in real fibers, due to slight
ellipticities in the core cross section, imperfections
in the core cladding interface, variations in the refractive
indices throughout the core, effects due to
bending, and other causes, there is usually some coupling
between the different directions of polarization
and some variations in the velocity of each of the
waves with different polarizations. These effects must
be considered in certain applications. They will be
diacussed later when lightwave polarization effects in
ainglemode fiberoptic sensor applications are considered.
Returning again to a consideration of the spatial
modes of lightwaves in optical fibers, consider
the case of a fiber that can support four separate electromagnetic
modes. This occurs when the V-value is in
the range 2.4 < V < 3.8, as shown in Fig. 2.13. The
WAVEGUIDE PAR&METER
V
1 ,..
//EEE1 *:. :;:( ~Eol
HE)) I .
!+.3,
T,o,
“,22
& @
CLADDING
.--——- ,~,,
HE,,
,.21

in the right center of Fig. 2.13. They increase in
magnitude from zero along the axis of the core to a
maximum and then decay as the core-cladding interface
is approached, as shown in the lower right. As already
pointed out for the HE1l mode in this case, the fields
again extend beyond the core into the cladding.
Returning to the graph at the left in Fig.
2.13, as V is increased further, for example by decreasing
the wavelength, ,10, of the light injected into
the fiber, additional relatively lossless modes are permitted
and, very rapidly, propagation phenomena change
from the single or few mode types to multimode behavior.
In fact, for V > 10 the number of allowed modes is approximately
equal to V2/2 for a step-index fiber. As
already pointed out above in the discussion of the radial
electric field distribution for the HE1l and TEOl
modes, shown in the lower right in Fig. 2.12 and 2.13,
respectively, the ~-fields may extend well beyond the
core cladding interface. In fact when each mode is
first allowed much of its energy is associated with
fields that penetrate the cladding. This phenomena is
shown in Fig. 2.14 where the ratios of the power in the
cladding, pclad, to the total power, F’, in a particular
mode are plotted as functions of the V-parameter. At
low values of V, for example V less than 1.0, most of
the energy transmitted by the HE1l mode is associated
with the field in the cladding. The spatial character
of each new allowed mode becomes more complex within
the V-values, for example, most of the energy transmitted
by the HE1l mode is associated with the fiel~s in
$he cladding. As the V-value is increased, the E and
H fields of the HE1l mode extend a smaller distance
into the cladding and a larger portion of its transmitted
energy is confined to the core, reading approximately
80% of the total when V = 2.4, as shown in Fig.
2.14. At this value of V, the TEOl, TMOl, and HE21
modes first come into existence and initially, again,
pcladtpz 1. As the V-value increases further the energy
associated with these three modes also become more confined
to the core. At V = 3.8, three additional modes,
the HE12, EH1l, and H31, are allowed. In this case, due
to the radial and azimuthal structure of their ~ and P
fields they initially propagate with approximately half
of their energy in the core and half in the cladding,
so that the power ratio Pclad/P starts off at 0.5 and
and then decreases rapidly as V increases.
This characteristic of mode propagation in
optical fibers is employed to advantage in a number of
fiber sensor applications. It is the basis of operation
of evanescent wave couplers, or beam splitters,
wherein a portion of the light propagating in one fiber
is transferred to a second fiber by bringing their
cores close together by etching or lapping away a portion
of the cladding. Another application of this same
phenomenon is as the transduction mechanism in a number
of different intenaity-type aensors, where, through
carefully controlled micro-displacements induced by
bending, light can be ejected from the loosely-bound
high-order core modes. These and other useful applications
of this core-into-cladding energy transfer of the
electromagnetic wave fields are discussed in detail in
later sections.
After the above brief discussion of the ray
and the waveguide theories of light propagation in optical
fibers, it is appropriate to return to a more
general consideration of the macroscopic propertied of
fibers. The conceut of attenuation will be discussed
next. Assume that-a pulse of light, of peak intensity
(optical power) 1., is injected at the left into the
core of a fiber, as shown in Fig. 2.15. In general, as
OUTPUT INTENSITY DECREASES WI’H INCREASING
IIZ)=Ioe–az
Fig. 2.14 The variation of the ratio of optical power
in the cladding to the total optical power
in a fiber as a function of the V-parameter
(V-value).
ATTENUATION EXPRESSED IN DECIBELS PER KILOMETER (dB/km)
I(z)
FOR Z . 1 km, dB/km=–lOloglo~
2-7
Fig. 2.15 Light intensity (optical power) relative
attenuation as a function of distance in an
optical fiber.
it propagates through the fiber its intensity, I, will
decrease exponentially so that the intensity of any
point (transverse plane) z in the fiber is given by:
I(z) = Ioe-az (2.20)
where 10 is the intial intensity of the point of entry
into the core (z = O), z is the longitudinal distance
along the fiber, and = is the intensity attenuation coefficient.
Thus, as indicated in the graph in Fig.
2.15, if in traveling a particular distance, z1, the
intensity decreases to 0.51., then at z = 2z1, it will
be 0.251., i.e., at the end of each Z1 incremental in-

crease in distsnce the intensity is reduced to l/2 of
the intensity at the beginning of the incremental increase.
For example, for this case, at the end of 521
the intensity will be 2-5 = 1/32 of the initial value.
For optical fibera, the attenuation rate is uaually
specified in terms of the decibels loss per kilometer,
i.e., (dB/km). In the case of z = 1 km, the attenuation
rate may be defined by the equation:
Attenuation Rate = -10 loglO(I1/Io) dB/km (2.21)
In a fiber with an attenuation rate of 10 dB/km the intensity
(optical power) will fall to one tenth of the
incident intensity after traveling one kilometer. A 3
dB/km attenuation rate corresponds to a reduction to
one half the incident intensity after one kilometer,
since loglo 0.5 is equal to 0.3. In this latter caae,
after 5 km the intensity would be down 15 dB from the
initial value, i.e., the attenuation will be 15 dB.
A historical picture of the change in attenuation
rates of available fibers, from about 1968 to the
present, is shown in Fig. 2.16. The graph indicates
o
0
‘%a
0011 I , , , , ,
1968 1970 7972 1974 1976 1978 19s0 1982 1984 +
,
YEAR
0
0
absorption, ia due to absorption of optical energy into
the electronic energy levels of transition metal impurities,
such as iron, copper, chromium and nickel, and
into the vibrational levela of hydroxyl ions (OH-) in
the core and innermost sections of the cladding. In
this case, energy is absorbed from the optical beam and
reradiated into the molecular lattice in the form of
heat. The second type of attenuation is due to bendin~
losses of which there are two typea. One is due to
:regular bending of the entire fiber at nominal radii.
For example, bending loss may be due to winding the fiher
on a small-diameter mandrel. The second, referred
1:0 as mlcrobend loss, arise because of random variations
in the direction of the axia of the core. These may
even be microscopic, due to external forcea, imperfections
in the coating or cladding, ripples in the core-
(:ladding interface, ticrocracks, and other causes. In
either caae, light will be injected from the core into
the cladding, and thus cause a decreaae in the light
intensity transmitted through the core to the output
end of the fiber. Finally, there are three types of
scattering losaes. The first, called Rayleigh scattering
la cauaed by microscopic density fluctuation that
are frozen into the random molecular structure of the
glass making up the fiber core when it cools to its
relatively high solidification temperature. These density
fluctuations may be resolved into spatial frequencies
that have wavelengths much shorter than the optical
wavelength. Rayleigh scattering losses vary inversly
as the fourth power of the optical wavelength. In addition
to the static denaity fluctuations, there are also
dynamic density fluctuation due to thermal sound waves.
These waves originate and propagate becauae the temperature
of the glass is above absolute zero. These propagating
density fluctuations (thermal phonons) lead to
Brillouin scattering. Finally, there is scattered
light caused by absorption and reradiation from atomic
vibrational and rotational energy levels, i.e., Raman
scattering. These latter two scattering processes,
i.e., Brillouin and Raman, are non-linear processes
and are significant only at high optical intensities.
The strength and wavelength-dependence of
some of these loss mechanisms is shown in Fig. 2.17.
Fig. 2.16
The reduction of fiberoptic attenuation
rates over the years. The + is a projected
value.
351
I I I I I I
why fiberoptic communication links were impractical in
the late 1960’a, since attenuation rates in the range
1000 to 100 dB/km correspond to a decrease to one tenth
of the input intensity after traveling only 10 to 100
metera, respectively. A very evident atep decreaae in
attenuation rate occurred around 1970, with the introduction
of a new fiber fabrication technique, the vapor
phaae deposition proceas. This led to the availability
of the first high-priority silica fibers, and the development
of a group of related techniques for producing
extremely high purity, low leas fibers. Today fibers
are available with minimum lossea, at selected
wavelengtha, in the range 0.2 to 1.0 dB/km so that the
repeaterless optical communication links of longer than
50 kilometer are an achievable reality.
A clear understanding of the factors that effect
attenuation in optical fibers is of importance not
only to the fiber designer but also to the fiber user.
The causea of attenuation may be divided into
three aeparate categories: The first, called material
2-8
30
25
c
20
2
~.
15
x
0 J
10
5
0
05 06 07 08 09 10 11
WAVELENGTH (MICRONS)
● TRANSITION METAL IMPURITIES (Fe, Cu, Cr,Ni)
● HYDROXLION (OH)-1 PPM—~ldB/km@.95#m
● RAYLEIGH SCATTERING w l/A4
● LEAKAGE LOSSES (MICROBEND, REGULAR BEND, ETC.)
Fig. 2.17 Sources (causes) of optical power attenuation
rate as a function of wavelength in a
typical optical fiber.

The vertical height of the various cross-hatched regions
represent the loss as a function nf the wavelength
arising from the various sources. Note that the
minimum total attenuation at approximately 0.8 micron
wavelength is approximately 10 dB/km. This is a somewhat
mediocre fiber by today’s standards. The lowest
four regions in Fig. 2.17 correspond to the loss due
to 1 part per million by weight, in silicon oxide (Si02)
glass, of the metallic impurities Cu, Ni, Fe, and Cr,
from bottom to top, respectively. The peak in the
vicinity of the 0.95-micron wavelength is due to the
third harmonic of the hydroxyl (OH-) vibrational mode,
and corresponds to roughly a 20-part-per-million impurity
content. The black dots are predicted values of
losses based on calorimetry-type optical absorption
measurements made on the glass sample from which the
fiber was drawn. The upper cross-hatched region represents
the attenuation due to Rayleigh scattering while
the white region is the remaining difference between
the total loss versus wavelength (the uppermost curve)
and the sum of the previously mentioned losses. The
latter is attributed to regular bending and microbending
losses.
The attenuation versus wavelength curve shown
in Fig. 2.18 is for a currently available very-low-
5.0 . ‘.
3.0 — ‘.> ‘.
2.0 —
‘\
1.0
tion. In the bent region, the ray intersects the corecladding
interface at an angle 13 that is greater than
‘dC and thus it will be partially transmitted out of the
core and into the cladding. This will occur at each
successive reflection from the outer interface and large
losses may occur. Another qualitative explanation of
this type of loss is as follows. In the beam propagating
in the fiber, assuming plane wavefronts, if the
velocity at the center of the core in the bent section
were equal to the c/nl, the “proper” velocity in the
core, then the velocity at the outer edge of the front
would have to be higher than c/nl, which cannot occur.
Radiation in the form of core-to-cladding scattering
results. Finally, from the electromagnetic wave theory
it may be shown that in a waveguide with a constant
bend radius, all of the solutions of the wave equation
represent waves that decay with
along the centerline of the core.
increasing distance
6
6< 9.
e’ 70,
\
/
/
/
0.5 -
\
Fig. 2.19 Leakage of optical power froman optical
fiber at a constant-radius bend.
Fig. 2.18
0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6
WAVELENGTH (pm)’
Attenuation rate of optical power in a low-
10SS optical fiber as a function of wavelength.
The arrows along the abscissa indicate
the wavelengths of commercially
available lasers.
loss, single mode fiber. The arrows along the lower
abscissa correspond to the wavelengths of currently
available lasers. The peak in the loss curve at the
1.4-micron wavelength is due to the OH- radical, which
has been reduced to a relatively low concentration
level. The minimum at approximately the 1.3 micron
wavelength is of special interest, not only because the
attenuation rate is down to 0.5 dB/km, but also because
this wavelength is very close to the zero-dispersion
wavelength of Si02 which is of special interest in some
applications, as will be discussed shortly. Fig. 2.18
shows that extremely low attenuation rates attainable
with current fiber fabrication techniques at wave -
lengths where high intensity long-life, solid state
laser sources are becoming commercially available. It
is now up to the fiber user to devise techniques and
configurations that can maintain this low loss by not
introducing significant regular (macro) bending and
microbending losses.
Using the latter approach it is possible to
compute the expected loss due to a constant bend radius.
The results of such calculations are shown in Fig. 2.20,
where loss curves versus bend radius are shown for
singlemode fibers at the 0.83-micron wavelength having
different numerical aperture (N.A.). Note the strong
dependence on bend radius and N.A. Referring to Fig.
2.20, consider a fiber with a numerical aperture of
0.1. When a 10-meter length is wound on a l.2-cmradius
mandrel, the attenuation due to bending is approximately
6 dB, i.e., 75 percent of the light energy
injected into the core at the input end is scattered
out of the core while propagating in the ten meters
to the output end. Nhen 10 meters of identical fiber
are wound on a 1.0 cm radius mandrel, the attenuation
due to bending will increase by a factor of about
250,000 to 60 dB, so that only about one millionth of
the original light remains at the end of the fiber.
Just about all of the input light is scattered out of
the core. On the other hand, using the 1.2 cm radius
mandrel and increasing the numerical aperture (N.A.)
to 0.12 reduces these attenuations to 0.16 dB and 1.6
dB, respectively. Therefore, care must be taken in
designing fiberoptic sensors that require bending and
winding of fibers and in specifying fibers for such
applications.
A ray picture of the regular (constant) bend
radius loss mechanfsm is shown in Fig. 2.19. Assume a
ray is traveling to the right at an angle of o less
than the critical angle ec in the straight fiber sec - 2-9

-2 3 4 5 6 7 8 9 10 11 12
BEND RADIUS (mm)
Fig. 2.20 The variation of optical power attenuation
rate as a function of bend radius for constant
radius bends in typical optical fibers
for various values of constant numerical
apertures (N.A.) using 0.83-micron wavelength
light.
C.H. Bulmer, private communication.
Fig. 2.21
The effect of a microbend on ray propagation
in an optical fiber is shown in Fig. 2.21. A ray pro-
+==2si-
The angle between an incident ray and the
core-cladding interface surface exceeds the
critical angle and therefore total internal
reflection does not occur at the microbend,
allowing part of the ray to leave the core
and enter the cladding.
pagating in the core at less than the critical angle
is totally reflected before it reaches a section of
fiber distorted by a small imperfection. On successive
reflections from the core-cladding interface it is incident
at an angle with the interface surface larger
than the critical angle so that some light is transmitted
into the cladding. Random distortions such as this,
due to imperfections in the core-cladding interface or
due to bending or tensile forces exerted at scattered
points along the interface surface of the fiber can induce
microbends in the core surface that lead to substantial
cumulative losses. Such distortion losses are
usually undesirable and detrimental, for example, when
they arise in fiber cabling operations. on the other
hand, microbending is employed in fiberoptic sensors
as a transduction mechanism, as will be discussed later.
2-1o
The optical fiber property to be considered
last is velocity dispersion, i.e. , differences in velocity
among various portions of the light that may be
propagated in the core of a particular fiber. It will
be shown later how dispersion directly affects the behavior
of specific fiberoptic sensors. For now, the
significance of dispersion will be illustrated in terms
of how it affects pulse broadening and thus limits
bandwidth in fiberoptic data links and other communication
applications.
In the introduction to this chapter, it was
pointed out that one of the aims of the optical-fiber
designer is to design a fiber that will preserve the
information impressed on a beam of light as it propagates
through its core. A measure of success in this
regard, as pointed out in the discussion of Fig. 2.2,
Subsection 2.1.1, is how well the width of an individual
narrow pulse is maintained without broadening.
When a light pulse is injected into a step-index multimode
fiber, its energy is divided among several different
modes. Each mode travels at a particular velocity,
or range of velocities, and thua they may arrive at the
output end of the fiber at different times depending on
their velocity and the length of the path they take.
Obviously this contributes to pulse broadening and, in
fact, this modal dispersion is the major source of pulse
broadening in step-index multimode fibers. This type
of dispersion is reduced substantially in graded-index
multimode fibers in which the various modal propagation
times are nearly equal to one another and thus
the various portions of an injected pulse arrive at the
end of the fiber at the same time though their propagation
velocities and paths will differ. In this case,
however, the next lower level of pulse broadening effects
becomes evident. This is the so-called material
or chromatic dispersion that occurs because the velocity
of an electromagnetic (light) wave is usually a
function of the wavelength in dielectric material. If
an optical source emits a pulse of other than purely
monochromatic (single-wavelength) radiation, the various
wavelengths preaent will propagate at different
velocities and thus lead to pulse broadening.
The effects of modal and material dispersion
are shown in Fig. 2.22 where the theoretically-predicted
dipersion or pulse broadening, expressed in nanoseconds
increase of pulse width for each kilometer of
travel in a fiber, is plotted as a function of numerical
aperture (N.A.) for various operating conditions.
Two types of 0.85 micron nominal wavelength optical
sources are considered. One is an injection laser emitting
light with a apectral width (linewidth or variation
of wavelength) of 20 Angstroms. The other is a
light emitting diode (LED) emitting light with a spectral
width (linewidth) of 350 Angstroms. When narrow
pulses of light are injected into either graded-index
or step-index fibers, Fig. 2.22 shows that for laser
sources and for numerical apertures less than 0.15, the
predicted broadening is only 0.2 nsec/km for the graded-index
fiber, however, the dispersion is more than 10
nsecfkm for the step-index fiber. This increase is due
to modal diaperaion, because increasing N.A. corresponds
to increasing the waveguide V-parameter so that
additional optical modes are allowed. Initially at low
N.A. values with the light emitting diode, material dispersion
leads to a broadening of approximately 5 nsec
per km in commercially available step-index and graded-index
fibers,
further increases
values.
and then modal dispersion leads to
in step-index fibers at higher N.A.

60
40
20
10.C
~8
x
z
6
n
u 4
%
c
62
m
u
$ 1.0
00.8
06
04
02
AO = 0.85 pm
LED S1 FIBER
/
PRACTICAL LED
PRACTICAL LASER
GI FIBER
\
shown in Fig. 2.18. There are two other types of dispersion
effects that usually occur when singlemode fibers
are employed. The first of these is called waveguide
dispersion which results from the variation in
the propagation constant, B, or wave velocity (phase
velocity), clneff, with changes in the V-parameters,
and thus the wavelength, 1. This was considered earlier
in the discussion of Fig. 2.11, but for the present
discussion, it is useful to present the same information
in another form as follows.
In Fig. 2.23, typical curves of the optical
angular frequency, w, are plotted as functions of the
propagation constant, 6, for a few of the lower-order
allowed modes in a fiber waveguide. This graph shows
RADIATION
MODE
REGION
cln~
0.1
I 1 I I I I I I I II I I I I 1 I I I I I I I I I I I
o 0.05 0.10 0.15 0.20 0.25 0.28
NUMERICAL APERTURE
Fig. 2.22 The variation of dispersion in nanoseconds
per kilometer as a function of numerical
aperture (N. A. ) for step-index (S1) and
graded-index (GI) optical fibers driven by
laser or LED optical sources.
After C. Keo and J. Goell,
16, 1976.
Electronics, 113, Sept.
The above results also can be expressed in
terms of the bandwidth of the modulation signals that
may be transmitted by fibers. The bandwidth capacities
(bandwidth-length product) currently attainable with
various types of available fibers are summarized as
follows:
Modal-dispersion-limited behavior:
Step-index fibers:
Graded-index fibers
Research grade
Production grade
Material-dispersion-limited behavior:
Graded-index fibers (0.85 Urn):
LED (350 ~ spectral ~idth)
Injection laser (20 A)
30 MHz-km
1000 MHz-km
400 MHz-km
150 MHz-km
2500 MHz-km
The capacities are expressed as the product
of the highest modulating frequency in megahertz that
can be applied (without excess decay) multiplied by the
fiber length in kilometers. Thua, using high quality
graded-index multimode fibers, it is now possible to
send signals with frequency components in excesa of 1
GHz over fiber lengths approaching 1 km, or in excess
of 5 GHz over fiber lengths approximately 200 m, and
so on.
In singlemode fibera, material or chromatic
dispersion IS a significant factor. In silicon oxide
(si02), the main constituent of the core and cladding
of most high-grade glass fibers, the curve of the refractive
index as a function of the optical wavelength
has a minimum point at approximately 1.3 microns as
2-11
Fig. 2.23
----
~ ‘MODE ~
PROPAGATION CONSTANT B
The optical angular frequency, u, as a
tion of the propagation constant, B, for a
few low-order modes for lightwaves propagating
in typical optical fiber, showing
the phase and group velocities.
the difference between the phase velocity of a singlefrequency
continuous optical beam and the group velocity
of an optical pulse. The wave velocity (phase
velocity) is defined by the values of the ratio u/fi for
any point on the curves for the allowed modes. These
curves terminate on the straight lines that define the
plane wave phase velocity in the core and cladding
i.e., cfnl and c/n2, respectively.
A narrow impulse of light, by its very nature,
consists of a band of modulating frequencies and the
narrower the pulse, the broader is its modulating frequency
spectrum. Light at a wavelength of 1 micron in
a vacuum has a frequency of 3 x 1014 Hz. If it is pulsemodulated
to produce impulaes 0.1 nsec wide, their
bandwidth would exceed 10 GHz (Actually 20 GHz if the
Nyquist criterion is applied). The velocity of propagation
of such a pulse would be defined as the velocity
of the maximum of its envelope, referred to as the
group velocity, Vg, which can be shown to be equal to
the slope d~ld~ of the modal curves in Fig. 2.23.
Since the individual frequencies, or wavelengths, making
up the pulse propagate at different velocities the
pulse tends to broaden and this is the source of the
waveguide dispersion.
Another type of dispersion or velocity variation
that may affect propagation in singlemode fibers
is referred to as polarization dispersion. It has not
been emphasized up to this point, but in fact optical
fibers operating in a so-called singlemode are in fact
at least bimodal. This is due to birefringence, or

azimuthal dependence of the refractive index, i.e.,
variations of the optical wave velocity, with changes
in the direction of the radial component of the electric
field vector. 7!his will be discussed in more detail
later. The concepts are mentioned at this point
because birefringence can be a source of pulse broadening
and related effects in singlemode fiber due to
randomly-induced transitions between different polarization
atates.
In cloaing this section on the various properties
of optical fibers, it is appropriate to compare
some of the propagation characteristics of optical fibers
with thoae of more conventional waveguide communication
links. This is done in graphical form in Fig.
2.24. Three curves are shown that represent the attenuation
of radio frequency (RF) signals with bandwidths
in the frequency range from 1 MHz to 1 GHz for various
widely-uaed coaxial cablea. Also shown ia the range of
attenuation rates currently obtained for lightwaves,
propagating in high quality fibers, that are modulated
by signala over the same frequency range. For modulation
frequencies above a few megahertz, optical fibera
are far auperior to even the largeat diameter (> 2 cm)
RG/u219 coaxial cable. Signals with a bandwidth up to
1 GHz may be propagated up to fifty kilometers in highquality
fibera without using repeaters (signal processors).
2.2 OPTICAL FIBER FABRICATION
It was indicated in Section 2.1, and shown in
Fig. 2.1, that many fibera consist of a core of refractive
index nl; a cylindrical cladding layer of alightly
lower refractive index n2 surrounding the core, and an
outer layer that serves as a protective jacket. It was
1000
500
cient that determines the rate of the exponential
decay of the core light intensity with increasing distance
of travel within the core; the dispersion (pulse
broadening) that depends on the differences between
the propagation velocities of the various allowed modes
and the variation of the modal velocities with optical
wavelength; and finally the strength of the fiber that
depends on how free from scratches and other imperfections
the outer surface of the cladding is immediately
after drawing, and on how well the cladding surface
is protected during spooling, cabling, and use.
This brief listing of some of the important
parameters of optical fibera emphasizes the need for
precise control of the refractive indices of the core
and cladding.
2.2.1 Refractive Index Profile Control
There are several techniques being uaed by
optical fiber manufacturer for maintaining preciae control
of refractive index profiles and refractive index
differences.
A step-index fiber with a cladding of pure
silica (ailicon oxide, Si02) that has a refractive index
of 1.458 for a lightwave of wavelength of 0.83 ~m and
that has a core of refractive index 1.461, has a numerical
aperture of 0.10 as ahown in the following table:
DEPENDENCE OF NUNERICAL APERTURE ON CORE INDEX
SILICA CLADDING n2 = 1.458 (0.83pm)
N.A. = (n12 - n22)1/2
N.A.
1 .:*1 0.10
1.464 0.14
1.469 0.18
1.472 0.20
When the refractive index of the core is increased to
1.472, and the cladding index remains at 1.458, the
numerical aperture increasea from 0.10 to 0.20 and thus
changes the critical acceptance cone apex angle from
11.5” to 23.0”. From the above table it may be seen
that the refractive index of the core must be controlled
to about one part in a thousand to obtain a desired
N.A. and hence an appropriate acceptance angle to wfthin
a few degrees.
5
3
2
1
12 5 10 20 50 100200 5001000
MODULATION BANDWIDTH (MHz)+
Fig. 2.24 The variation of attenuation rate as a
function of modulation bandwidth for several
coaxial cables and a fiberoptic cable.
T. Giallorenzi, Proc. IEEE ~, 744 (1978).
alao shown that important parameters of optical fibe~a
~:~)f~~, ~;~rical aperture (N.A.), equal tO (nl -
is, the sine of one-half of the apex
angle of the cone of light that can be injected and
trapped in the core of the fiber; the radius of the
core, which together with the numerical aperture, determine
the modal atructure of the electromagnetic waves
that may propagate in the core; the attenuation coeffi-
2-12
The desired refractive index of the core is
usually obtained by adding varioua typea of other
glasaea or dopants, to the pure silica. For example,
suppose that germanium oxide (Ge02) iS added to the
silicon oxide (Si02). The addition of Ge02 to Si02
increases the refractive index of the mixture as ahown
in Fig. 2.25a. The addition of 10 percent, by molecular
content, of Ge02 to pure Si02, increases the refractive
index from 1.468 to approximately 1.471.
Si02 and Ge02 form glaasy (vitreoua) materials.
They have microscopic molecular structures in
which the moleculea are somewhat randomly distributed
and disoriented rather than arranged in highly-ordered
crystalline-type lattices. They have indefinite solidification
temperaturea and behave aa liquida that have
extremely high viscosities. Thus, under ordinary conditions,
glaas fiber may be considered as consisting of
super-cooled liquida. The core glaas, as diacussed
above, may be considered as a mixture of two supercooled
liquids, Si02 and Ge02. Their molecular density and
thermal expansion coefficient are so closely matched
that in the mixed state their combined structure is re-

: 1.5
z
o GeOz
0
~
=1.49
u
w
>
~1.48
1-
0 v
:1.47 a
L
E
:1.46
v u
,4, ~
10
(a) DoPANT CONCENTRATION
(MOLE PERCENT)
x
1.49 r
1.48
1.47
P*05
1.46
K
1.45 ~10
20 30
(b) DOPANT CONCENTRATION
(MOLE PERCENT)
were shown as Fig. 2.12 in Section 2.1 are shown again
in Fig 2.26 together with data that shows the increase
in attenuation observed in fibers with various N.A.lS,
obtained by adding dopants to the Si02 in the core or
cladding. Dopant concentration high enough to produce
numerical apertures of 0.2 or greater cause scattering
and absorption leases in exceas of 10 dB/km, which is
the theoretically predicted bending loss for an 0.2 N.A.
fiber wound on a 3 mm radius mandrel. Thus in this respect,
it may be necessary for the fiber designer and
user to optimize the dopant concentration of fibers
specified for a particular application.
2.2.2 Fiber Fabrication Processes
Fig. 2.25
<
f
u 5 10 15
K
(c) DOPANT CONCENTRATION
(MOLE PERCENT)
The variation of the refractive index of
silica glass (Si02) as a function of the
concentration of various dopants.
Several different methods are being used to
produce fibers with particular dopant conce~trationa,
gradients, and refractive-index profiles throughout the
core and cladding.
2.2.2.1 The Double-Crucible Process
The most direct method is the double-crucible
proceas. The construction of the furnace portion of a
double-crucible system ia shown in Fig 2.27. The core
latively strong and free of localized stresses. The
addition of phosphorus pentoxide (P205) to pure silica
glass (Si02) also brings about an increase in refractive
index as shown in Fig. 2.25b. Thus, P205 is frequently
employed as a core dopant. On the other hand,
the addition of boron trioxide (B203) to pure silica
(S102) produces a decrease in the refractive index as
shown in Fig. 2.25c. Thus, B203 is employed as a dopant
for cladding glass. The addition of dopants to pure
silica, and to other glasses that are used to make optical
fibers, yields the refractive indices required
for the core and cladding, to produce fibers with particular
numerical apertures.
Large numerical apertures allow light from
wide entrance angles (large acceptance angles) to be
accepted into the fiber cores and still maintain total
internal reflection. It was indicated in Section 2.1
that bending losses are lower in fibers of higher N.A. ,
so that when it is necessary to wrap fibers on small
mandrels, in order to make fiberoptic sensors, it again
appears to be desirable to employ fibers with as high
an N.A. as is possible. Unfortunately, the addition
of dopants to either the core or the cladding causes an
increase in the oDtical attenuation, as shown in Fig.
The attenuation versus bend “radius curves that
(b)
Fig. 2.27
cOREF=:G-n l-cMDD’NG FEED ROD
R
CLADDING GLASS
INNER CRUCIBLE
L~
TO FiBER DRAWING
MACHINE WINDING DRUM
IBLE
The double-crucible process for optical
fiber fabrication.
glass is contained in the inner crucible, usually made
of platinum, while the cladding glass is in the outer
crucible , which is actually a cylindrical shell that
surrounds the inner crucible. The two glasses are
heated in such a way that they begin to flow out of the
orifices at the bottom of the two crucibles as very
highly ViSCOUS liquids. They then are cooled rapidly
to below the solidification temperature almost immediately
after they are combined in the region below the
orifices. The resulting fiber is drawn under controlled
tension so that its outer diameter is held nearly
constant. As the fiber is drawn, the glass in the two
crucibles may be maintained at a conatant level by
slowly feeding rods of core and cladding-type glasses
continuously into the two crucibles.
A simplified overall view of a double-crucible
fiber drawing system is shown in Fig. 2.28. As the
fiber is drawn from the bottom of the furnace it passes
.3 EK’RADIUS (mm,
NIJ$.4ERICAL WE RT”RE
through a non-contacting thickness gage and a feedback
EFFECT OFFENDING
EFFECT OF COMPOSITION
system that controla the rate of rotation of the take-
Fig. .26 2. The variation of attenuation in silica UP drum to maintain a constant outer diameter of the
glass (Si02) optical fibers as a function cladding. The fiber then passes through a pool of the
of ordinary bend radius, numerical aperture jacketing material (or materials) that coats the outside
of the cladding. The fiber is then dried, cured,
(N.A.), and type of dopant at a wavelength
of 0.83 pm.
and wound continuously on to the take-up drum.
C. H. Bulmer. private communication.
2-13

Fig. 2.28
FURNACE—
PREFORM —
n
II
THICKNESS GAGE — - - -
JACKETING UNIT z+
P
DRYING FURNACE —-----r!l II
+
TAKEUP DRUM -
6)
~> ‘
The double-crucible optical fiber drawing
system.
In principle, the double-crucible process has
the advantage that it may be used to draw continuous
fibers of any desired length. Unfortunately, because
the core and cladding glasses must be contained and
heated within the crucibles, it is difficult to maintain
the very high purity levels required to yield the
very low-loss fibers.
A much different procedure for producing extremely
low-losa fibers was developed during the early
and middle 1970’a. Though several variations of the
same approach are being used by manufacturer, they
all are based on the production of glass fiber using a
vapor-phase oxidation (VPO) process.
2.2.2.2 The Inside Vapor-Phase Oxidation (IVPO)
Process
The inside vapor-phase oxidation process
(IVPO) is shown in Fig. 2.29. Vapors of various metal
SiCl 4
J.
GeC14
Q
r
MIXING MANIFOLD
AND FLOW
CONTROLLER
SILICA BAIT TUBE
‘+== BURNER
H2+02TORCH
1
shown in Fig. 2.29. In each case, the halides are introduced
into the mixing manifold by means of a vapor
distillation process. For example, high purity oxygen
may be bubbled through the liquid silicon tetrachloride
(SiC14)”and germanium tetrachloride (GeC14). This process
reduces the level of impurities in the halide
vapors that are fed into the reaction tube. Heat is
applied to the outside of the tube using a movable
hydrogen-oxygen torch. This leads to oxidation of the
metal halides, yielding a precipitate of very fine
glass particles (soot) that builds up on the walls of
the bait tube.
The tube is mounted in a glass-working lathe
and continuously rotated during the oxidation process
so that the precipitate deposits uniformly around the
inner circumference of the tube, as shown in Fig. 2.30.
BAIT TUBE
/
REACTANTS
_ SOOT FORMATION_
(METAL HALIDES+ 02)
SINTERED GLASS
TRAVERSINiG BURNER
EXHAUST
:)
u’
SOOT DEPOSIT
Fig. 2.30 The inside vapor-phase oxidation (IVPO)
process for producing optical fibers.
After P. Schultz, Appl. Opt. Q, 3684 (1979)
The traversing burner not only provides the heat required
to oxidize the various metal halide vapors but
also transforms the porous soot deposit into thin
sintered glass layers that are built up as the burner
slowly traverses back and forth along the length of the
bait tube. By controlling the concentration of the
various reactants fed into the bait tube it ia possible
to build up layers of Si02 glass with any desired level
of doping. These will eventually form the cladding and
the core of fibers that may be drawn from the resulting
glass boule (preform) that is produced in this process.
Several other steps are carried out before
the tube is ready for fiber drawing. These are show
in Fig. 2.31. After the cladding and core glasses are
depoaited, the tube is heated so that under surface
Fig. 2.29
i)He
The vapor-phase oxidation (VPO) process for
producing optical fiber preforms.
halides are mixed with oxygen and helium to desired
highly-controlled concentration levels and fed into a
hollow silica cylinder (bait tube). The chlorides of
silicon and germanium exist as liquids at atmospheric
pressure and room temperature, while those of phosphorus
and boron must be stored under high pressure, as
2-14
SUSSTRATE
TUBE
CLADDING
DEPOSITED
CORE
DEPOSITED
COLLAPSED
PREFORM
Fig. 2.31
c1 Q+ ,- d
I
/
FIBER DRAWING
‘1 ~ÿÿÿÿÿÿÿÿÿÿÿ
@ /; SUBSTRATE REMOVED
DRAWING
gjjj/p”FIBER
1// THIN LAYER DEPOSITED
‘, //
—u
(3”
oc’? FIBER ORAWING
Stages in the processing of preforms in
production of optical fibers.
the

tension it collapses to eliminate the remaining center
hole. In order to obtain various desired physical properties,
fibers can be drawn either without removing
the substrate tube, after removing the substrate tube,
or after a final layer of glass haa been deposited on
the outside of the collapsed preform, as shown in Fig.
2.31.
In the drawing process, the boule is placed
in an induction furnace and fibers are drawn and coated
in almost exactly the same manner as in the double-crucible
technique that was shown in Fig. 2.28.
2.2.2.3 The Outside Vapor-Phase Oxidation (OVPO)
Process
Preforms also are made by precipitating soot
on the outside of a rod that is turned in a glaas-working
lathe, as shown in Fig. 2.32a. In the outside vapor
(a) SOOT DEPOSITION
g“’+ww’””’
4—.—...
(b) PREFORM SISTERING
o:,::.#.:~C:DING
>0 INDEX n
(c) FISER DRAWING
Fig. 2.32 The outside vapor-phase oxidation (OVPO)
process for producing optical fibers.
After P. Schultz, Appl. Opt. l&, 3684 (1979).
phase oxidation (OVPO) process, the core material is
deposited first and then the cladding is deposited on
the outside, just in the IVPO process described earlier.
The amount of doping may be continuously varied during
the core material deposition process. It is thus poasible
to produce preforms for graded-index fibers, as
well as for step-index fibers, as shown in the example
of refractive index versus radial displacement curve at
the extreme upper right in Fig. 2.32. The refractive
index of the porous material deposited on the center
bait rod decreases monotonically out to what will correspond
to the core-cladding interface, and then it
remains constant to the outer surface of the porous
cylindrical shell.
fed to the burners, a porous preform with the desired
radial variation of refractive index is built up, beginning
at the end of the silica rod. The rod is slowly
pulled vertically upward as deposition continues at a
constant rate at the lower end of the porous preform.
The porous section then passes through a concentric
heater ring that collapses and sinters the porous section
to form a clear glass rod with the desired radial
refractive index profile. The entire process is carried
out inaide a reaction chamber with a carefully controlled
inert atmosphere to reduce the level of impurities.
The VAD process permits the production of large
preforms capable of yielding single pieces of fiber
over 100 km long. The optical quality of current VAD
fibers is very high. Data on attenuation rates versus
wavelength for VAD and IVPO fibers is shown in Fig.
2.34. The IVPO process produces a fiber with a relatively
large attenuation rates peak at 1.4 pm and smaller
peaks in the vicinity of 1.23 pm and 0.94 Um. These
are due to the vibrational mode absorption lines of the
OH- radical. In the VAD process, the OH- radical contamination
is reduced substantially by careful drying
during the preform fabrication process thus eliminating
these attenuation peaks.
-..
(’ ;=> STARTING SILICA ROD
}! T
&
SiC14+BBr3
f--l
II
TRANSPARENT PREFORM
$!!$ . -- -— -. CARBONHEATER
‘..-=-, .,.. .,,,,,,.,,, =..
1’ I
l..
t
I :
POROIJS PREFORM
+ I
,..
I
% ~%-.+’
‘\
FINE GLASS PARTICLES
~~•
QOxy-HyDROGEN BURNERS
SiC14+GeC14+PC13
Fig. 2.33 The vapor axial deposition (VAD) process
for producing optical fibers.
After P. Schultz, Appl. Opt. l&, 3684 (19791
Thus, preform fabrication by the OVPO process
is a multistage procedure, including center bait rod
removal, followed by porous preform sintering and the
collapsing of the central hole, either prior to or during
the fiber drawing process. Aa in the IVPO process,
the deposition process is carried out on a glass-working
lathe. Thus, the preforms produced by both processes
have a limited size so that usually fiber lengths
from 10 to 20 kilometers may be drawn from a single
preform.
2.2.2.4 The Vapor Axial Deposition (VAD) Process
Length limitations are overcome in the vapor
axial deposition (VAD) process that is ahown in Fig.
2.33. Core and cladding glass particles ejected from
oxygen-hydrogen burners are deposited longitudinally
and radially on to the end of a silica rod. By carefully
controlling the concentration of the metal halides
2-15
Fig. 2.34
0.8 1.0 12 1,4 1.6 1.8
WAVELENGTH (pm)
The variation of attenuation as a function
of wavelength in optical fibers produced by
the vapor axial deposition (VAD) and the
inside vapor-phase oxidation (IVPO) processes.

2.2.3 Fiber Strength
The operational and shelf-life of fiberoptic
sensors will depend to a large extent on the mechanical
strength of the glass fibers used in them. In a certain
way, glass fiber is much atronger than steel.
Short, pristine silica fibers, immediately after drawing,
have elastic limits, and ultimate and breaking
tensile strengths, greatly exceeding that of steel
wires. Stress-strain curves for priatine silica fiber
and steel wire are shown in Fig. 2.35. The elaatic
1 I I 1 ! , ( ! , , ,
99 - *# .:
80 -
60 -
./”
./”””
~ 40 - /
u
m
3
~ 20 GAGE LENGTH= 60cm
if
8 -
4
10’0
- 109
“E
~
$ 108
w
u
G
107
106
WIRE
FIBER
10–4 10–3 10–2 10–’ 10°
STRAIN
Fig. 2.35 Stresa versus strain curves for steel wire
and pristine silica (Si02) fiber under ideal
conditions.
limit of steel typically uaed in wire is about 0.2 x
10-9 Newtons/m2 at a atress of about 0.1 percent. Steel
wires tend to break at strains of the order 0.5 percent
and a stress of about 1.5x109 N/m2. On the other hand,
unscratched fibers remain elastic to strains in excess
of 10 percent, corresponding to stresses of about 5 x
109 Newtona per square meter. However, unlike steel,
which may be made malleable and capable of flow-healing
small surface cracks, glass is brittle. Thus, very fine
cracks in glass fibers tend to become stress concentration
centers that propagate transversely across the fiber.
They lead to exceasive strain and ultimately to
complete rupture.
A length of fiber is only as strong as its
weakest section. Under constant tension a length of
fiber will tend to break at its weakest point. The
break will most likely occur where there is a scratch
on the outer surface of the fiber. A long length of
fiber ia more likely to have a weakest point that is
weaker than the weakest point of a short length of
fiber. Thus, fiber strength determination is a procesa
of collecting statistics of failure. This is illustrated
by the reaults of a seriea of tests performed on
a group of test samples, each 60 cm long, cut from sections
distributed uniformly along a 1 km length of fiber.
Each sample was streased to rupture in a tension
test machine. The percentages of the total number of
specimens that failed below a given stress level are
shown as a function of the breaking stress in Fig. 2.36.
Fig.
1 , I I , [
0.5 0.8 10 2.0 3.0 4.0
TENSILE STRENGTH (GN/m2)
2.36 The percentage of optical fiber specimena
that failed as a function of breaking tenaile
strength.
From the graph it may be seen that the first apecimen
broke at approximately 0.5 x 109 N/m2, approximate 10
percent of the specimens broke at 0.8 x 109 N/m J or
leas another 10% broke at atresses between 0.8 and 1.0
x 10 4N/m2, and so forth. A few of the s eclmens, however,
withstood stresses of 4.0 x 109 N/m % before breaking.
From a practical, application-oriented viewpoint,
it is the weakest point in a length of fiber
that determines ita overall strength. Thus, in specifying
fibers for a given application, the maximum
streas or strain to be encountered ahould be determined
and the entire length of fiber to be employed should
be pre-tested at some acceptable safety margin above
this level. Such testing is usually done by reeling
the fiber from one spool to another at a fixed rate,
while maintaining the interreel section under the fixed
specified stress (tension).
There is evidence that preform preparation
and treatment, as well aa the manner in which fibers
are handled after they are drawn, contribute substantially
to their overall atrength. Data on the breaking
or tensile strength of a particular type of fiber drawn
from identically produced preforms is shown in the bargraph
in Fig. 2.37. In the upper portion of Fig. 2.37,
the number of specimens versus breaking strength ia
plotted for 40 specimens taken from a length of fiber
drawn from an ordinarily prepared preform that was
heated as usual in an RF induction furnace. As indicated,
the breaking strengths ranged from approximately
0.50 x 109 N/m2 to 5.5 N/m2 with a maximumof 12 specimena
that broke at 3.0 x 10 4N/m2. Results are presented
in the center aection of Fig. 2.37 on 46 specimens from
a length of fiber drawn, using the RF induction furnace,
from a preform that had been fire-polished prior
to drawing in an effort to eliminate any fine cracks
(microcracks) and other imperfections that might have
existed in its outer surface. In this caae, the first
specimen to break withstood stresses up to 1.8 x 109
N/m2 and 36 of the specimens broke at a stress exceeding
3.8 x 102 N/m2. In the third case, as ahown in the
lower portion of Fig. 2.37, 42 specimens were tested
from a fiber that waa drawn using an infrared laser to
heat the preform, that also had been fire polished
prior to drawing. All of the specimens withstood tensile
atresses up to 4.0 x 109 N/m2 before breaking.
However, instead of being distributed over a very wide
range of breaking tensile strengths, the breaking points
were all in the range from 4.0 to 5.25 x 109 N/m2.
2-16

MAXIMUM TENSILE STRENGTH (GN/m2 = lo g N/m2)
INSULATOR
CONDUCTOR
NO FIRE POLISH
N = 40
FURNACE FIRE POLISH ~
N = 46 ;
:
10
5
; ~z”NDucT’oN’’NE~
K
Lu
BAND-GAP EG
—
61~
VALENCE BAND
— —
b
m
LASER FIRE POLISH :
N = 42 ~
z
:L_.—dJu
o 200 400 600 800 1,000
P-TYPE SEMICONDUCTOR
N-TYPE SEMICONDUCTOR
I 1 I 1
I 1
DONOR LEVEL I a. a. * a. I
ACCEPTOR LEVEL
MAXIMUM TENSILE STRESS (KPSI)
Fig. 2.37 The variation of maximum tension stress of
a number of optical fibers for unpolished,
furnace polished, and laser polished fibers
showing the number of fibers that failed at
the various stress levels in total tested
for each polishing condition.
These results clearly indicate how important it ia to
carefully prepare the preforms and to accurately control
the drawing process in order to maintain the strength
of the final drawn fibers and thus get as cloae as possible
to the ideal strength of silica glass.
2.3 SOLID STATE FIBEROPTIC LIGHT SOURCES
Solid state optical sources and detectors
utilized in compact fiberoptic sensors will be discussed
in this section. This information will serve as a
background for understanding later discusaiona of sensor
noise and packaging. In order to understand the
trade-offs required, a knowledge of light production
mechanisms and fabrication processes is helpful.
Finally, such information is important for estimating
what is likely to be available in the future.
2.3.1 Energy Levels In Semiconductors
Electrons in free atoms are normally tightly
bound in discrete energy levels. When the atoms are
located in a crystalline structure these discrete
energy levels are replaced by energy bands. Some of
the electrons remain tightly bound to the atom while
other, more energetic electrons, have energies corresponding
to the valence or conduction bands. Those in
the valence band are atill localized at individual atoms
but have the highest energy of such bound electrons,
while electrons in the conduction band are free to move
throughout the crystal. Materials can be divided into
a number of classes depending on the energy gap (separation
between the top energy level of the valence and
the bottom energy level of the conduction band) and
upon the number of electrons, if any, in the conduction
band and lack of electrons in the valence band as shown
in Fig. 2.38. Electrons cannot possess energies that
lie in the gap.
In an insulator the valence and conduction
energy bands are separated by a wide energy gap. If
the gaps in Fig. 2.38 were drawn to scale, the gap
between the valence and conduction bands of the insulator
would be much wider than that of the other materials.
The conduction band in insulators is normally
devoid of electrons while the valence band is filled.
Therefore, when an electric field is applied across
Fig . 2.38 Energy band diagrams in which the crosshatching
symbolizes that there are many
electrons in the various energy bands for
various types of materials.
the insulator, no current flows. If sufficiently high
temperatures are applied (thousands of degrees) it is
possible to excite some of the electrons with valence
band energies up to the energy level of the conduction
band. At such an elevated temperature, insulators become
conductors with conduct ivities that increase with
temperature. Electrical conductors, such as metals,
consist of materials in which electrons fill the valence
band and about half the conduction band. In this
case when an electric field is applied the electrona
move through the crystal easily and the material is
referred to as a conductor. In metals an increaae in
temperature increases lattice vibrations and electron
scattering, therefore the conductivity decreases with
increasing temperature. Materials with properties between
insulators and conductors are known as semiconductors.
Semiconductors are similar to insulators in
that the valence band is filled and the conduction band
is empty. However, the energy gap separating the conduction
and valence bands is much smaller than that of
insulators. For such semiconductors, thermal energy
can excite a few electrons from the valence to the conduction
band. Such materials are known as intrinaic
semiconductors. Their conductivity increases with increasing
temperature. By doping these materials with
certain impurities, it is possible to greatly increase
the number of carriers and increase the conductivity.
If the dopant has carriers with an energy level that
lies in the band gap just slightly below the conduction
band, then thermal motions can readily excite electrona
from these impurities (or dopants) into the conduction
band where they are free to move through the crystal
causing the material to become more conductive. Such
dopants are known as donors and the resultant materials
are known as negative or n-type semiconductors due to
the fact that the carriers are electrons. Galium arsenide
(GaAs) crystalline materials are important as roomtemperature
light-emitting diodes (LED’s) and diode (or
injection) lasers. In these materials, tin and tellurium
serve as dopants that contribute (or donate) electrons
to the conduction band while germanium (an acceptor
impurity) introduces trapping sites with energy
levels slightly above the valence band in the band gap
itself. In the case of an acceptor, thermal motions
will provide sufficient energy to permit electrons from
the valence band to be trapped by an acceptor impurity
atom. The holes left behind in the valence band act
as positive conductors.
p-type semiconductors.
An important
These materials are known as
semiconductor energy state is
2-17

shown in Fig. 2.39. This state is known as the population
inversion state. It corresponds to the condition
in which holes exist in the valence band and electrons
exist in the conduction band simultaneously. This
leads to the production of photons. The energy gap is
indicated by E in Fig. 2.39. When electrons from the
conduction ban~ lose some of their energy and drop down
Fig. 2.39
T
CONDUCTION
BAND
+
BAND-GAP,EG
Q—Fc
hv
Fc= CONDUCTION SANO
ENERGY LEVEL
SPONTANEOUS: h.=EG
FERMI
STIMULATED: tWCEFc
‘EFV
PHOTONS AMPLIFY
THEMSELVES
Electrons (cross-hatch) from the valence
band are stimulated to the energy level of
the conduction band in a population inversion
situation. Their return to the valence
band causes the emission of photons.
into the valence band they recombine with holes and
photons are produced. This process is known as recombination.
In the desired case, the energy is given up
entirely in the form of photons. If this process occurs
spontaneously, the energy of the emitted photon
iS approximately equal to the band gap energy, Eg. The
photons produced travel in random directions. On the
other hand, if sufficient density of photons exist in
the recombination region both spontaneous emission (or
recombination) and stimulated recombination occur. The
stimulated photons that are produced travel in the same
direction as the primary photons. In the latter case
the photon energy is less than the difference between
the Fermi energy level in the conduction band, EFc, and
the Fermi level in the valence band, EFV. These conditions,
spontaneous and stimulated emission, are necessary
for the proper operation of light emitting diodes
(LED’S) and diode lasers, respectively. In order to
understand how LED’s or diode lasers can be produced
and operate in practice, consider the condition at a
p-n junction as shown in Fig. 2.40. In this case, GaAs
}
&
1%z
w
P
-
CONDUCTION BAND
m
I
1
,
I
, 1 I
N
4
P-N JUNCTION
Fig. 2.40 The
I
1:~~
energy levels in a p-n junction.
is doped with an acceptor material on one side of the
junction, resulting in a p-type semiconductor region,
and with a donor material on the other side, resulting
in an n-type semiconductor region. The spatial separation
between the p- and n-type regions is known as the
p-n junction. The electron energy levels in the conduction
and valence bands are as shown in the upper
part of Fig. 2.40. Notice that when a bias voltage is
not applied, as on the left, a population inversion
does not occur. Electrons from the valence band of the
p-type region flow into the conduction band of the n-
type region until the electron energy levels on each
side of the p-n junction are equal, then essentially no
more electrons flow across the junction. The energy
level difference across the junction constitutes a barrier
to further current flow. If a forward bias voltage
is applied, as shown on the right of Fig. 2.40,
electrons are forced or injected into the n-type region
and holes are formed in the p-type region. When the
energy level of a sufficient number of electrons are
raised to the energy level of the conduction band, their
electron energy level exceeds the barrier energy and
electrons flow across the junction into the p-region.
More detail is shown in Fig. 2.41. In the population
L
cc
1,1
4, hv
rFv
Fig. 2.41
I
RECOMBINATION
l-REGlON*HOMOJuNcTlON
!
.1 ‘ I ‘ I ~
VG= EG/e
FORWARD BIAS
The various regions and energy levels at a
forward-biased p-n junction of a semiconductor
diode.
inversion region, just on the left of the p-n junction,
electrons can spontaneously recombine with holes producing
photons. Since in this region there is a finite
lifetime for the electrons depending upon the average
time it takes for such recombination to occur (typically
3 to 5 ns), the inversion region is restricted in
spatial extent as shown in Fig. 2.41. In this case the
junction is known as a homojunction and under proper
conditions may be used to fabricate a homojunction LED
or diode laser.
Current density is directly proportional to
the thickness of the recombination layer. Therefore,
in order to reduce the current it is important to reduce
the thickness of the recombination layer. This can
be accomplished in a gallium arsenide (GaAs) crystal by
the use of layers alloyed with varying amounts of aluminum
(Al). The substitution of aluminum (Al. ) for gallium
(Ga) occurs with little or no distortion of the
crystal lattice. The energy gap plotted against the
fraction of aluminum that replaces an equal fraction
of gallium ( Ga) , forming gallium aluminum arsenide
(GaAIAs) is shown in Fig. 2.42. For up to 37% Al substituted
for Ga, the energy gap increaaes from 1.43
electron-volts to 1.92 electron-volts. This is approxi-
2-18

mately a 0.5 electron-volt increase. For fractional
parts of Al greater than 0.37, i.e., x > 0.37, mechanisms
in addition to simple photon production occur during
recombination with the result that not all of the
energy goes into producing photons, part of it goes into
thermal energy with the possibility of crystal damage
and a reduced tendency for lasing. The wavelength
can be obtained from the photon energy relation E t
= hf
and from the wavelength-frequency-velocity relation ~f=
= c/n, from which the relation 1 = hc/nEt is obtained,
where h is Planck’s constant, c is the velocity of light
in a vacuum, n is the refractive index taken as unity,
and E t
is the energy lost by a particle. For a particle
with a charge of one electron that loses energy
equal to the gap energy, A = 1.24/Eg, where h is the
wavelength in microns and Eg is the gap energy in electron-volts.
Thus for GaAs, 1 = 0.90 micron and for 37%
Al, 1 = 0.64 micron. Longer wavelength lasers (1.1
micron to 1.6 micron) can be produced by using the
quarternary alloy iridium-gallium-arsenic-phosphorous
(InGaAsP).
1 P,
A —P —~ qi - N—
I
I
I
I
1
1
++++++++++++++++++++++++++
I
1
Gal.xA~As:Ge ,~Ga l-y A’yAs ~ Gal_xAlxAs:Sn/Te
I
Ge ‘
S;;Te
Fig. 2.43 The energy levels of a semiconductor forward-biased
double heterostructure laser in
a junction of lower concentration alumlnum
surrounded by higher concentration aluminum.
‘“’~ “’:;’v:;:N:;GAp0.37COMPETING
9 /.
~ ,- PROCESSES OCCUR MAKING
/-
m2.O
u ...” ONSET OF LASING LESS
..0” PROBABLE
n-
a
>
0 AIXGal.XAs ● FOR X INCREASING FROM
OT00.37 THE REFRACTIVE
%
300”K
z
INDEX DECREASES BY 5%
u.1 15
[1111111111
o 0.5 1.0
GaAs x AIAs
Fig. 2.42
The band-gap energy level versus aluminum
galium arsenide composition (AIXGA(l-X)AS).
Another important effect is that as the fractional
part of Al, x, increases from zero to 0.37 the
refractive index decreases by 5%. Thus, as x increases,
the energy gap increases and the refractive
index decreases. The energy gap increases by almost
30% and the refractive index by about 5%.
The energy band structure for a crystal in
which a higher concentration of aluminum in two regions
sandwich a third region of lower aluminum content between
them is shown in Fig. 2.43. The corresponding
crystal structure can be formed by a number of processes
one of which is the liquid-phase epitaxial growth
process. Epitaxial growth is the growth of a crystal
from the surface. For the case of interest the following
is a highly simplified description. The process
begins with a crystal of gallium arsenide (GaAs), one
surface of which is put in contact with a high temperature
solution of gallium aluminum arsenide (GaAIAs).
The crystal is maintained at a slightly lower temperature
than the liquid and crystal growth occurs from the
surface. Once the proper thickness of this particular
composition has been achieved, the crystal is removed
from the bath and put in contact with another liquid
having the composition corresponding to that of the
next layer. A crystal results with a p-type and an n-
type layer, each of which have a higher aluminum content,
larger energy gap, and lower refractive index,
2-19
and between which is a recombination layer with lower
aluminum content, smaller energy gap, and higher refractive
index. The amount of aluminum in the recombination
layer determines the wavelength of the light
emitted. In this manner the structure corresponding to
the energy diagram shown in Fig. 2.43 can be formed. By
this process the recombination layer can be made thin,
often as small as a few tenths of a micron. The longer-wavelength
quarternary InGaAsP alloys are produced
by liquid-phase epitaxial growth on an iridium phosphorus
(InP) substrate.
The recombination layer has lower aluminum
content and therefore, a smaller energy gap, while the
layers on each side have greater aluminum content and
a resulting larger energy gap. In this case, when an
electrical bias is applied, electrons are introduced
from the n-type layer into the recombination layer.
Recombination occur overwhelmingly more often in the
layer with the lowest energy gap.
2.3.2 Light Emitting Diodes (LEDs) and Diode
Lasers
The use of crystal structures to fabricate
either an LED or a diode laser is shown in Fig. 2.44.
Electrons are introduced into the bottom of the crystal
and holes are introduced into the top. In the recombination
layer, holes and electrons recombine to form
photons that tend to move outward in all directions as
shown on the left of Fig. 2.44. In this case, the device
behaves as an LED. The light, emitted in all directions,
results from spontaneous emission.
In order to produce a laser it is necessary
to confine and guide the emitted light. This increases
the light intensity to the level where stimulated emission
occurs. This is accomplished in the following
way. The recombination layer has less aluminum therefore
it has the lower energy gap and recombination occurs
here. The use of some aluminum in the recombination
layer allows the wavelength to be adjusted but in
addition it reduces the probability of crystal damage.
Furthermore, the layer with the smallest energy gap
also has the highest refractive index. Thus, a higher
refractive index layer is sandwiched between two layers
of lower refractive index. This is exactly the situation
that leads to lightwave trapping in optical fibers.
Similarly for the structure shown on the right in Fig.
2.44, photons tend to be reflected from the lower refractive
index surface back into the higher-refractiveindex
recombination layer. Photons are retained in the

WOTO
hu=Eg
LED
“’SPONTANEOUS”’ RADIATON
\
LASER
‘“STIMULATED’’RADIATION
m
The emitted optical power versus applied direct
current is shown in Fig. 2.45. The emitted optical
power initially increases linearly with current.
This is the region where spontaneous emission dominates.
Once a sufficiently high photon intensity level is
reached, stimulated emission begins to dominate and the
emitted optical power increases sharply as shown in Fig.
2.45. The spontaneous emission portion of the curve is
relatively temperature independent compared to the
stimulated emission portion. The electrical current
level corresponding to the onset of stimulated emission
increases with increasing temperature, however the slope
of the stimulated emission curve remains approximately
constant, as shown by the T1 and T2 curves in Fig. 2.45.
Thus, diode lasers are mounted on heat sinks and may
require temperature control devices and feedback circuitry
to control the light intensity. LED’a operate
by spontaneous emission and do not require such temperature
compensation. If one extrapolates backward the
steeply riaing stimulated emisaion region of the curve,
the intersection with the current axis, known as the
threshold current, is temperature dependent. In the case
shown in Fig. 2.45, the threshold current is approximately
360 ma at temperature T1. Currently, diode lasers
exhibit threshold currents in the range of 20 to 200 ma.
The solid curve shows the optical power emitted versus
current and the superimposed dots indicate repeated
measurements taken after 8000 hours. As can be seen,
no essential change in laser characteristics occurred.
The operational lifetimes of currently manufactured
diode lasers are as long as 106 hours.
T2>T1
Fig. 2.44
The structure of a light emitting diode
(LED) and a diode laser showing radiation
of photons from recombination.
4 -
recombination region for a longer period of time by the
partially reflecting mirrors that are in effect formed
at the cleaved ends by the difference in refractive index
between the crystal and air, as shown on the right
in Fig. 2.44. Thus, photons formed in the recombination
layer tend to reflect back and forth a number of
times. In this process, the light intensity is increased
in the recombination region. When the light intensity
becomes sufficiently high, stimulated emission begins.
This is the condition for lasing. When the number
of energy gains matches the number of energy losses,
for every photon that escapes one or more is formed
within the recombination layer, thus resulting in an
everincreasing recombination rate and photon production.
Ultimately, equilibrium is reached and the number
of photons being emitted (radiated) from the ends equals
the number of photons being produced. The requirement
for this to occur is that both carriers (electrons and
holes) and radiation (photons) tend to be confined to
the recombination layer. The carrier confinement results
in the required population inversion. This insures
that electron-hole recombination and the resulting
photona will occur in the recombination layer. The
higher refractive index in the recombination layer and
the effectively partially-mirrored ends reflect or
guide the photons back into the layer thus increasing
the light intensity by several orders of magnitude
above that of spontaneous emission.
Fig. 2.45
2 - SPONTANEOUS
0
0 100 200 300 400 500
DIRECT CURRENT (mA)
The optical power emitted by a diode laser
as a function of applied electrical current.
Diode lasers produced in the manner described
above are known as double heterojunction lasers. The
characteristics of such a laser are shown in Fig. 2.46.
The refractive index is plotted on the left and the
band gap energy is plotted on the right, both relative
to the layera of the laser. The refractive index and
energy gap both undergo step-function changes at the
edges of the recombination layer. Other fabrication
characteristics of the diode laser include the partially-mirrored
ends and the electrical contacts parallel
to the recombination layer. Holes and electrons are
injected into the recombination region. Optical energy
is distributed across the recombination
approximate Gaussian distribution shown
layer in the
in Fig. 2.46.
n
)—INDEX
Fig.
2.46 A double-heterojunction
The smaller the volume of the recombination
laver the lower the reauired threshold current. As
previously stated. recombination layers in double
~eterojun~tion diode lasers are as thin as several
tenths of a micron. However, the layer shown in Fig.
2.46 extends across the entire crystal. With a recombination
layer this wide, the onset of lasing does not
occur uniformly throughout the layer. Lasing can start
<
Eg=O.3eV
S~GAP
ENERGY
laser.
2-20

I
in one portion of the recombination layer but not in
another. ‘Lhis is known as filamentary lasing. Such
lasing behavior tends to produce noise. If the width
of the layer is less than 10 microns, it is too narrow
for such filamentary behavior to occur and when lasing
does begin it occura uniformly throughout the layer.
Furthermore, when the width is less than 15 microns
singlemode propagation usually occurs. Finally, the
less the width of the recombination layer the less the
required threshold current. Double-heterojunction diode
lasers with threshold currents as low as 20 ma have
been produced. However, trade-offs may be required.
For example, reducing the recombination layer width
also reduces the maximum safe photon intensity. A safe
cw optical power output that can be maintained without
danger of facet damage is approximately 1 mW for each
micron of recombination layer width. Thus, a laser with
a recombination layer 10 microns wide can produce 10 mW
of optical power safely.
A striped-geometry injection laser diode,
such as that shown in Fig. 2.47, has the desired thin
and narrow recombination region. With this geometry,
the emitted light spreads out in the vertical direction
by as much 50” and in the horizontal by 8° or more.
The dimensions of the recombination layer are of the
order of 0.3 microns thick, 10 microns wide, and Up to
500 microns long. These dimensions and light spreading
angles must be taken into account when the laser is
coupled to an optical fiber or substrate.
TRANSVERSE
(m)
u 1
Y
UDINAL (q)
FUNDAMENTAL MODE
{ (!:;)
,-I 2ndMODE
,’‘ ‘,,, (m::)
~
E LATERAL(s)
DISTANCE
Fig. 2.48 The light intensity as a function of distance
across the face of a laser for the
fundamental and second lightwave modes generated
by a laser.
METAL CONTACT
-’”’
P
(a) STRIPE CONTACT
METAL CONTACT
)
II(Zn-DIFFUSED)
/[ n
P
N
euBsTRATE
(c) DOPING-PROFILE
P
METAL ~ONTACT
PROTON
SOMSARDED
(SEMI t+SULATING)
METAL CONTACT
‘P
-4 l-+=
(b) PROTON-BOMBARDMENT
(d) STRIPE MESA
Fig. 2.49 End views of various stripe geometry diode
lasers.
Fig. 2.47
A GsAs-GcAIAs geometry CW injection laser
diode.
The distribution of optical energy across the
lasing region is shown in Fig. 2.48. The fundamental
and second harmonic of the longitudinal modes are shown.
In the longitudinal fundamental mode, the energy tends
to be concentrated more heavily towards the center, and
tapers off towards the edges in a Gaussian distribution
curve. If this lasing region is sufficiently wide, the
second harmonic mode can occur and the emitted optical
energy is concentrated in two regions.
Several techniques have been employed to fabricate
such stripe geometry. Some of these are shown
in Fig. 2.49. The upper left (a), an oxide protective
stripe is shown between the metal contact and the crystal.
The stripe is formed where the oxide layer is
omitted in the center. Electrons tend to be injected
into this region only. In this case, the current can
spread out underneath the oxide layer where it is not
confined. Another technique, shown at the lower left
(b), reduces such current spreading by increasing the
resistivity in the regions on each side of the stripe.
This can be accomplished by photon bombardment that
2-21
produces a semi-insulating layer on each side of the
stripe. A third technique, shown at the upper right
(c), uses the diffusion of a dopant, such as zinc, into
the stripe region to significantly lower the resisti-
Vity. Finally, almost complete electric current conf
inement occurs in the structure shown at the lower
right, (d). A stripe mesa (plateau or table) such as
this is formed during the process of growing the crystal.
Often such a mesa is buried by depositing additional
material over it.
For diode laser operation one major concern
has been the reduction of the spontaneous emission region
that was shown in Fig. 2.49. However, spontaneous
emission is the mechanism responsible for light emission
in LED’s. These devices are cheaper. Simpler
construction techniques may be used. The light they
produce is not coherent and is emitted over a much
wider angle (approximately 180° ) with the result that
less optical power may be coupled into a fiber. On
the other hand, the spontaneous emission portion of
the optical output power versus input direct current
curve is far less temperature dependent than the stimulated
emission region. Thus , because LED’s are less
temperature dependent than diode lasers, temperature
control and optical feedback problems are reduced.

LED’s are fabricated both as edge and surface
emitters. An example of surface emission is shown in
Fig. 2.50. A well is etched in the substrate to within
EPOXY=
d
FIBER
ELECTRICAL
N
CONTACT N RECOMBINATION
GE~SUBSTRATE
LAYER (N OR P)
Fig. 2.50
INSULATING
/
LAYER
A surface-emitting LED with an etched well.
approximately 1 micron of the recombination layer. This
puts the surface close to the recombination layer and
reduces the tendency for the light generated in the recombination
layer to be reabsorbed before it can escape
from the crystal. The optical fiber into which the
light is being coupled is epoxied to the LED is also
shown. This arrangement is satisfactory for a multimode
optical fiber but, for coupling into singlemode
fiber, edge emitters mounted in the same manner as
diode lasers are more desirable. The waveguide character
of the heterojunction structure leads to improved
coupling efficiency and greater directionality, that
is, it confines the emitted light to a narrower beam.
In this case, the ends are cleaved at an angle several
degrees from the normal to the surface of the recombination
region in order to breakup optical standing waves
and thus extend the region of spontaneous emission.
In the discussion so far, the production of
photons by electron-hole recombination has been considered.
The reverse can also occur. A photon can be absorbed
and thus produce an electron-hole pair. This
phenomenon occurs in photodetectors and will be considered
next.
2.4 PHOTODETECTORS
The simpleat type of photodiode is the homojunction
or p-n diode as shown in Fig. 2.51. The most
1
>DEpLET10t4 REGloN
L-
1- ABSORPTION
REGION -1
successful photodetectors employ silicon ( Si ) although
galium arsenide (GaAs) is sometimes used. When the
device is reverse (back) biased as shown, the electric
field is not uniform. It peaks around the p-n junction
as shown the bottom of Fig. 2.51. Thus , electron-hole
pairs formed by the absorption of photons in this region
are swept away (depleted) , electrons going to the
n side and holes to the p side. This region of increased
electric field is known as the depletion region.
A S shown, the depletion and absorption regions
do not necessarily coincide, the absorption region
tending to be larger. Electron-hole pairs, formed by
the absorption of photons from the depletion region,
randomly diffuse, often recombining to produce photons.
A depletion region may exist even without a reverse
(back) bias, but then it is narrow. However, there
are circumstances where unbiased operation is important,
such as for low electrical power operation. Also
with a bias, a “’dark field” current (dark photocurrent)
flows due to thermally generated electron-hole pairs
even in the absence of light. Removing the reverse
(back) bias eliminates the “dark field” current. Operation
with zero bias that is, without a bias supply, is
known as photovoltaic operation.
In order to make the depletion region as
large, or larger than, the absorption region, the arrangement
shown in Fig. 2.52 is used. Here a wide re-
P-REGION
LIGHT
3~
FDEPLETIONREGIONfi
INTRINSIC REGION
l—ABSORPTION~
REGION
R
1-,1~1
BIAS SUPPLY
b
N-REGION
●
OUTPUT
Fig . 2.52 A positive-intrinsic-negative (PIN) photodiode
with bias supply.
gion with little or no dopant is placed between heavily
doped n-type and p-type regions on opposite ends. An
undoped semiconductor is referred to as an intrinsic
semiconductor, therefore the broad lightly-doped region
is called the intrinsic or i-type region, or simply the
i-region. Such photodiodes are known as poaitive-intrinsic-negative
or PIN diodes. The corresponding electric
potential curve is also shown in Fig. 2.52. The
highly doped n- and p-type regions at each end have low
resistivity and therefore make good electrical contact.
The resistivity of the i-region is often so high that
even without a reverse (back) bias the depletion region
extends half way through the i-region. The voltage required
to extend the depletion region completely through
the i-region ia called the ‘punchthrough voltage.”
Fig. 2.51
The electric field and regions of a p-n
(homojunction) photodiode with bias supply.
When considering fiberoptic microbend sensors,
reference will be made to dark field operation.
A current exists in a reverse-biased photodiode even
with no incident light. This current is called the
dark field current and results from the thermally gen-

crated electron-hole paira that are driven by the bias
voltage. Thus, the amount of dark current depends on
the temperature of the photodiode, the energy gap, and
the geometry of construction. Silicon photodiodes have
been manufactured with very low dark currents.
In order to insure that nearly all of the
photons are absorbed (high quantum efficiency) the width
of the i-region should exceed that of the absorption
region by a factor of 2 or 3. However, the photodiode
should be as thin as possible for fast response. Thus,
high quantum efficiency and fast response represent design
tradeoffs. Photodiodes such as those shown in Fig.
2.53 are known as avalanche photodiodes (APD). Here a
highly-doped layer of p-type material is sandwiched
between the i- and n-regions. This results in a region
of high electric field just before the positive contact.
In this arrangement, an electron freed in the i-region
drifts toward the positive electrode. When it enters
the high field region it speeds up achieving sufficient
kinetic energy to produce another electron-hole pair if
it collides with the lattice. The new carriers generated
in this manner can likewiae produce additional carriers.
Thus, a “primary” electron freed in the i-region can
free numerous “secondary” electrons in the high field
region. The resultant devices exhibit high quantum efficiency.
An example of one type of APD construction
is shown in Fig. 2.54. The temperature dependence of
APD’s is greater than that of either p-n or PIN photodiodes.
hi~
w
kDEpLETION REGION+SECONDARY ELECTRON
PRODUCTION REGION
LIGHT P I P N
34
OUTPUT
-111~+
BIAS SUPPLY
Fig. 2.53 Field regions in an avalanche photodiode
(APD) with bias supply.
v ‘k;:;;:;LL
/,;;;; ,,//:: 4’, *;,
P-.~
A
L!IGH!
,,, ,;;; ::,, ,,, ,,,,,:< ,,
R
b OUTPUT
P
INTRINSIC
—
BIAS
.—– SUPPLY
+
N
ELECTRICAL
CONTACT
Fig. 2.54
[
r * I
,’,, , ,,’ ,~,,,’,
T
The physical construction of an avalanche
photodiode (APD).
2-23

CHAPTER 3
FIBEROPTIC COMPONENT INTERCONNECTION
Optical power loss (attenuation) has been
drastically reduced in optical fibers since 1970. A
power loss of 0.2 dB per kilometer has been achieved
and the prospect is good for another order of magnitude
improvement to 0.02 dB per kilometer. If this occurs,
approximately 50 kilometers of fiber would exhibit only
a 1 dB leas. One consequenceof this progress inreducing
attenuation in fiber is the increased importance of
the attenuation associated with component-to-fiber,
fiber-to-fiber, and fiber-to-component interconnections.
Little is accomplished if 0.02 dB per kilometer
attenuation is achieved in optical fibers and at the
same time a number of Interconnections are required,
each resulting in an appreciable fraction of a dB loss.
In the case of fiberoptic sensora, where much shorter
lengths of optical fiber are utilized than in communication
systems, such as several hundred meters of fiber
or less per sensor, and where the fiber used in most
cases is not chosen for low 10SS, problems with interconnections
may be less important although connection
insertion losses can still be a large portion of the
total loss in a fiberoptic sensor. Interconnections,
especially singlemode fiber interconnections, are still
required and therefore of importance. The current
state of their development and manufacture will be considered
in the following discussions.
3.1 ‘FIBEROPTIC CONNECTORS AND SPLICES
Some of the uses of interconnections in the
fabrication of fiberoptic sensors include joining
sources and detectors to fiber , splitting the output of
a source (especially laser diodes) among a number of
sensors, beam splitting and combining of light in interferometers,
and providing fiber-to-fiber interconnections.
All interconnections must be designed taking
reflection and consequent insertion losses into account,
with the aim of minimizing the insertion losses.
into which light is being introduced will be designated
the “sink” fiber.
In connectors and splices, power losses fall
into two general classes: intrinsic and extrinsic.
Intrinsic losses are due to variations or imperfections
in the fiber that occur during the manufacturing process
and are not mechanically or externally correctable.
Extrinsic losses are those that occur after the manufacturing
process and are mechanically or externally
correctable, such as incorrect finishing of the fiber
end-surfaces or incorrect mechanical mating of fibers.
Some of these effects are shown in Fig. 3.1. Only the
x
INTRINSIC
(I:C
CORE AREA MISMATCH
NUMERICAL APERTURE MISMATCH
PROFILE MISMATCH
EXTRINSIC
~ ~d
-c
END SEPARATION
+ p’-
ANGULAR MISALIGNMENT
-L /
t
LATERAL OFFSET
Fig. 3.1 Some causes of intrinsic and extrinsic
power losses in optical fiber interconnections.
Interconnections can be grouped into three
classes, namely (1) connectors (remountable interconnections
between fibers or between a fiber and some
component, such’as a source, a detector, or an integrated
chip), (2) splices, (fusion joints or permanent
joints between two fibers or a fiber and some optical
component, and (3) couplers (connections that redistribute
energy between two or more fibers). In the case
of singlemode fibers, splices are relatively easy to
form. Splices and connectors with less than one tenth
dB insertion loss per splice can be achieved. Also,
in the case of singlemode couplers, especially simple
four-port couplers having two input ports and two output
ports, losses of less than a dB have been achieved.
Multimode connectors and couplers are now commerically
available and their singlemode counterparts are just
beginning to become available also. In the case of
multimode connectors, the average loss is about 1 or 2
dB. Goals are set for less than 0.5 dB. For purposes
of discussion, the fiber from which light is emerging
will be designated the ‘source” fiber while the fiber
3-1
fiber cores are shown in these sketches. Intrinsic
effects are shown on the left of Fig. 3.1. If the
core areas of the source and sink fibers are not the
same, the mismatch can result in a power loss. Differences
in numerical aperture (NA) between the two fibers
can also result in losses. For the case of graded
index fibers, discussed earlier, a refractive index
profile mismatch can lead to intrinsic losses. Losses
occur only when directing light from a fiber of larger
core or NA into a fiber of smaller core or NA. In
these cases some of the light from the core of the
source fiber will not be trapped in the core of the
sink fiber. For the reverse, small-to-large core or
NA, losses due to the mismatch do not occur.
Examples of causes of extrinsic losses are
shown in the right column of Fig. 3.1. If the light
input to a sink fiber or output from a source fiber
diverges, such as at cone angles of 15° to 20”, a core
separation will allow some of the light emanating from
the core of the source fiber to miss the core of the

sink fiber. Likewise angular misalignment can lead to
a portion of the light from the source fiber entering
the aink fiber at angles that will not allow trapping
in the core. Finally, losses can occur due to lateral
offset between two fibers because they are not properly
aligned or their cores are not concentric with respect
to the outer diameter of the fiber even when the outer
surfaces of the cladding are properly aligned. In general,
fibers are lined up by their outer surfaces.
There are a number of other extrinsic effects that are
not indicated here. The fiber end might not be smooth.
‘rhis can lead to scattering loaaea. The fiber ends
may not be flat cauaing lensing effects to occur. Thus,
it is esaential that care be taken in the manufacture
or acquisition of optical fibers, connectors, and
splicea in order to inaure that the intrinaic and extrinsic
leases are or can be minimized. h effect that
can be corrected easily ia reflection from the ends of
both fibers due to refractive index difference between
glass and air. For silicon dioxide (Si02) this reaulta
in a 0.4 dB loaa. In order to correct thia it is only
nesaary to employ an index-matching liquid or potting
material between the ends of the two fibera being buttjoined.
the same fiber. For a fiber with a 50-micron core it
would be necessary to hold the dimensions to + 5
microns, but when dealing with singlemode fibers w~th
a 5 micron core or less it is necessary to hold the diametera
to within a half a micron. Differences in numerical
aperature also need to be controlled accurately,
however in general, refractive indices are being controlled
within and among fibers to within a variation
of only a few percent. Thua, the primary problem is
the variation in the core diameter among fibera and
within the aame fiber.
The effect of the mismatch between either the
core areas or the fiber numerical apertures is shown in
Fig. 3.2. A problem exista when a source fiber with a
1.0
0.8
0.6
~ 0.2
rn
S 01
~ 0.08
0.06
0.04
0.02
0.001 A I 1 1 I 1 1
2 4 6 8 10 12 14
PERCENT OF DIFFERENCE IN CORE DIAMETERS
OR FIBERNA
Fig. 3.2 Approximate losa in dB due to larger-tosmaller
core diameter difference or fiber
numerical aperture difference for two buttjoined
optical fibers.
larger core or larger numerical aperture ia joined to
a aink fiber with a smaller core or a smaller numerical
aperture. Furthermore, as their difference in numerical
aperturea or core diameters is increased, the loss
will increase. The curves in Fig. 3.2 ahow the optical
power loaa in dB as a function of either the percentage
difference in core diameters of larger source cores
butt-joined to amaller aink corea, or source fibers
with larger numerical apertures butt-joined to aink
fibers with amaller numerical aperturea. These specific
curves actually apply to step-index fibers but the general
trenda shown are also true for graded-index fibers.
A 10% mismatch in either the core diameters (larger to
amaller) or the numerical aperturea (larger-to-amdler)
would cauae approximately a 0.5 dB loss. For the larger
multimode fibers it is not a difficult problem to maintain
diameters to within 10% of each other or within
3-2
Fig. 3.3
The extrinsic leas due to end separation for
atep-index fibers is shown in Fig. 3.3. The core diab
01 0.2 0.3 0.4 0.5
END SEPARATION (S/D)
Variation of connector power loss with endseparation-distance-to-diameter
ratio between
two atep-index air-gap optical fiber
ends for several valuea of numerical aperture
(N.A.).
meter ia indicated by D and the separation by S. The
coupling leas in dB is plotted as a function of S/D.
This effect is alao a function of numerical aperture.
The greater the numerical aperture (NA) the greater the
spreading of light from the source fiber and therefore
the larger the percentage of light that will miss the
core of the aink fiber. In thia figure, results are
plotted for NA ranging from 0.15 to 0.50. For the
fibera used in fiberoptic sensora the NA of Intereat
is below 0.20 and in fact more nearly 0.15. In thia
case, as can be seen in Fig. 3.3, a difference of 10%
in the core diameters will produce only a couple of
tentha of a dB loaa. Indeed, for NA = 0.15, an end
separation of half the core diameter will produce about
0.7 dB coupling loaa. In the caae of aplicea there is
no end separation therefore this losa does not occur.
The effect of axial transverse (lateral) displacement
of equal-diameter cores is ahown in Fig. 3.4.
The fiber core diametera, D, and the transverse displacement,
d, la shown. As can be seen, a 10% transverse
displacement, which for ainglemode fibera can be
0.5 urn (micron) can reault in a 0.5 dB losa. When purchasing
fiber, carefully apecified fiber dimensions are
important, e.g., fiber outaide diameter should be maintained
uniform to ~ 1% of some nominal value and corea
should be concentric to within 0.5%. For an 80 urn
fiber, a 1% variation in the diameter is 0.8 pm. It
could lead to a 0.4 ~m transverse displacement, which
for 5 ~m core could lead to d/D = 0.08 corresponding to
a leas of approximately 0.4 dB.
Another extrinsic effect, an axial angular

technique is also shown in Fig. 3.6. The fiber is
lightly scored and then pulled. Care must be taken so
as not to bend the fiber. If the fiber bends a lip
tends to form when it breaks and a smooth endface does
A)STRIPJACKET
B)SCORE
~FILE
t
FIBER
6 ?
Fig. 3.4
o 0.1 0.2 0.3 0.4 0:5
TRANSVERSE DISPLACEMENT (d/D)
Connector power loss due to transverse
(lateral) displacement of the cores of two
step-index optical fiber butt-joined enda.
P
C) RESULTS OFFENDING
v
&d
h
D) RESULTS OF PULLING
—~.
misalignment is shown in Fig. 3.5. It can occur when
the fibers are not lined up axially or are not cleaved
exactly at right angles to the core axes. This effect
is also a function of NA, increasing as NA increases.
As little as a 5° angular misalignment produces approximately
a 0.4 dB loss in the connection between two
fibers each with NA = 0.15.
Fig. 3.6
A method of cleaning an optical fiber and
the results obtained.
not necessarily result. An alternative approach to
amooth cleaving consists of polishing the ends to provide
a flat surface. This can be rather costly and”
take a great deal of time. Once a smooth end has been
formed, the fiber can be inserted into a connector or
spliced to another fiber that alao haa a smooth end.
A simple snug-fit connector is shown in Flz.
3.7. A hole in- the c&nector is provided so that tie
o 1“ 4
~(DEGR&
Fig. 3.5
Connector power loss due to axial angular
misalignment of the cores of two step-index
optical fiber butt-joined ends.
As indicated above, an important criterion
for the success of either a connector or a splice is
the proper end-preparation of the fibers themselves.
Optical fibers used in sensors usually consist of a
glass core surrounded by glass cladding that is in turn
jacketed by a buffer material used to protect the surface.
One type of jacket is made of acrylic material
that can be removed with acetone and a swab. Another
type of jacketing material consists of a IOO-micronthick
layer of silicone rubber surrounded by another
100- or 200-micron-thick layer of a harder plastic,
such as Hytrelc. This may be removed with a razor
blade. In order to prevent scratching of the fiber,
the blade must be held at a very shallow angle with respect
to the axis of the fiber. Furthermore, a blade
should be used only once. After the jacket has been
removed the fiber can be cleaved in any of several ways.
One of these is shown in Fig. 3.6. Another technique
consists of laying the fiber on a curved surface with
approximately a 5 cm radius and applying a tension of
about 1/4 pound (120 grams). The fiber is then scribed
with a file causing a smooth cleave to occur. Another
Fig. 3.7 A simple snug-fit connector with hole for
index-matching fluid.
index-matching fluid can squeeze out as the fiber ends
are inserted. This is not an easily remountable type
of connector. A fairly good splice can be formed in
such a manner by using an index-matching epoxy in place
of the index-matching liquid. If the splice is snug
enough to hold the fiber fixed, an index-matching liquid
can be used. The difficulty with such remountable connectors
is that in order to be mounted and demounted
many times it is necessary to maintain a radial clearance
of at least several microns. This technique is
not practical for singlemode fibers because no more
than an 0.5 urn lateral displacement is allowed In order
to avoid excesaive power losa.
A connector, recently marketed by TRW Incorporated
is shown in Fig. 3.8 (see Ref. 1 in Subsection
3.1.1). Four relatively large diameter glass rods are

fused together. The ends are bent at an angle of approximately
6° and the hole formed along the axis is
enlarged at both ends. The fiber is factory filled
with an index-matching liquid or a fluid curable with
ultraviolet (UV) light. The fibers to be connected
are inserted into opposite ends. The curvature causes
the fibers to be pressed into the V-groove formed between
two of the larger fibera thus aligning the fibers
being connected as they are brought together. The resultant
arrangement ia inserted into a spring loaded
holding device. The resulting splices cause losses of
0.02 to 0.34 dB. These may be mounted and demounted
many times. If LJV-curable fluid is used they may be
permanently fused.
is applied and a second piece of plaatic-glass (Plexiglass)
or some other flat material is placed on top to
hold the fibers in position. A connector formed in
this way is shown in Fig. 3.11.
LENGTHWISE SECTION
/ \
Fig. 3.10 Joining two optical fibers using grooved
plastic-glaas (Plexiglass) to form a substrate
splice.
Fig. 3.8
A single-mode remountable optical fiber
connector recently marketed by TRW Incorporated.
Accurately etched V-grooves in a silicone subatrate
may be used for aligning fibers. A small pressure
is applied to keep them firmly seated. The use
of such V-grooves to align fibers is shown in Fig. 3.9.
The fibers are then welded with an electric arc. A
number of fairly simple techniques may be used in the
laboratory. These techniques prove to be quite effective
in forming splices and remountable connectors but
they are not very useful in a more permanent environment.
The use of a sheet of thermoplastic material
(Plexiglasc) into which a section of fiber is pressed
to form a groove is shown in Fig. 3.10. An elevated
temperature may be used to facilitate the process. The
groove so formed is then utilized to align two aimilar
fibers. An index matching liquid or potting material
FI . 3.11 h optical fiber splice formed with two
pieces of Plexiglasc.
A fusion splice is shown in Fig. 3.12 at the
OPTICAL FIBER
Fig. 3.9
ELECTRODE
Splicing two optical fibers with an electric
arc.
3-4
CLAD
/ ~ORE
— //
(a) BEFORE HEATING
(b) tititiING HEATING
\ 4
(c) AFTER HEATING
x = AXIS OFFSET
z
o
1=
v
Lu
z
o
v
THEORETICAL CURVE
6.0
/
5.0
+ BEFORE HEATING
~ AFTER HEATING
4.0
1/
/
3.0
2.0 i
,/ ,’1
1.0
--&.-4--+”- 4
0L
0 0.5 1.0 1.5 2.0 2.5 3.0
(x/a)
Fig. 3.12 Fusion splicing of two singlemode optical
fibers.
Adapted from Tsuchiya and Hatakeyana, Proc. Conf.
Opt. Fiber Transmission, Williamsburg, VA Feb. 1977.

left. The ends of the two fibers are brought together
wittmut necessarily eliminating lateral displacement.
Upon heating, the fiber melts and surface tensions tend
to align the fibers as shown. The graph on the right
side of Fig. 3.12 shows connector loss as a function
of lateral displacement both before and after heating.
The results prior to fusing is a theoretical curve with
experimental reaults superimposed. As can be seen a
significant reduction in loss is realized as a reault
of fusion splicing.
One method of connecting an optical fiber to
an encased laser diode is shown in Fig. 3.13. The laser
prevent damage to the mirrored faces of the laser, a
alight separation must be maintained. For butt coupling,
utilizing an index-matching liquid and no additional
optical elementa, it is us~i to couple less
than 5% of the emitted light into the fiber. From 10
to 20% coupling of the light would be considered excellent.
If lenaes are used to focus the light into the
fiber it is possible for 70% or more of the light to
be coupled into the fiber and trapped. The manner in
which such a lens can be formed from the core of the
fiber is shown in Fig. 3.15. In this case the core
OPTICAL SPOT
EMITTING SOURCE
/ /1 I n
Fig. 3.15
Fabrication of an integral elliptical lens
at the end of an optical fiber.
Fig. 3.13
SOURCE PACKAGE
A laser-to-optical-fiber connection.
surface is displaced from the fiber end because of the
covering that protects the laser face. The resulting
displacement between the fiber and laser source causes
a great deal of the light to miss the fiber due to
spreading. A lens can be used to collect the light and
focus it into the core. The problem is illustrated in
Fig. 3.14. At the top, the spreading (divergent) angle
from the laser and the acceptance angle into the fiber
are ahown. The laser emission is such that light
apreads out in a 20° to 40° cone, while the acceptance
angle (cone) for the fiber is 10° to 14”. Thus, even
if the fiber is brought into actual contact (butt
coupled) with the laser face aa shown at the bottom of
Fig. 3.14, a large portion of the light being emitted
will mlaa the core or go into the core at such an angle
that it will be trans~tted through the core-cladding
interface, into the cladding, and lost. In order to
glass haa a lower glass transition (softening) temperature
than the cladding. Thus, the end of the fiber can
be heated and preasure applied to force a portion of
the core to bulge out aa shown, forming a lens. A
variety of other techniques for connecting lasers to
fibers have been developed and described in technical
literature. These should be reviewed In the event
such an Interconnection is required.
A mechanical device used to align and hold a
fiber and laser is ahown in Fig 3.16. The fiber is
positioned on one anvil in a V-groove and epoxied in
place. The laser sets on a second anvil that also aerves
as a heat aink. The two structures are brought together
and the smooth faces are butted, aligned, and
epoxied. A sleeve is placed over the connector. In
this way a rather small fiber pigtailed laser can be
formed.
ELECTRICAL LEAD
LASER
@ ,oo--
ER
EMISSION PROFILEOF
ALASERIN THE PLANE
PERPENDICULAR TOTHE
JUNCTION
LASER PELLET
+
a.
E:
ACCEPTANCE CONE FORA
TYPICAL STEP-INDEX FIBER
FIBER
LIGHT LAUNCHED ATAN ANGLE GREATER
THANaWILLBE LOST
CUTAWAYA
Fig. 3.16
3.1.1 References
A pigtailed anvil for laser-to-optical
ber connection.
1. Fiberoptic Technology, p. 115, Dec. 1981.
fi-
Fig. 3.14
Loas of optical power in a pigtail connection
between a laser and an optical fiber.
The angle = is equal to or less than the
critical angle.
2-5
3.2 FIBEROPTIC COUPLERS
It is often necessary to divide the beam emitted
from a laser and insert it into two or more fibera.

A laboratory beam splitter set-up used to accomplish
this is shown in Fig. 3.17. It consists of a heliumneon
(HeNe) laser, a prism 3-dB divider, an objective
lens to collect and focus the light into a fiber, and
the associated micropositioners. The prism coupler is
shown in Fig. 3.18. In order to accomplish the same
purpose with a solid state device, the cores of two or
more fibers must be brought sufficiently close and
parallel to each other such that the energy distributed
in and around one core overlaps that in the other. As
shown earlier, the energy is not guided entirely in the
core but tends to be guided evanescently by the cladding
material itself. The cores are surrounded by a
relatively thick cladding that must be removed in order
to achieve coupling. After the claddings have been removed
and the cores are brought close together, the
degree of overlap is adjusted in order to achieve the
desired coupling ratios. It is then necessary to cement
or fuse the fibers together in order to fix their relative
position (ruggedize) and thus to maintain the
coupling ratios. The coupling ratios ahould remain con-
stant with temperature.
A great deal of effort is being devoted to
the development of singlemode fiber couplers, particularly
3-dB couplers that couple light from an input
fiber equally into two output fibers. Such couplers
are under development at Stanford University; the ITT
Electrooptic Product Division; the Gould Research Laboratories;
the U.S. Naval Research Laboratory; and the
U. S. Naval Underwater Sound Center.
The use of pigtailed laaers and bulk couplers
can reduce volume by several orders of magnitude. Two
such devices are considered next. The method developed
at Stanford University is shown in Fig. 3.19. A fiber
(a) EMBED (b) POLISH (c) OVERLAp
Fig. 3.17
A helium-neon laser with 3-dB coupler
(beamsplitter) and lens in a laboratory
set-up for coupling light into optical fibers.
Fig. 3.19 Steps in fabricating a polished fiberoptic
coupler.
After Digonnet and Shaw, J. Quant. Electron, QE-18,
746 (1982).
is cemented into a grooved slab and the combination is
then ground or polished until nearly half of the fiber
is polished away virtually exposing the core. Ideally
it is desirable for some cladding to remain so that the
core-cladding interface is not disturbed. A coupler is
formed by joining two such slabs with their faces together
and adjusting the amount of overlap or alignment
to achieve the desired coupling ratio. A satisfactory
method of accomplishing temperature-independent fusing
has not been developed.
The technique developed by Sheem, et al, (see
Ref. 1 in Subsection-3.2.1) is-sho~ in Fig. 3.20~ The
INDEX
MATCHING
POTTING
(b) ETCH (C) RUGGEDIZE
Fig. 3.18
A 3-dB priam coupler in a laboratory.
Fig. 3.20
Steps in
coupler.
fabricating an etched fiberoptic

fibers are cleaned carefully after removing the jacket.
Then they are twisted together and while remaining
twisted they are etched to remove most of the cladding,
leaving approximately one or two microns of cladding
around the core. The diameters of the fibers after
etching are less than 10% of their initial diameters,
therefore the resulting sections of fibers are quite
fragile. The joint IS held fixed (ruggedized) by either
potting in an indexmatching material or by fusing under
an axial tension that prevents the fiber from sagging
due to gravity and at the same time stretches the fiber
slightly, thus forming a biconical taper. This is shown
in Fig. 3.20 on the right. Index matching silicone
liquids have been proven to be highly temperature dependent.
Better results are obtained with index-matching
silicone rubber. However, there is still a temperaturedependence
problem. A great deal of success has been
achieved recently using a gel glass material (see Ref.
2 in Subsection 3.2.1) that is initially in liquid form.
This material consists of metal oxides dissolved in an
organic material. When heated the organic material is
driven off and the metal oxides form a glass. The refractive
index of the resulting glasa, and therefore
the degree of coupling, can be controlled by adjusting
the temperature and the length of time utilized to cure
or form the gel glass.
Temperature dependence can be minimized if
the fibers are actually fused. The biconical taper
arrangement mentioned above is shown in Fig. 3.21. To
aturized bulk optical components similar to the laboratory
devices shown in Figs 3.16, 3.17, and 3.18. These
bulk components and fibers may be connected by various
means, such as GRIN rods.
Using similar techniques star couplers have
been fabricated that allow the light from one fiber to
be coupled equally into as many as 32 other fibers.
Such devices would be useful for permitting a single
optical source to simultaneously furnish optical power
to a number of sensors.
In summary, satisfactory techniques now exist
for forming low-loss singlemode splices and remountable
connectors and for fabricating low insertion loss
singlemode couplers. Recently, commercially available
remountable connectors have appeared on the market.
Singlemode biconical tapered couplera are also becoming
available. Several other types of couplers are under
development by a number of groups and thus can be expected
to appear on the market in the near future.
3.2.1 References
1.
2.
3.
S. Sheem, Appl. Phys. Lett ~, 869 (1980).
D. Tran, K. Koo, and S. Sheem, J. Quant. Electron.
QE-17, 988 (1981).
R. Ulrich, S. Rashleigh, ‘Beam-to-Fiber Coupling
with Low Standing-Wave Rtutio”, Appl. Opt. ~, 2453
(1980).
END VIEW
OF FIBER
4.
G.B. Hocker, “Unidirectional Star Coupler for Single-Fiber
Distribution System”, Opt. Lett. ~, 124
(1977).
5.
S. K. Sheem, T. G. Giallorenzi, “Single-Mode Fiber
Optical Power Divider: Encapsulated Etching”, Opt.
Lett. ~, 29 (1979).
6.
J. G. Ackerhusen, “Microlenses to Improve LED-to-
Fiber Optical Coupling”, Appl. Opt. ~, 3694
(1979).
Fig. 3.21
CROSS SECTION
VIEW
OF FUSED COUPLER
A biconical (tapered)
fiberoptic coupler.
7.
8.
M. Saruwatari, K. Nawata, “Semiconductor Laaer to
Single-Mode Fiber Coupler”, APP1. Opt. ~, 1847
(1979).
H. Kuwahara, N. Tokoyo, M. Sasaki, “Efficient
Coupling from Semiconductor Lasers into Single-
Mode Fibers with Tapered Heimspherical Ends”,
Appl. Opt. g, 2578 (1980).
make this coupler a portion of the cladding is removed
from each of ‘the fibers. These are then twisted together
and etched until the thickness of the remaining
cladding is about half the core diameter. The twisted
pair is then fused under some axial tension causing a
decrease in diameter, especially in the region of contact,
i.e., the interaction region. The original core
dimensions indicated in the upper right of Fig. 3.21
are reduced as shown in the lower center of Fig. 3.21.
The result is that optical energy that initially was
confined close to the core tends to spread into the
cladding in the region where the core diameter has
been decreased. This results in a stronger overlap and
therefore a higher coupling ratio. The Electrooptics
Product Division of ITT has recently developed a specialized
optical fiber that allows them to produce
fused copulers by this method without the necesaity of
etching. These couplers are available for sale. An
alternate to these fiber couplers is the use of mini-
3.3 FIBEROPTIC CABLES
3.3.1 General
Just as with conventional wire interconnections
and communication links, there is a need for fiberoptic
cables to accomplish a number of different
purposea. In many ways, the individual fibers in an
optical cable are treated very much like varnished or
plastic insulated copper wires. The individual fibera
consist of 100- to 200-micron-OD core-cladding waveguide
elements having an outer coating that may be as
thin as several microns of lacquer or as thick as 200
to 400 microns of plastic, such as nylon, teflon, or
polypropylene. Cabling serves the purpose of spacedivision
multiplexing, combining anywhere from a few to
many individual fibers into a single conveniently-pack-
3-7

aged multichannel unit. High-strength reinforcing members
are usually added to the structure and additional
inter-fiber separators (apacers) and outer protective
jacketing are provided within a cable with a relatively
small outer diameter. The jacket reducea the effecta
of cabling and protects the individual fibers from the
externl environment. Unlike copper wire and coaxial
cables, crosatalk between individual fiber waveguides
is virtually nonexistent. The equivalent of low resistance
shorts between two wirea and ground loopa do not
exist for fiber interconnection. Breaks can occur in
fibers just as in wirea. However, increases in optical
power loaaes in fibers due to microbend effects must be
considered. These may be introduced during cable construction
or installation. They also may be produced
by environmental disturbance that cause differential
stress or thermally induced bends. Care must be taken,
in cable design to prevent such effecta, particularly
when low-leas fiberoptic links are required.
optic communication purpoae are shown in Fig. 3.24 and
3.25. The first is an International Telephone and
Telegraph cable that has a group of plastic-jacketed
multimode fibers relatively looaely packed within a
central polyurethane jacket surrounded by a layer of
high-atrength Kevlarc fibers and an outer plastic jacket.
The second is a SIECOR cable in which a group of
Corning lacquer-jacketed multimode fibers are threaded
loosely through individual loose fitting protective
tubes that are distributed around a central steel reinforcing
wire. Theae tubea are surrounded by two successive
layera of Kevlarc fibers separated by inner and
outer plastic jackets. In each of these two cablea,
special care haa been taken to allow some flexibility
and freedom of motion for the individual optical fibers
to minimize the introduction of cabling-induced microbenda.
3.3.2 Commercial Fiberoptic Cables
POLYETHYLENE
OUTER JACKE1
An example of how conventional cabling procedures,
developed for the communication industry for
wire tranamiasion media may be employed for optical fiber
cables is shown in Fig. 3.22. The figure ahows the
POL
FIBERS I
OUTER JACKET
12x12 FISER ARRAY
Fig. 3.23
A fiberoptic cable produced
phone Laboratories.
by Bell Tele-
COND
KEVLAR STRENGTH MEMSERS
‘UTER
CENT
HEAVY DUTY CASLE WHICH CAN SE INSTALLEDBY REGULAR CREWS.
EXTERNAL CONSTRUCTION FOLLOWS TRADITIONAL TELEPHONE CASLE PRINCIPLES
Fig. 3.22 A fiberoptic cable produced by General
Cable.
structure of a heavy duty, combined wire and optical
fiber cable manufactured by General Cable deaigned for
use by the telecommunication industry. As indicated,
it conaiats of two almoat identical multiwire and multifiber
sandwich-like stripa that are parallel to each
other on opposite sidea of a channeled plastic rod that
aeparates them. The atripa are held in place with tape
wrapping. l%is is surrounded by a welded aluminum tube
that forms the main strengthening element of the cable,
which in turn is aheathed by inner and outer plastic
jacketa that encaae a corrugated steel reinforcing wrap.
A aecond type of cable developed for uae in
standard telephone applications is shown in Fig. 3.23.
Produced by Bell Telephone Laboratories, it contains
144 separate multimode fibers. Twelve fibers are fuaed
in each of twelve plastic ribbona that form a 12 x 12
matrix that runs through the center of the cable. This
is wrapped with paper tape and surrounded by inner and
outer plastic jackets aeparated by flexible fiber and
steel wire strengthening elements.
Fig. 3.24
//
;HicK PLASTIC JAcKETING
A fiberoptic cable produced by International
Telephone and Telegraph.
LOOSE FITTING
PTFE TUSES
STEEL WIRE
STRENGTH MEMBER
Fig. 3.25
KEVLAR STRENGTH
MEMBERS
/
..’$’’.,:
/’”
‘y OUTER
.7 JACKET
k
PLASTIC INNER
JACKET
/*w
LACOUER COATED
FISERS
A fiberoptic cable produced by SIECOR.
TWO other aimilar cables produced for fiber-
3-8

Two cables manufactured in Japan by SUMITOMO
for underground and indoor telecommunication applications
are shown in Figs. 3.26a and 3.26b, respectively.
In the cable designed for underground installations a
set of four multimode fibers, separated by plastic
strings are spaced uniformly around a cushioned central
strength member and surrounded first by a cushioning
sheath and then a second high-strength outer polyethylene
jacket. This cable has an outer diameter of only
18 millimeters. The multifiber cable designed for indoor
test is even smaller. As shown in Fig. 3.25b, it
has an outer polyvinylchloride (PVC) jacket only 8 mm
in outer diameter, and an inner cushioning sheath that
surrounds a set of plastic-jacketed graded-index optical
fibers.
used, especially for relatively short-run applications
where microbend losses introduced by cabling are not
excessive. For low-loss long-run applications, unique
designs aimed at eliminating random bending and the
effects of cabling and environmental disturbances have
been developed that are capable of preventing the addition
of more than 1 or 2 dB/km to the original optical
power losses in the uncabled optical fibers.
Discussions of fiberoptic cable risetime budgets,
power budgets, bussing schemes, design parameters,
environmental factors, and their use in connection with
fiberoptic sensor arrays and telemetry systems is given
in Chapter 6.
PLASTIC STR
PLASTIC TAPE
ISmmOD ~ PESHEATH
mO.D
STRENGTHM
A. underground CABLE B. INDOOR CABLE
Fig. 3.26
Two fiberoptic cables produced by SUMITOMO
of Japan.
A somewhat different cable design is employed
by HITACHI to reduce losses induced by cabling and installation.
As shown in Fig. 3.27, channels are formed
in the outer periphery of a plastic spacer that is reinforced
with a central high-strength metal or plastic
tension member. The individual plastic-jacketed optical
fibers, and copper wires if some are required, fit
loosely in the channels and are held in by a thin outer
sheath. Thus, each fiber is well isolated from both
external and internal stress.
CU WIRE
16mm
SPACER \
O.D
NONMETALLIC CABLE
co MPOUNDCASLE
Fig. 3.27
A fiberoptic cable produced by HITACHI of
Japan.
3.3.3 Summary
From the above brief discussion of current
fiberoptic cabling procedures, it should be clear that
in some cases conventional cabling techniques are being
3-9

CHAPTER 4
LIGHTWAVES IN FIBEROPTIC SENSORS
4.1 INTERFEROMRTRIC FIBEROPTIC
4.1.1 Intensity Interferometry
4.1.1.1 Basic Principles
SENSORS
The basic transduction mechanism employed in
many fiberoptic sensors now being developed is the phase
modulation of coherent light propagating through a section
of singlemode fiber by the action of the energy
field that is to be detected. The techniques of optical
interferometry may be used to detect these phase
shifts in lightwaves. These techniques allow for the
extremely high sensitivity that is achievable with the
various types of interferometric fiberoptic sensors.
Until recently, optical interferometry has been a research
tool used in laboratories rather than an applied
or operational technique. With the development of low-
10SS singlemode optical fibers, subminiature aolidstate
laser light sources, photodetectors, and other
related purely optical and electrooptical devices,
it is now possible to construct practical interferometric-type
devices for use in operational systems. Fiberoptic
sensors have the potential to revolutionize sensor
technology.
mirror is less than the coherence length of the laser,
the two beams transmitted to the detector can be made
to interfere with one another. The detector output
will go from a maximum to a minimum and back to a maximum
each time the movable mirror is displaced by one
half the optical wavelength. With this technique, it
is ossible to detect mirror displacements as small as
10- ? urn, e.g. 0.63 x 10-13 m, for a He-Ne laser red
light.
LASER
SPLITTER
TRANSDUCER
Four different interferometric configurations
currently are being employed in fiberoptic aensors.
These are the Michelson, the Mach-Zehnder, the Sagnac,
and the Fabry-Perot configurations. It is convenient
to review their operation in terms of a nonconventional
schematic arrangement using airpaths and bulk optical
components before considering how they may be constructed
with optical fiber elements.
There is one important aspect that these interferometric
sensors have in common. In each one, the
output beam from an optical source is split into two or
more portions. After traveling along different paths,
these separate beams are recombined and allowed to actuate
a photosensitive detector.
4.1.1.2 The Michelson Interferometer
The basic principle is illustrated first in
Fig. 4.1 for the case of an air path Michelson interferometer.
The beam splitter is shown as a partiallyreflective,
partially-transmissive mirror. It sends one
portion of the output beam from the laser upward to the
fixed mirror where it is reflected back to the beam
splitter, where it is then partially transmitted to the
optical detector and partially reflected back toward
the laaer. The other portion of the laser output beam
passes through the beam aplitter, 1S reflected from
the movable mirror to be partially reflected to the
optical detector and partially transmitted back toward
the laser. If the difference in the the path lengths
back and forth to the fixed mirror and to the movable
4-1
4.1.1.3 The Mach-Zehnder Interferometer
The Mach-Zehnder interferometer configuration
is shown in Fig. 4.2. The laser output beam is split
Fig. 4.2
BEAM
w
Fig. 4.1 The principle of the Michelson interferometer.
“’’R’-
1
BEAM
SPLITTER
LASER
I “ ‘
1 , ,
MOVABLE
The principle of the Mack-Zehnder interferometer.
by the lower beam splitter. After traveling the upper
and lower optical paths the two beams are recombined
so that they may interfere with each other at the optical
detector. This arrangement may also be employed to

detect displacements of the movable mirror as small as
10-13 m. l%is configuration has the advantage that
little or no light is fed directly back into the laser.
This is in contrast to the Michelson configuration. A
more detailed description of how such feedback can lead
to laser instability and noise is contained in Section
4.2. It should be noted that there are two other beams
not shown explicitly in Fig. 4.2, that travel upward
from the second beam splitter, i.e. a reflected portion
of the upper horizontal beam and a transmitted portion
of the righthand vertical beam. These could be fed to
another optical detector to yield a second output signal
, which may be employed to advantage in certain applications.
4.1.1.4 The
Sagnac
Interferometer
Fig. 4.4
—
1
FIXED
t
MOVABLE
MIRROR
MIRROR
TRANSDUCER
The principle of the Fabry-Perot interferometer.
The
shown in Fig.
Sagnac interferometric configuration is sive mirrors. The reflectivity of these mirrors usually
is quite high, e.g. 95% or even higher. Assuming
4.3. With this arrangement, the two porthat
the reflectivity (reflection coefficient) is 95%,
at any instant 95% of the output light from the laser
source will be reflected back toward the laser and 5%
will be transmitted into the Interferometer cavity.
When this portion of the incident light reaches the
right-hand mirror, 95% of it will be reflected back
toward the left-hand mirror and 5% will be transmitted
through to the detector. This will combine with light
that has been reflected back and forth successively an
increasing number of times between the two mirrors.
Neglecting losses other than the 5% transmission (at
each interface), each successive output beam intensity
will be reduced from the previous one by the factor
II
II
(0.95)2 = 0.9025. Assuming that the laser has a coher-
) 1 11/ I A ence lenzth manv times the distance between the two
mirrors, the optical signal intensity incident on the
LASER
I
Fig. 4.3 The principle of the Sagnac interferometer.
tions of the laser’s output beam are sent in opposite
directions around the closed path formed by the beam
splitter and the two mirrors. They are then recombined
to be sent on to the photodetector and also back toward
the laser. If any of the mirrors is displaced perpendicular
to its reflecting surface, both path lengths
would be changed by the same amount and there should
be no detectable change in the interference process
at the photodetector. On the other hand, if the table
on which the interferometer is mounted were set into,
say clockwise, rotation about an axis perpendicular
to the plane of the beams, the beam traveling clockwiae,
i.e. In the direction of rotation, would be
delayed with respect to the counterclockwise traveling
beam. The clockwise beam has to “catch up” to the end
moving in the same direction. The counterclockwise beam
runs into the end moving in the opposite direction.
Thus, the Sagnac interferometer may be employed as a
sensitive rotation detector and, in principal, it is the
basis for the design of the ring laser gyroscope currently
in use in a number of inertial guidance systems.
4.1.
tion
4.4.
.5 The Fabry-Perot Interferometer
The fourth type of inter ferometric conf igurathe
Fabry-Perot interferometer, is shown In Fig.
It consists of two parallel, partially transmis-
4-2
detector may be found by forming the vector sum of the
electric fields of the various transmitted beams.
4.1.1.6 Interferometer Sensitivity
The sensitivity of various interferometers is
shown graphically in Fig. 4.5. Consider first, what
occurs in the first three type of interferometers that
were considered earlier. For the Michelson, Mach-Zehnder,
and Sagnac configurations, two separate optical
beams are combined at the sensitive interface of the
photodetector. As indicated in the upper left, the
wo electrical fields are represented by the vectors
~1 and 22 which are assumed to be of equal magnitude
and linearly polarized in the same direction. The optical
intensit is proportional to the square of their
vector sum, E z ( 8 ), which is at its maximum when the
temporal and spatial relative phase angle between the
two vectors is zero. If the length of one of the interferometer
paths changes the phase angle varies, and
E2( e ) and the intensity vary as indicated in the graph
in the upper right in Fig. 4.5. , i.e. , the intensity
drops to zero as 13 increases from O to n radians, varying
as cos e. For further increases in e, E2( e) oscillates
from zero to its maximum and back to zero again
each time 13 varies by 2T radians.
The corresponding diagrams for the Fabry-
Perot interferometer are shown in the lower portion of
Fig. 4.5. As pointed out earlier in this case, there
is a set of electrical field vectors, in principle infinite
in number, each successive one down from the
previous by a factor R2, where R is the amplitude reflection
coefficient. When the mirror separation is
some integral number of half wavelengths, all of these
vectors are in phase and the output intensity is at a
maximum. When the separation is increased slightly,
each successive vector is shifted with respect to the
previous one by the same angle. By continuing the vec -

tor addition indefinitely, as indicated in the lower
left, one can easily show that E2(13) in this case is a
sharply peaked function with maxims at = O, Zm, 411,...
and s. forth; E2(e) rapidly decreases and remains CIOSe
to zero for values of f3 only slightly different from O,
2n, 41r,... etc., as indicated in the vector diagram at
the lower center in Fig. 4.5c. Thus, in the vicinity
of its maxima, the Fabry-Perot interferometer is an extremely
sensitive position and length measuring device.
It is in fact, one of the most sensitive displacement
measuring devices available to modern science.
that are currently available, it is already possible to
construct relatively small-sized, highly-stable, and
quite rugged interferometric fiberoptic sensors that
are capable of withstanding the rigors of many fieldtype
applications.
Sketches outlining “all fiber” configurations
of the four different types of interferometers are
shown in Fig. 4.6. In the Mach-Zehnder fiberoptic in-
A) MICHELSON
A) MICHELSON, MACH-ZEHNDER AND SAGNAC
3dB COUPLER
B) FA6Ry-pEROT
El > ~
A
RELATIVE PHASE SHIFT (RADIANS)
=;:’’:;s
RTRANSDUCER
B) MACH-ZEHNDER
E’[@),
r
5’=i!4._-!=-!’=f
\
DISPLACEMENT- O.25 05 0.75 I MICRON
C) SAGNAC
LASER
El
DETECTOR
Fig. 4.5
4.1.2
The sensitivity of various typea of interferometers
as a function of relative phase
difference between two interfering lightwavea.
Fiberoptic Intenaity
Interferometer
Up to this point, the various interferometers
have been depicted aa they exist in the typical optics
laboratory, with air paths and lumped optical devices
such as beam splitters and mirrora. Their extremely
high displacement sensitivity has been used to measure
atrain and streas. In addition, they also have a very
high dynamic range. This will be brought out in more
detail in later discussion. If the many advantages
of the use of fiberoptic, electrooptics, and integrat -
ed-optics are added, one can conceive of configurations
and systems that are capable of revolutionizing sensor
technology.
By employing single-mode optical fibers for
the interferometer paths, the rather stringent limitation
on their length is immediately removed. Path
lengths of the order of a kilometer are easy to achieve
and are being used in practice. Extremely small, longlife,
solid-state laaers and detectors that are capable
of being used in hostile environments are becoming
available. Elements such as etched or lapped fiber-tofiber
couplers and their integrated-optic counterpart
are being developed and tested. By incorporating items
D) FABRY-PEROT
LASER - 1 !- DETECTOR
a
\: ‘/
PARTIAL TRANSMITTING MIRRORS
Fig. 4.6
The configuration of various types of fiberoptic
interferometera.
terferometer shown in Fig. 4.6b, the two beam splitters
are replaced with two etched or lapped 3-db couplers
that divide the laser output beam into two equal portions
and they also recombine the light that haa traversed
the two optical paths. It is possible to buttcouple
the laser output beam directly into the fiber
and to similarly couple the output fibers directly into
the two photodetectors. Thus, between aource and detectors,
the interferometera consiats only of fiber
elementa. By combining integrated circuit techniques
with current electrooptic capabilities, all of the other
elements, including the laser, detectors, and signal
processor, could be packaged in a single miniature chip
to which the fibers will be butt-coupled. Though the
device is not an off-the-shelf item today, there is
little doubt that they will be readily available in the
not too distant future.
4-3
4.1.3 Polarization in Fiberoptic Sensors
Earlier in this discussion of interferometers
it was mentioned, but not especially emphasized, that

the fiber interferometer should employ singlemode
fibers. In this case, the lightwaves injected into each
arm of the interferometer would propagate at a unique
velocity. In fact, the so-called singlemode fibers are
really at least two-mode fibers in the sense that there
are two different states of optical polarization that
can be propagated, i.e. the electric field vector can
be resolved into two mutually perpendicular component
that are perpendicular to the axis of the fiber. In
an ideal, straight, imperfection-free fiber with circular
symmetry, the propagation velocity is independent
of the direction of polarization. Polarized light injected
into such a fiber would maintain ita direction
of polarization. Thus, in an interferometer application,
one could have available two similarly polarized
optical beams that can produce the optimum interference
effects. That ia, if their intensities are equal, their
electric field vectora can interfere destructively and
thereby completely cancel. This can occur only for
beams of the same polarization.
The occurrence of such changes of polarization
may be observed in the laboratory in the following
situation. Referring to Fig. 4.8, imagine a beam of
linearly polarized light injected into an ellipticallycored
“two-mode” fiber in such a way that the input
energy is aplit equally between the HEIIX and HEIIY
modes. The modal velocities are different therefore
the polarization state will change continuously along
the length of the fiber, aa shown at the left in Fig.
4.8. The HEIIX and HE1lY modes are linearly polarized
along the X and Y axea, respectively, and at each position,
z, along the axis of the fiber the state of polariza~ion
is *determined by the time varying vector sum
of Ex and ‘Y”
Beginning at some point (a) where the
two modes are in phase, the polarization state will
change from linear polarization at (a) to circular
polarization at (b); back to linear at (c), rotated,
however, by 90” from its direction at (a); to circular
at (d), but in the opposite direction from that at (b);
back to linear at (e), just as at (a); and ao forth
down the length of the ”f~ber.
In reality, however, ideal fibers with perfect
symmetry do not exist. The complications that
this introduces can be illustrated by considering a
fiber with an elliptical core, as ahown in Fig. 4.7.
In this case, there will be two preferred direction
of polarization, those along the major and along the
minor axes of the elliptical croas section aa ahown by
a and b along the x and y axes in Fig. 4.7.
(a)
(b)
BEAT LENGTH L=;
OBSERVER
@(z) =(px–py)z=o
—
(c)
t Y
(d)
-------——-—-——- —— z
(e)
Fig. 4.7
I
\
x\
b optical fiber with an elliptical cross
section.
Linearly polarized light injected into the
fiber with its direction of polarization at some angle
other than along the x or y axes will propagate in two
aeparate.modea, the ao-called HE 11 and HE 11 modea,
that travel at alightly different velocitie ~ . Such a
fiber is aaid to have a modal birefringence, B, defined
by:
B= (~-~)x/211 (4.1)
where the two 6’s are the propagation constanta of the
two polarization modes and i is the wavelength in a
vacuum. Under this condition, the direction of polarization
will continuously change along the length of
the fiber. Even when light that is polarized along
one of the two major axes is injected into a fiber
there will be some coupling into the other mode due to
imperfections in the core-cladding interface, index of
refraction fluctuations, and other mechanisms. Thua,
both static and dynamic changes in polarization along
the length of the fiber may occur.
Fig. 4.8
The effecta of birefringence, 6, of polarized
light in an optical fiber.
In this situation, if the light intensity in
the core Is high enough so that the core-to-cladding
scattered light ia visible to the naked eye in a darkened
room, one may obaerve an apparent cyclic variation
in the intensity of the acattered light along the
length of the fiber, with the darker region being
spaced a distance, L, apart, as shown at the right in
Fig. 4.8. The darker regions correspond to aections of
the fiber from which only a small amount of light is
acattered towarda the eye of the obaerver. These correspond
to regions where the reaultant electric field
vector in the core ia parallel to the line of view, so
that, from a classical electromagnetic (E&M) viewpoint,
the radiation pattern of the oscillating electric vector
(dipole) has a minimum in this direction. As the
polarization state changea continuously in going from
(a) to (c) the component of the * vector perpendicular
to the line of view increases and, therefore, the
light scattered toward the viewer’s eye alao increas-
4-4
Due to a similar pro-
scattered light appears to decrease back to
in the section of fiber from (c) to (e).
es, reaching a maximum at (c).
cesa, the
a minimum
ponds to
2n radian
The distance, L, between two minima corresa
one wavelength relative shift, i.e., a
phase ahift, between the HEllx and the HEIIY

modes. Since at point (a) the two electric fields are
assumed to be in phase, the relative phase angle o (Az)
at some distance Az displaced from (a) la given by
O(AZ) = (Bx - BY)Az (4.2)
Thus at (b) ~ =m/2 and at (c) @c = II and ao forth. At
(e) where Az = L:
o(L) = 2T (4.3)
= (M-BY)L (4.4)
Earlier in Eq. (4.1) the birefringence, B, was defined
as:
B = (BX - BY)I(2TIA) (4.5)
So that for a two-mode fiber that has, at a given wavelength,
A, a birefringence, B, one obtaina:
L = h/B (4.6)
where L la defined as the beat length.
Over the distance, L, the polarization state
of light propagated in a two-mode fiber may pasa through
the entire cycle ahown at the left in 4.8. In terma of
this process there are some applications where it is
deairable to have a fiber with a long beat length, or
small birefringence, B, and others for which a short
beat length, or large birefringence, is preferable.
For example, in the deaign of an optical
fiber electric current aensor employing the Faraday effect
as the transduction mechanism, a relatively ahort
fiber element may be employed and a long beat length,
L, is preferable. When attempting to detect magnetically-induced
birefringence, any slight changes in a
large inherent birefringence, B, i.e., small L, might
maak the polarization changea induced by the magnetic
fielda associated with the electric current under measurement.
In certain applications of interferometrictype
sensora, “two-mode” fibers with high birefringence,
and short beat lengtha can be uaed to advantage. As
already indicated, the output beams from the two patha
of the interferometer not only must be equal in amplitude
but alao polarized in the same direction if they
are to totally cancel one another when they are out of
phaae by~ radians. In many interferometer sensor applications
fiber path lengtha of aeveral tens to aeveral
hundreds of metera are employed. It is irnpoaaible
to draw perfect fibers without variations and fluctuations
in core dimensions and refractive indices, and
without core-cladding interface ripplea. Therefore,
even when the direction of polarization of the injected
light la along one of the preferred axes in an elliptical
fiber, there will be at least random coupling due
to auch perturbations. Thus, as the propagation distance
increases, light originally in the HEIIX mode, ia
transferred into the HE1lY mnde. If the birefringence,
B, is different from zero, (even if it only fluctuates),
there will be some changes in the direction of polarization
and theae could reault in a reduction in the detection
sensitivity of the interferometer.
One method of improving detection sensitivity
is to employ fibers that have high birefringence and
short beat lengtha. In this case, due to the large difference
in the electric field profilea associated with
the HE1lX and HE ~y modes, the probability that a given
perturbation wil 1 cauae a transition between modea la
much lower than in the case of a fiber with amall birefringence,
B. In this senae, a high B fiber is a polarization-maintaining
fiber and therefore may be uaed to
advantage in Interferometric-type senaors.
One way in which a high-birefringence fiber
may be made is shown in Fig. 4.9. At the left an
~] (,3J)
/“n\
~cQER
IDEAL FIBER \ /
PREFORM
Fig. 4.9 The production of high birefringence optical
fibera.
idealized fiber having a rectangular core and cladding
structure is shown. Ita bimodal structure can be reprepresented
as the sum of two planar waveguide modes,
one where the height of the core croas section is the
determining factor and the other where the length of
the core croaa aection la the determining factor. These
modes would have substantially different propagation
constants and the B value would be large.
Several approaches have been taken to produce
fibers that approximate this ideal atructure. One
technique is shown at the center of Fig. 4.9. A preform
is produced consisting of a circular core and a
two-layered circular cladding. The dotted line in the
figure la the outline of its original outer circumference.
Large semi-circular segments of the outer cladding
along the length of the preform are removed aa
indicated and then two additional slots are cut to
expoae a section of the inner cladding. Thia element
is then heated until, under the action of surface tension,
it returns to a circular croaa section. The core
and inner cladding each aasume an elliptical ahape.
Fibera are then pulled from this modified preform. The
reaulting fibers have relatively large birefringence, B.
4.2 PHASE AND INTENSITY DETECTION
4.2.1 Phase Detection
As will be ahown, phaae modulation will be
converted to amplitude modulation prior to detection.
Thus, it is useful to first conaider the procesa involved
in amplitude modulation. An optical source input,
Iin, into an intensity-type aenaor la ahown in
Fig. 4.10. A graph of the optical input to the sensor
versus time is shown at the bottom left. In the aensor,
a baseband input signal, Sb, amplitude modulatea
the optical aource input, Iin, to produce the output
signal from the sensor aa ahown in the graph at the
bottom center. Finally, the amplitude-modulated optical
output signal from the aenaor is photodetected resulting
in an amplitude-modulated electrical output
aignal from the photodetector aa ahown at top and bottom
right of Fig. 4.10. Phaae modulation cannot be
directly detected due to the fact that the light frequency
is approximately 1014 Hz. Photodetectors are
unable to respond to such high frequencies, i.e., they
4-5

I
1
cannot follow the inatantaneoua valuea of such highfrequency
variations. Thus , in order to accomplish
phase detection, an interferometric technique must be
uaed to convert the phase modulation to amplitude modulation
prior to detection.
OPTICAL
SOURCE
IIN
sb
t
SENSOR
‘OUT
OPTICAL
DETECTOR
ikiki&
T IME TIME TIME
Fig. 4.10
‘OUT
Input-output relations in an intenaity-type
fiberoptic senaor.
The phaae angle, $, measured with reference
to the plane of entry into a fiber, of a lightwave of
wavelength A in a fiber of length L ia given by:
4 = 2nL/i = 2mIlL/lo (4.7)
where A. la the wavelength of light in vacuum and nl la
the refractive index of the fiber core. If L and X. are
expresaed in the same units, $ will be in radians. If
the fiber undergoes a change in length, AL, relative to
the fixed plane of entry, the phase angle at the end
plane of the fiber becomes:
$+A41=2ml(L+AL)/~ (4.8)
These two caaea are shown in Fig. 4.11. An assumption
is made here that the value of nl does not change
throughout the fiber during its change in length. While
this is not true, it will be approximately true in many
of the caaes to be considered later.
Consider the situation in which there are two
optical fibers, one located in each of the two arms of
an interferometer. A lightwave is simultaneously introduced
into the left ends of these two fibera, initially
of the same length or differing in length by an integral
multiple of 2TT rad. Assume the upper fiber in Fig.
4.11. is the reference fiber. Consider the case in
which the output of the two fibers is initially in phase
and when combined interfere constructively. If the
length of the lower fiber increases due to an applied
stress or a thermal change, the output intenaity of the
interferometer will decrease, reaching a minimum when
the length of the lower fiber haa increased by A/2,
i.e., T rad. At this point if the lower fiber continuea
to change, then the output amplitude will increase,
returning to ita maximum value when the length of the
lower fiber has increased by another i/2, i.e., m rad.
The reaulting current out of a photodetector placed at
the end of the fibera is shown in the upper curve of
Fig. 4.12. The ordinate is the photodetector current
lr
o+ZD‘--–-–– ‘- ‘MAX
:+
~~
SE
~ > .- –-– - - - - - - - - - - - TMIN
Ov
30 ~
Fig. 4.12
2% 37r
L+(RAOIANS)
A+4RAOIANS)
● PHASE DRIFT CAUSES PtiOTO -
DETECTOR CURRENT (i) TO VARY
❑ ETWEEN TM,N AND IMAX (FADING)
● PHASE SENSITIVITY -d,ld(A.$)
● MAXIMUM SENSITIVITY FOR
A+=V2 ,3v~
● V2 PHASE BIAS REIIJIREO FOR
MAXIMUM SENSITIVITY (QUADRATURE
CONDITION)
Photodetector output current and its derivative
resulting from lightwave phasechange
fiberoptic sensor output.
o
+0
t
FIBER
CORE
0
i
+=
?
27r LENGTH 2%nL
.— 1
WAVELENGTH A I
+0 -A++
++A~= —(L+ 2un AL)
A
Fig. 4.11 Phase change of a lightwave through an optical
fiber of original length L that has
been stretched by a length AL.
L
and the abscissa is the difference in phase between the
lightwaves in the two arms. This output ia typical of
the effect of a phaae drift (shift) aaaociated with the
return to thermal equilibrium following a step function
increase in temperature. In general, such oscillations
are undesirable especially when the signal being measured
produces phase changea many orders of magnitude
smaller. A case where such oscillations are a measure
of the signal being detected is described below.
A simple technique for meaauring the rate of
change of presaure for large presaure changes ia ahown
in Fig. 4.13. The sensing element consista of a length
of fiber, L, tightly (prestressed) wound on a mandrel
of a compliant material such aa Teflonc. The pressure
may be applied either to the outside of the fibermandrel
combination or, for the caae of a hollow mandrel
to the inside. Aa the length of fiber in the senaing
arm changes the output of the photodetector will
sweep through maxima and minima as ahown by the upper
curve in Fig. 4.12. The time rate of change of pressure
can be related to the frequency of oscillation in a
atraight forward manner. The number of oscillations per
unit time is proportional to the change in fiber length
per unit time, where the change in length is expreased
4-6

as a number of wavelengths. An expression for the frequency
can therefore be obtained by dividing the change
in the fiber length per unit time by the wavelength of
light. This is given by the expression:
Where lo/nl
f= (nl/Ao)(dL/dt) (4.9)
is the wavelength in the fiber core.
From the expression for the volume of the
mandrel, V = rr2D, it follows that:
~V/V = 2Ar/r + AD/D (4.10)
where r and D are the radius and length of the mandrel
respectively. For hydrostatic pressure AD/D . ~r/r and
Eq. (4.10) becomes:
The compreaaibility,
can be written:
AV/V = 3Ar/r. (4.11)
K = (1/V)(dV/dP), of the mandrel
K = (3/r)(dr/dP). (4.12)
Since for a compliant mandrel, the change in fiber
length is cauaed primarily by the change in r, where
L = 2nNr, it follows that:
to 5 x 104 atmoslsec). Assuming the maximum counting
error is one cycle, the maximum error will range from
1% at the loweat rate of change to 10-4% at the highest.
The time rate of change of pressure versus frequency
is given in Fig. 4.14 for various lengths of fiber.
For lengths as short aa 0.1 m a significant error
will ariae due to the uncertainty in the number of
turns. This source of error will decrease as the number
of turna increases.
LASER
BC
n
PRESSURE APPLIED
TO MANDRELTO
CHANGE THE
LENGTH OF FIBER
I
RSENSOR
59 ‘ANDRE’
1!BC
L# u PHOTODETECTORS
)
(1/L)(dL/dp) = (1/r)(dr/dP) (4.13)
and substituting Eq. (4.13) into Eq. (4.12) yields:
Letting:
K = (3/L)(dL/dP). (4.14)
Fig. 4.13
A homodyne Mach-Zehnder-type interferometer
detection aystem.
in Eq.
dL/dP = (dL/dt)(dt/dP) (4.15)
(4.14) and solving for (dP/dt) results in:
,.3
dP/dt = (LK/3)/(dL/dt). (4.16)
Finally, substituting Eq. (4.9) into Eq. (4.16) yielda
the deaired expression for the time rate of change of
pressure in terms of the frequency of oacillationa:
~
co
,.2 -
dPldt = (3Ao/KLnl)f. (4.17)
The quantity on the right multiplying f is the acale
factor. Since the length of fiber, L, is very much
greater than the expected change in length, the scale
factor remains approximately constant. (A stress of
100 Kpsi is required to produce a one percent change in
fiber length.) For large changea in pressure the values
of Kand nl also vary, but in oppoaite directions. The
scale factor in Eq. (4.17) can be changed by employing
a mandrel exhibiting a different sensitivity. In general,
however, the largest changea in acale factor can
be accomplished by changing the length of fiber. Care
must be taken to inaure that the mandrel doea not exhibit
resonant frequencies which are excited by transients
associated with the time rate of change of pressure.
Such resonances may constitute the upper limit
of measurements.
Choosing ~
Si02, and for Teflon?
= 0.85 X 10
K .3.6 x ;:-iT’cm3)d;:”;;e&
dP/dt = 4.85 x 105 f/L (pascala/aec). (4.18)
l%us for 1 m < L < 100 m and 100 Hz < f < 10 kHz, the
time rate of change of pressure detected will vary between
5 x 105 palaec and 5 x 109 pa/see (5 atmos/sec
~
~
= 100 -
a
v
1(J’
Icrz
,.2
103 104
OUTPUT FREQUENCY (Iiz)
Fig. 4.14 Relation between time rate of change of
pressure and frequency for varioua lengths
of optical fiber.
The above derivation assumed hydrostatic
pressure. Thua, the change in preasure acrosa the sensor
muat be smell compared to the rate of change being
measured. For a senaor whose dimension along the direction
of propagation ia 3 cm, and assuming the velocity
of propagation for sound at high pressure or for a shock
wave to be 3000 mlaec, the pressure differential acroas
the sensing element will be 0.5 atmos, or one part in
105 of the pressure change being measured.
4-7

Next consider the other extreme: the detection
of changes in length (or more exactly, phase) very
much smaller than a wavelength, such as 10-6 radians.
Any large amplitude drift (change) greatly increases
the difficulty of measuring small changes. The signal
to be considered will appear as a small amplitude perturbation
as was shown on the upper curve in Fig. 4.15.
The sensitivity to phase changes varies as the slope
of this curve. Thus, the lower curve, obtained by taking
the derivative of the photodetector output with
respect to$ is the phase sensitivity for amall amplitude
changes. The maximum sensitivity occurs for odd
multiples of T/2 while zero sensitivity occurs for even
multiples of n/2. This is shown in Fig. 4.15. Here the
photodiode current is plotted against the bias (phase)
angle. In order to demonstrate the sensitivity, a cw
(sinusoidal) signal of amplitude ~ 10” (electrical degrees)
is superimposed about a bias (quiescent or op-
+
5
K
lx
a
U
8
s
6
1
L
I
I
I
----=-.—.—
I >\
PHASE VARIATION
I
-20 0 20 40 60 80
BIAS ANGLE(”)
CURRENT OUT
II
Fig. 4.15 Sensitivity of fiberoptic
at O“ and 90° bias angle.
100 120 140
homodyne sensor
crating) point at O“ and at 90”. The amplitude of the
resulting output current is obtained by projecting the
phase oscillation (input signal) upward on to the solid
curve graphically and plotting the resulting output current
about a horizontal line as is normally done graphically
with any transfer function. At 90° the resulting
current is large and of the same frequency as the input
signal. At O“ bias however the amplitude of the photodetector
current is small and exhibits a frequency twice
the excitation frequency because oscillation is on both
sides of the maximum. Thus, consider such a signal initially
at the 90” bias point. Now for the magnitude of
input signal shown in Fig. 4.15, if the 90” relative
phase between the two arms of the interferometer drifts
toward the 0° point, the amplitude of the photodetector
current would decrease, and at leas than 10° biaa a
second harmonic would appear. The current amplitude
would become minimum at 0° bias at which point the fundamental
component will have become zero with only a
small second harmonic left. This process is referred to
as fading. The 90” bias condition is known as quadrature.
l%is mode of detection is called homodyne detection.
4.2.2 Homodyne Detection Applications
As pointed out in the discussion above, homodyne
detection requires quadrature operation and in addition
some means of compensating for large amplitude
4-8
drift. In addition laser noise reduction will be shown
to be necessary.
A schematic of the Mach-Zehnder fiberoptic
interferometer using phase-locked homodyne detection is
shown in Fig. 4.16. The light in the laser beam is
3dS COUPLER
REFERENCE ARM
SENSING ARM
/
OUTPUT HIGH PASS
-SIGNAL
SIGNAL“4+ F ILT ER $p
K(
LOW PASS
I
SIGNAL & NOISE
FILTER
3CU3COUPLER
Fig. 4.16
AMPLIFIER
& SUMMER
ePHOTODIODES
A Mach-Zehnder fiberoptic interferometer
employing phase-locked homodyne detection.
split by the 3-dB coupler into the two arms of the interferometer.
The arm on the right is taken to be the
signal arm and the arm on the left is taken to be the
reference arm. The latter contains the phase shifter
described below. The light through the two arms is recombined
by the lower 3-dB coupler that converts the
phase modulation to an intensity modulation. The two
optical outputs of the 3-dB coupler are each photodetected.
The electrical outputs of the two photodetectors
are fed into a differential amplifier. It in turn
feeds the compensator circuit. The compensator circuit
provides an output signal, the signal required for the
phase shifter, and a reset signal. A detailed discussion
is given in the next subsection.
There are many types of laser noise, such as
phase noise, amplitude noise, and noise due to multimode
and satellite mode operation. This is especially
important when the source is a diode laser that is
closely coupled to a fiber.
4.2.3 Phase Noise
The output noise of the interferometer in dBV
as a function of path length difference between the two
arms of the interferometer expressed in millimeters is
shown in Fig. 4.17. The system noise determines the
minimum detectable phaae shift. The minimum detectable
phase shift, measured in a 1 Hz bandwidth, is shown
plotted in radians using the ordinate scale on the
right in Fig. 4.17 (see Ref. 1 in Subsection 4.2.8).
Experimental data is given for 50 Hz, 500 Hz and 2 kHz.
The interferometer was operated in quadrature. On the
log acales used, a straight line plot of decreasing
noise at each frequency is obtained as the path length
is reduced. Notice that varying the path length from 1
mm to 1000 mm, that is, to 1 meter, results in a 60 dB
increase in output noise. The curves shown terminate
at a 1 mm path-length difference, but data points corresponding
to a 0.1 mm path difference are shown for
all 3 frequencies. As can be seen, little further reduction
in output noiae is achieved by decreasing the
path-length difference from 1 to 0.1 mm. Thus, if the
arms of the interferometer are matched to within 1 mm,
phase shifts of 10-6 radians can be detected at 2 kHz.
Attempts at reducing the path length difference to less
than 1 mm would be futile. This is due to the fact that
for an interferometer whose arms contain as much as a

100 meters of fiber, length changes on the order of 0.1
mm can be expected as a result of changes in temperature,
presaure, tension, and other environmental conditions.
Thus, the fluctuation in laser optical output amplitude
is eliminated. The subtraction is actually accomplished
electrically in the differential amplifier following
the photodetector as was shown in Fig. 4.7.
Experimental verification of common mode rejection
is shown in Fig. 4.18 (see Ref. 2 in Subsection
6-
a
II
~ 10.0 ~
k
OUTPUT FROM ONE PORT
F
m
u
(n
u 1.0 -
I
L
w
d
a
01 -
!3 OUTPUT OF BOTH PORTS
u
USING COMMON-MODE REJECTION /
h
a
I
I
01 1 10 100 1000
PATH LENGTH DIFFERENCE (mm)
Fig. 4.17 Variation of homodyne interferometer output
noise as a function of sensing arm path
length difference for several output frequencies.
After A. Dandridge, et al., Appl. Phys. Lett. ~, 77
(1981)
4.2.4 Amplitude Noise
Common mode rejection refers to a method for
the elimination of laser amplitude noise. Expressions
for the optical intensity at the two output ports of
the lower 3-dB coupler that was shown in Fig. 4.16 are:
and
11 = (1/2)(1 + ~sin~st) (4.19)
12 = (1/2)(1 - ~sinust) (4.20)
where I is the output optical intensity (power) of the
laser minus the various insertion and fiber absorption
losses. Aa is the amplitude of the phase shift produced
by a signal of angular frequency us. Conservation
of energy dictates the plus and minus signs in Eqs.
(4.19) and (4.20) respectively. Summing Eqs. (4.19)
and (4.20) yields I as required. Multiplying Eqs. (4.19)
and (4.20) by 1 + AI/I where AI/I is an amplitude fluctuation
whose ma nitude is the same order of magnitude
as As, e.g. 10 -5 or 10-6, yields:
and
211 = I + AI + IAssinost (4.21)
212 = I + AI - IAssin@st (4.22)
where higher order terms in the infinitesimals AI/I and
As are neglected. Subtracting Eq. (4.22) fromEq. (4.21)
results in the expression:
11 - 12 = IA a
sinost (4.23)
4-9
Fig. 4.18 Minimum detectable phase shift versus fre -
quency in a fiberoptic homodyne interferometric
sensor using common-mode rejection
of laser amplitude noise.
After Dandridge and Tveten, Appl. Phys. Lett. ~, 2337
(1981).
4.2.8). The minimum detectable phase shift, expressed in
microradians, is plotted versus frequency. The squares
represent the output from a single port of the interferometer.
The solid line is the average of these points.
The circles are the data obtained when the output from
both of the ports of the interferometer are detected
and the different signals taken. By comparing these
results it is seen that an order of magnitude decrease
in the minimum detectable phase shift is achieved at
low frequency. At frequencies above 1 kHz a minimum detectable
phase shift of 0.1 urad (10-7 radians) is accomplished.
This is representative of the kind of sensitivity
that canbe achieved when common mode rejection
is employed and the arms of the interferometer are
matched to within 1 mm as was the case in this experiment.
Laser noise due to satellite modes and multimode
operation was also eliminated.
4.2.5 Satellite Modea and Multimode Operation
The influence of various amounts of optical
feedback on the modal output of a Hitachic HLP 1400
diode laser is shown by the output spectrum of the
laser plotted for varioua conditions of optical feedback
as shown in Fig. 4.19 (see Ref. 3 in Subsection
4.2.8). Spectrum (a) is for the free running laser with
a spectral width of 5 MHz. The spectra (b), (c), and
(d) illustrate the effect of increasing amounts of feedback
(from 0.04% to 1.5%). Notice that for spectra (b)
and (c) the horizontal scale remains the same (i.e.,
from -0.2 to +0.2 A) but for spectrum (d) the scale has
changed, going from -6.0 to +6.0 A. The second and
third curves correspond to 0.04% and 0.06% feedback.
Here satellite modes appear and increaae as the amount
of feedback increases. Such satellite modes arise as
the result of coupling two resonant cavities: one the
laser itself and the other the resonant cavity formed
by the length of fiber from the laser to the primary
reflection. Effects due to optical feedbacks of up to
0.06% are eliminated when the interferometer lengths
are matched to within lmm.

(a)
&
A
FREE RUNNING
Av = 5MHZ
(c)
(b)
11
I
u
0.2 0 0.2 0.2 0 0.2
A
A
SATELLITE MODES
Av = 0.02GHz Av= .12GHz
0.04% 0.06%
FEEDBACK FEEDBACK
(
606
A
MULTIMODES
Av = 5GHZ
1.5%
FEEDBACK
Fig. 4.19 Influence of optical feedback on the modal
output of a Hitachi HLP 1400 diode laser.
Adapted from R. Miles et al., Appl. Phys. Lett. ~,
990 (1980).
Spectrum (d) shows the effect of 1.5% feedback.
Multimode laser operation results. In order to
eliminate this effect, the back reflections into the
laser must be maintained below approximately 0.06%.
This is achievable with care. To accomplish this, it
is necessary to assure that reflections from the end
of the fiber are avoided. This requires the use of
index-matching liquid between the laser and the fiber
and furthermore the end of the fiber must be cut at a
slight angle. All splices and couplers have to be
carefully fabricated in order to reduce insertion loss.
In the discussion of connections, it was shown that
fiber misalignment would lead to insertion loss. These
same misalignments will also lead to undesirable reflections.
4.2.6 Phase-Locked Loop Operation
The circuitry required to provide and insure
quadrature operation in the presence of low frequency
drift is shown schematically in Fig. 4.20 (see Ref. 4
Fig. 4.20
TWO STAGE INTEGRATOR,
UNBIASED
AMPLIFIER.
PHOTODIODES
CIRCUIT
RESET
KO
M
/)+“+ \
/ I
TO PZT PHASE SHIFTER
J L 1
-
w /
AMPLIFIER, HIGH PASS
/
..,FILTER. CUT OFFAT
KD
DIFFERENTIAL
LOW FREQUENCY
AMPLIFIER FOR
LIMIT OF SIGNAL RANGE
COMMON MODE
REJECTION
A phase-locked loop
Cuit.
t
BANDPASS
OUTPUT
homodyne detection cirin
Subsection 4.2.8). TWO photodiodea are shown on the
left. The photodiodes are operated in an unbiased condition
in order to eliminate dark current noise. Their
outputs are combined in a differential amplifier that
provides common-mode rejection as well as amplification.
This is followed by two stages of integration
that provide additional amplification. These two integrator-amplifiers
pass all signals from DC up to the
higheat frequency of interest. The output of the two
stage integrator-amplifier is applied to a phase shifter
located in the reference arm of. the interferometer.
The phase shifter consists of either a lead zirconatelead
titanate (PZT) cylinder around which the fiber in
the reference arm is rather tightly wound or a section
of polyvinylidene-floride (PVDF)-jacketed fiber. Both
PZT and PVDF are piezoelectric materials. The output
of the integrator-amplifier is just equal to the low
frequency noise and the signal of interest. The effect
then is to produce a phase ahift in the reference arm
equal to that in the sensing anm, causing the interferometer
to remain balanced, i.e., to phase-lock the system.
If the phase were exactly locked there would be
no output signal from the interferometer. However,
there must be an error signal at the photodetectors in
order to have a feedback signal. The amplification in
the feedback circuit thus increaaes the error signal
from the interferometer back up to the level of the
signal being detected. If the system is initially at
a bias (operating or quiescent) point away from quadrature
there is insuffient output from the interferometer
for the compensation circuit and the system till tend
to drift toward an increasing error signal and therefore
toward quadrature.
The signal out of the compensating circuit is
alao fed through a high-pass filter that has its low
frequency limit set at the lowest frequency of interest.
Therefore, the resulting output is a band of frequencies
corresponding to the frequency range of interest.
This constitutes the output of the interferometric sensor.
Operational amplifiers (OPAMPS) are used in
the feedback circuit and combined metal oxide semiconductor
(CMOS) components in the reset circuit. The
levels of voltage that can be applied by these circuits
to the phase shifter are the order of + 10 volts. On
the other hand, the range that the ph~se shifter can
accommodate ia hundreds or thousands of volts. Furthermore,
in many cases the amplitude of the phase drift
resulting from temperatuze or pressure changes is much
larger than the phase shift that would be generated by
applying ~ 10 volts to the phase shifter. Thus, it is
necesaary to keep track of how much voltage has been
applied to the phase shifter and if the limit of the
circuit begins to be reached it is necessary to rapidly
reset the circuits back to the initial condition from
which point it can start over. This is the purpose of
the reset circuit indicated in Fig. 4.20. The phaae
change associated with a large amplitude slow drift is
compensated by a number of saw toothed-like amall amplitude
phase changes. Care must be taken to minimize the
noise introduced during the reset process.
The upper frequency at which a measurement
can be made is limited by the resonant frequency in the
phase shifter itself. Phase-locked loop homodyne detection
is particularly useful for frequencies below
10 kHz. On the other hand, for casea where it is desired
to make measurements at higher frequencies, say
from a few kHz up to nearly a megahertz, heterodyne
detection may be desirable.
4.2.7 Heterodyne Detection
Heterodyne detection is relatively insensi -
tive to optical intensity fluctuations and low frequen-
4-10

the aingle-sideband phaae noiae intercepts the 120 dB
level at about 1 kHz. The acoustooptic modulator drive
requirement is approximately +33 dBm. Asauming an output
of +10 dBm from the oscillator the amplifier shown
must provide 23 dBm of gain.
Fig. 4.21
cy noise. Phase trackers and the associated circuits
are not required. An interferometer employing heterodyne
detection is ahown in Fig. 4.21. The aystem difr
UJO+
SolMHz
aLINEARFM
DISCRIMINATOR
‘A
OU;PUT
A interferornetric fiberoptic senaor employing
heterodyne detection.
fers from the usual heterodyne syatem in that uae is
made of two Bragg cells. The firat cell also serves
as a 3-dB coupler. By placing a star coupler (or plaited
3-dB fiber coupler) at points A and B it should be
possible for a single diode laser and one pair of Bragg
cells to serve as the optical source for several dozen
aenaors. For the Bragg frequencies indicated in Fig.
4.21, bulk Bragg cells are required. In thia caae GRIN
rods must be used to focus the light in and out of the
fiber. If surface acoustic wave (SAW) Bragg cella are
employed, they must be operated at approximately 600
klllz (with a difference of 100 kHz). If the lowest signal
frequency of interest is fs, the oscillator must
exhibit phase noise less than -120 dB/Hz at an offset
of fs from the carrier frequency. The plot of single
sideband phase noise versus displacement from the carrier
frequency for two oscillators is shown in Fig.
4.22. The curve that corresponds to 600 MHz shows that
5
u -70
u
~ -80
$1
-90
w
~ -1oo
z -110
n
z -120
<
flj -130
Q
m -140
y -150
60-100 MHz
a ~ -160
m
I
1 , ! !
101 102
,03 ,04
105
,.6
FREQUENCY REMOVED FROM CARRIER
Fig. 4.22 Typical single-sideband phaae noise measured
relative to the carrier in a 1 Hz bandwidth
in a fiberoptic interferornetric
heterodyne sensor using fixed-frequency
crystal osallators as shown in Fig. 4.12.
4-11
The maximum optical power that a channel waveguide
will handle is about 120 uW. One pair of Bragg
modulators configured as shown in Fig 4.21 could supply
several sensors. However, with only 120 pW into the
first Bragg cell it would not be possible to provide
sufficient optical intensity to the detectors to insure
quantum-limited operation for more than four sensors.
Thua, for the operation of several dozen senaors from a
aingle laser and one pair of bulk Bragg cells, heterodyne
detection must be uaed.
The difference frequency constitutes a heterodyne
frequency of 100 kHz for the heterodyne detection
configuration shown in Fig. 4.21. This permits the use
of low-frequency, low-noise electronic circuits, such
as low-noise amplifiers and FM discriminators. Since
heterodyne detection is relatively insensitive to optical
intensity fluctuation and low frequency noise,
phase tracker circuits are not required. As in the
case of homodyne detection, there may be a need for
polarization-preserving fiber in order to prevent signal
loss. Also, Bragg cells that are highly atable relative
to each other, are required. Finally, in heterodyne
detection, aa in homodyne detection, optical feedback
into the diode laser greatly increases the laaer
noise. Thus it is necessary to employ the aame precautions
as were indicated above for homodyne detection.
A number of other detection schemes have been
suggested and are currently being considered. These
include simple homodyning employing a 3 x 3 coupler in
place of the input coupler (see Ref. 5 in Subsection
4.2.8). It can be ahown that this resulta in an operating
condition very close to quadrature. Synthetic
heterodyne operation is another. A high frequency dither
is employed on the phase stretcher. The output of
such an interferometer can be shown to exhibit the characteristics
of a heterodyne system.
In view of the significant effort being applied
to the detection problem further improvements can
be expected; however, such effort la also an indication
that the optimal detection acheme haa not been achieved.
Numerous trade-offs are required. Theae include frequency
range, sensitivity, dynamic range, cost, and complexity
of the detection circuitry.
4.2.8 References
1.
2.
3.
4.
5.
A. Dandridge, A. Tveten, R. Miles, D. Jackson, and
T. Giallorenzi, “Single-Mode Diode Laser Phaae
Noise”, Appl. Phya. Lett. — 38, 77 (1981).
A. Dandridge and A. Tveten, “Noise Reduction in
Fiber-Optic Interferometer Systems”, Appl. Opt.
20-, 2337 (1981).
R. Miles, A. Dandridge, A. Tveten, H. Taylor, and
T. Giallorenzi, “Feedback-Induced Line Broadening
in Cw Channel-Substrate Planar Laser Diodes”, Appl.
Physica. Lett. — 37, 990 (1980).
K. Fritsch and G. Adamovsky, “Simple Circuit for
Feedback Stabilization of a Singlemode Optical
Fiber Interferometer”, Rev. Sci. Instrum. ~, 996
(1981).
S. Sheem, “Fiber-Optic Gyroscope with [3x3] Directional
Coupler”, Appl. Phys. Lett. 37, 869 (1980). —

4.3 INTEGRATED OPTICAL CIRCUITS (IOCS)
The optical counterpart of the field of integrated
electronics is the field of integrated optics.
However, though integrated optical circuita have been
made, they are for the moat part not commercially
available. They are the subject of extensive research
and development efforta at a large number of laboratories.
The goal of these efforts is to commercially fabricate
in large quantities these miniaturized devices
with interconnected waveguides all on a single substrate.
The generation, detection, propagation, modulation,
switching, and coupling of light on such substrates
have been accomplished. Techniques for the
fabrication of substrates and the production of the
high resolution material distribution patterns required
for these integrated optical circuits exist. Most
integrated optical circuits and associated devicea
operate in a singlemode, therefore they are compatible
with singlemode optical fibers. In essence most LEDs,
diode lasers, and photodiodea are integrated optic
devices. Integrated optical circuits are considered
here because they are a part of second generation fiberoptic
sensor technology.
The waveguides used in integrated optical
circuits are usually of two types namely planar films,
that confine the light wavea in the vertical direction,
and planar strips, (channels) that confine lightwaves
in two dimensions. In both caaea, the waveguides are
made of a higher refractive index than the surrounding
material. Light is trapped in the layer or channel in
much the same way that it is trapped in the core of an
optical fiber. These planar waveguides can be formed
by sputtering glass on a substrate of lower refractive
index. A very uaeful type of channel waveguide can be
formed by evaporating titanium (Ti) onto lithium niobate
(LiNb03) or lithium tantalate in the desired
waveguide patterns, and diffusing the Ti into the aubstrate
thus forming a channel of higher refractive index.
This is shown in Fig. 4.23. The attenuation in
“’’”’””-r
LiNb03
SUBSTRATE
“1
OPTICAL
n2
CHANNEL&
nl>nz
Si02_
ELECTRODES—
Fig. 4.23
n1>n2>n3
(A) TITANIUM STRIP
ON LiNb03
SUBSTRATE
(B) TITANIUM DIFFUSEDAT
HIGH T INTO SUBSTRATE
FORMING CHANNEL
WAVEGUIDE
(C) PROTECTIVE LAYEROF
Si02 SPUTTERED
ON SURFACE
(D) ELECTRODES APPLIED
Steps in the fabrication of a channel waveguide.
auch channels is typically 1 dB/cm. A protective layer
of silicon dioxide (Si02) ia often sputtered on top in
order to protect the surface. Electrodes may be deposited
on the Si02.
Coupling a fiber to an integrated optic channel
has been accomplished as shown in Fig. 4.24. The
1 v “’SILICON
SINGLE-MODE FIBEti
IN ALIGNMENT
V-GROOVES IN SILICON
Fig. 4.24
An optical fiber pigtailed to a lithium
niobate (LiNb03) fiberoptic chip.
fiber is aligned and epoxied in an etched silicon (Si)
V-groove. The fiber end and the Si edge are polished
and butted against the polished edge of LiNb03. Indexmatching
liquid is used between the fiber and substrate
ends. Similar techniques are uaed to couple diode
lasers and photodetectors to the substrate. The dimensions
of channel waveguides are close to those of both
ainglemode fiber corea and the radiating areas of stripe
geometry diode lasers. For stripe geometry, the long
dimension of the channel should be oriented perpendicular
to the long dimension of the radiating area of the
diode. Insertion leases as low as a few dB can be
achieved.
Channel-to-channel couplers can be formed on
the integrated optical circuit aubstrate by paralleling
two channels in cloae proximity to each other for a
sufficient distance to achieve the desired coupling
ratio. The coupling length is defined as the distance
required for complete power transfer to occur. The
length required to achieve a apecified coupling ratio
depends on the separation between channels and the refractive
indices of the channels and subatrate. The
refractive index of LiNb03 ia a linear function of the
applied electric field. This is known aa the Pockels
effect. Thus, if electrodes are applied as shown in
Fig. 4.25, the refractive index can be varied and the
light can be awitched to the other of the two output
ports of the coupler. The direction of the electric
field is oriented oppositely in the two channels resulting
in equal and opposite refractive index changes.
When the proper value of voltage is applied, the coupling
length is made ahorter and the light will exit from
the same fiber it entered. When the voltage is not applied,
the coupling length is longer and the light will
emerge from both ports. The exit channels from this
switch may be combined to form the Mach-Zehnder interferometer
shown in Fig. 4.26. The result is an electrooptic
intensity modulator. When the light wavea recombine
they excite the fundamental mode of the exit channel.
When they arrive out of phase they tend to excite
the aecond mode but the second mode can’t propagate in
the singlemode channel, therefore it radiatea.
An acoustooptic modulator (Bragg Cell) is
ahown in Fig. 4.27. The interdigited ultrasonic transducer
is shown at the bottom. The surface acoustic wave
4-12

sets up periodic spatial fluctuations in the refractive
index of the waveguide. These act as phase gratings
deflecting a portion of the lightwave incident perpendicular
to the resulting grating. The lightwave that
passes straight through the grating exits with its frequency
unchanged, while the diffracted ray has its frequency
shifted by an amount equal to the acoustic frequency,
e.g., 500 MHz. Such Bragg cells can be used
for optical heterodyning.
nl—An
n, +dn
+ l-l+
ACOUSTIC ABSORBER
I
FREQUENCY
SHIFTED BEAM
ACOUSTIC
SURFACE WAVE —–—=
-—
LIGHT
.
INCIDENT——
UNDIFFRACTED
/’ /
BEAM
OPTICAL FIBER
/’
INTERDIGITED
CHANNEL / ‘ E3-- TRANSDUCER
WAVEGUIDE
ACOUSTIC ABSORBER
ELECTRODES ( n.
> LiNb03
+h - , , /s.BsTRATE
Fig. 4.27
A Bragg cell integrated acoustic modulator
in which an interdigital transducer is used
for frequency shifting in accordance with
an electrical input signal that develops an
ultrasonic wave in a bifurcated optical
waveguide.
Fig. 4.25
INCIDENT BEAMJ
WAVEGUIDE
A Pockels effect electrooptic binary switch
mounted on a lithium miobate substrate.
Technology exists for integrating an array of
channel couplers connected to an array of photodiodes
with charge-coupled device readout all on a single substrate.
Using flip-chip techniques (mounting the chip
face down) multiple fiber pigtails can be attached to
a single chip. Such integrated devices promise to significantly
reduce the size and cost of arrays of optical
sensors.
A
MODULATED LIGHT OUT
,-
OP
POLARIZ
Fig. 4.26
A Mach-Zehnder interferornetric electrooptic
intensity modulator mounted on a lithium
niobate (LiNb03) substrate chip.
4-13

CHAPTER 5
FIBEROPTIC SENSORS AND COMPONENTS
5.1 PHASE MODULATED FIBEROPTIC SENSORS
5.1.1 General
A large variety of phase-modulated fiberoptic
sensors have been demonstrated, including acoustic,
electric, magnetic, rate of rotation, acceleration,
electric current, trace vapor, pressure, and temperature
sensors. They are being applied to hydrophores,
magnetometers, gyroscopes, accelerometers, and other
devices. These devices exhibit numerous advantages,
the most important of which are geometric flexibility,
immunity to electromagnetic interference (EMI) and
electromagnetic pulses (EMP), large bandwidth, and
great sensitivity i.e., ability to detect extremely low
signal levels and small signal level changes. Phase
shifts as small as 10-7 radians have been detected (See
Ref. 1 in Subsection 5.1.7 at the end of this section).
For a wavelength of 0.83 microns, this is equivalent to
a length of approximately 10-14 meters, corresponding
to the size of an atomic nucleus. Transduction, i.e.
phase shifting, occurs as a lightwave travels throughout
the sensing length of the optical fiber. Coherent
light sources, singlemode fiber, and relatively complex
optical and electronic circuitry are required.
Consider
shown in Fig. 5.1.
LASER
that have traveled independently through the two arms
are recombined by a second 3-dB coupler that converts
the phase-modulation to an intensity-modulation. The
amplifiers and summing circuits combine the electrical
signals from the photodiodes, one for each of the two
output optical ports from the 3-dB coupler, in such a
manner as to reject common mode noise, e.g., laser
amplitude fluctuations. An integrator completes the
phase-locked loop. The output signal is filtered to
eliminate low frequency noise. In an alternate arrangement,
both arms of the interferometer have a portion
that is sensitive to the field being measured.
These portions are spatially separated and therefore
the combination is sensitive to the gradient of the
field being measured. Using a homodyne detection
scheme in a phase-locked loop configuration, phase
shifts as small as 10-7 radians have been measured at
frequencies above 1 kHz. The phase shifter in the reference
arm is used as part of the phase-locked loop. The
phase shifter can be fabricated by winding the fiber
around a PZT stretcher or by applying a piezopolymer
jacket on part of the fiber. In either case, the output
of the amplifier/integrator circuit is applied to the
phase shifter causing a phase modulation in the reference
arm of the interferometer equal to that in the
sensing arm. With this arrangement, the phase relation
between the two arms of the interferometer is locked
at the point of maximum sensitivity. This is known as
quadrature operation.
Various fiberoptic sensnr configurations are
shown in Fig. 5.2. A planar arrangement is shown in
Fig. 5.1
the Mach-Zehnder interferometer
Phase-locked loop homodyne detecm“:oDEs
A phase-locked loop Mach-Zehnder-type homodyne-detection
interferometer that cnnverts
phase modulation to intensity (amplitude)
modulation.
tion, which is especially
between 10 Hz and 20kHz, is
mode fiber-ui~tailed diode
suitable for frequencies
shown. Light from a singlelaser
is divided eaually
between the” ~ms of the interferometer using a ‘solid
state 3-dB fiber coupler. The sensing portion of the
sensor arm is designed to respond to the field to be
measured while the remainder of the sensing and reference
arms are insensitive. The two beams of light
Fig. 5.2
SPATIAL SHADING
aGRADlENT
Optical fiber configurations used in fiberoptic
sensors.
the upper left. The linear array of spiral wound sensors
in the lower left is suitable for beam forming.
A spatially shaded element, such as in the upper right,
where the spacings between windings vary according to
a Gaussian distribution, possess a beam pattern exhibiting
greatly reduced side lobes. Finally, the grad-
5-1

ient configuration in the lower right is produced by
utilizing both arms of the interferometer aa spatially
separated sensors.
5.1.2 Fiberoptic Acoustic Sensors
5.1.2.1 Acoustic Pressure Sensors
Extending the discussion for an acoustic sensor
in Subsection 4.2.1 and considering Eqa. (4.7) and
(4.8), the pressure variations associated with a sound
wave produce phase fluctuations given by:
A$ = kA(nL) = k(nAL + LAn) (5.1)
is more nearly valid. Thus, the phase of a lightwave
in Hytrelc-jacketed optical fiber, where the croas sectional
area of the Hytrelc is much greater than that
of the fused silica, responds to pressure according to
the Hytrelc compressibility. While the results shown
in Fig. 5.3 are for jacketed optical fibers, similar
results are obtained when bare optical fiber is wound
tightly on a Hytrelc or similar mandrel. In either
case, the more compressible plastic (either jacket
or mandrel), when subjected to fluctuating pressure,
carries (atretches or compresses) the optical fiber
along with it.
A$ = kL(nAL/L + An) (5.2)
where AL/L is the axial strain, S11; k is the wave num -
ber; n is the refractive index of the core; and An is
given by:
An = -(n3/2)[(Pll + P12)S12 + P12S11] (5.3)
where Pll and P12 are the Pockel’s coefficients and S12
is the radial strain. A constant volume assumption
yields the relation S12 = -S11/2. This assumption is
valid only for a material whose Poisson’s ratio is close
to 0.5. It is also quite good for the polyester jacket
material Hytrelc, but not as good for fused silica.
These materials exhibit values of Poisson’s ratio equal
to 0.483 and 0.17 respectively. More exact treatments
sre given in Refs. 2, 3, and 4 in Subsection 5.1.7.
Substituting these relations into Eq. (5.3) yields:
A$ = kLn[l+(n2/4)(Pll - p12)]Sll (5.4)
In fused silica Pll = 0.12, P12 = 0.27 and n = 1.46.
Substituting into Eq. (5.4) results in:
A$ = 0.92kLnSll (5.5)
For an isotropic material:
AL/L = Av/3v :(1/3V)(~V/aP)AP (5.6)
where AL/L = S11 is the axial strain, V iS the volume,
P is the applied pressure and (1/V)(aV/ap) iS the com -
pressibility, K. Thus:
S1l = (1/3)KAP (5.7)
With Kaa the wave number, Eq. (4.7) in Subjection 4.2.1
reduces to $ = kLn. Using this and combining Eqs. (5.5)
and (5.7) results in:
A@/@AP = 0.307K (5.8)
The compressibilities of silica and the pol~~
ester Hytrelc are 2.7 x 10-11 and 2.67 x 10-10 pascals
respectively, leading to:
A$/$AP = 8.3 x 10-12 pascal-l
for bare optical fiber and:
A$/$AP = 8.2 x 10-11 pascal-l
for Hytrelc jacketed optical fiber. Experimental values
of A$/$AP, shown in Fig. 5.3, (See Ref. 5 in Subsection
5.1.7) are 4.5 x 10-12 and 1.0 x 10-10 pascal-l respectively.
The calculated and measured values agree to
within 18% for Hytrelc and a factor of two for fused
silica. These are quite reasonable agreements especially
for Hytrelc where the constant volume assumption
~lo -
In
PIJSTICCOAT(lmm)
❑ DD
❑ ODDDU ❑
PLASTIC COAT (O.4 mm)
00
Ooooo(looooooooo(x o 0 0
Q$
SARE
$
<
ALUMINUM COAT
AAAAAAAAAAA A A 6 A A
1 1 , 1 1 1 1
0.2 0.4 O.b 0.8 10 12 1.4 16
FREQUENCY (kHz)
Fig. 5.3 Acoustic sensitivity vs frequency for various
typea of optical fiber jacketing.
Adapted from Lagakos et al., Opt. Soc. Am. ~, 460
(1982).
The discussion above is valid for the mandrelwound
or thick-jacketed fibers. For thinner jackets,
the phase sensitivity is a more complicated function
of the elastic moduli. A low Poisson’s ratio will result
in the thick-jacketed limit being approached with
thinner jackets. Baaed on the criteria of large compressibility
and low Poisson’s ratio, Teflon c appeara
to be an optimum material. In order to demonstrate the
effect of increasing jacket thickness. Ea. (5.2) is rewritten
as:
A$ = kLn(AL/L + An/n)
= kLN[(l/L)aL/aP +
and therefore, since $ = kLn as
A$/$AP = (1/L)aL/aP +
(1/n)an/aP]AP
indicated above:
(1/n)an/aP)
‘CL,Z + Cn,z+cn,r
J
1
(5.9)
where CL z corresponds to the first term in the brackets
and the 2n,z and cn,r correspond to the fiber axial and
transverse components of the second term in the brackets.
The last two terma are both associated with the
pressure-dependence of the refractive index, n. The
various values of the three components of A$/$AP are
shown in Fig. 5.4 (see Ref. 4 in Subsection 5.1.7). As
can be seen, the thick-jacketed fiber results were obtained
for a jacket thickness of approximately 600Pm.
5-2

-- ~ I
I T I I I I
1! 20 –
~ c n.z
9
10
‘0
= ~ n,r
0.0 ~— -–– –– ––––––––--–- - - - -
%
*
g –10
I
value of A~$AP below that of fused silica, as was shown
in Fig. 5.3. Theoretical results are shown in Fig. 5.6
--
1-a
I T I r I I I I
z –20
>
~ –W
%
:
y
:
0.5 –
0.0 -
%
“ –40
$
~ -50 -
< –so
I I I I I I
100 2(Y2 300 400 500 600
HYTREL THICKNESS (pm)
Fig. 5.4 The components of the per-unit phase change
of a lightwave in a Hytrelc-jacketed fiber
per pascal as a function of jacket thickness.
After Lagakos and Bucaro, Appl. Opt. ~, 2717 (1981).
In order to calculate the pressure sensitivity
of one meter of Hytrelc-jacketed fiber, consider the
experimental results that were given in Fig. 5.3. The
measured value of A /@jAP, corresponding to a l-mm plastic
jacket is 10-~0 pascal-l. Solving fOr A$/~ and
taking L = 100 cm, n = 1.5, k = 7.4 x 104/cm (for A =
0.85 microns) yields aA$/$of 10-6 radians for 10Q3
pascals. Thus, 103 micropascals produces a one microradian
phase shift. The pressure sensitivity per meter
for this case is 60 dB re 1 micropascal. Increasing
the length of optical fiber to 10 and 100 meters increases
the pressure sensitivity to 40 dB re 1 micropascal
and 20 dB re 1 micropascal respectively. These
results are only 5 dB greater than the quantum limited
theoretical results shown in Fig. 5.5. Included for
3–0.5 —
~
: –10 -
5~ –15 —
CALCIUM ALUMINATE GuSS
G
z
# –2.0 —
g
: –~,5 -
$
<
0 20 40 60 SO 100 120 140
COATING THICKNESS (pm)
Fig. 5.6 Acoustic response (phase shift of a lightwave)
in an optical fiber as a function of
coating thickness.
After Lagakos et al., Opt. Lett. ~, 460 (1982).
(See Ref. 6 in Subsection 5.1.7) for jackets of nickel,
calcium aluminate glass, and aluminum. A nickel jacket
as thin as 10 microns should reduce the acoustic sensitivity
of silica fiber to zero; however, the thickness
is critical. On the other hand, a 90-micron jacket of
aluminum is required for zero acoustic sensitivity but
the thickness is much less critical. The variation of
‘L,z~ ‘n,z~ cn,r, and A$/@P versus the thickness of
the the aluminum jacket are shown in Fig. 5.7 (See Ref.
5 in Subsection 5.1.7).
4,
--
I
2 -
z
:
c1
y
0g
%
* –2 -
~
E n,z
0 -––––––––––––-––-----–
---——
~ \ \
— t \ H56EOUIV \
d
~ 30 cOATEDFIBE’R 115fiW20ml
Y\Y
+
I
3 5 10 2 5 100 2 5 1,000 2 5 Io,orm
FREQUENCY (H,]
Fig. 5.5
Variation of acoustic energy spectrum level
as a function of frequency for two coated
fibers along with other noise levels in a
sea subsurface environment.
comparison in Fig. 5.5, are various ambient noises,
such as shipping, weather and seismic noiaes. Also
shown is the equivalent noise pressure of the U.S.
Navy’s H56 hydrophore.
o 20 40 60 80 100 120 140
ALUMINUM THICKNESS (pm)
Fig. 5.7 Pressure components per unit sensitivity
per unit pressure as a function of aluminum
jacket thickness on an optical fiber.
After Lagakoa and Bucaro, Appl. Opt. — 20, 2719 (1981).
5.1.2.2
Pressure Gradient Sensors
The effect of jacketing optical fiber with
aluminum (measured experimentally) is to reduce the
mined by
The direction of a sound source can be deterusing
either an array of omnidirectional sen-
5-3

sors or a pressure gradient sensor. Sensor arrays will
be considered in Chapter 6. Pressure gradient hydrophores
sense the pressure at two closely spaced points.
The distance between sensors, S, iS typically much less
than the wavelength of sound, k, in the propagation
medium, namely water in the calculations that follow.
A pressure gradient measurement can be accomplished by
means of either two distinct sensors, one at each point,
or by a single senaor apanning the distance between the
two points. Both types of sensora will be considered
here.
Since the output signal from a pressure-gradient
hydrophore is proportional to the preasure gradient,
ita reaponse ia proportional to the particle velocity.
Such sensors are therefore often called particle
velocity hydrophores. This is an advantage when operating
near a pressure releaae aurface where the particle
velocity almost doublea and the pressure itself goes to
zero. The tendency to reapond to particle velocity
renders them more aensitive to flow noiae than omnidirectional
hydrophores. Thia follows because particle
velocity fluctuations associated with flow are often
much greater than the particle velocity oscillations
associated with the acoustic signal being measured.
Consider the sine wave shown in Fig. 5.8 where the
Fig. 5.9
100
90
80
70
60
50
40
30
20
\
1
3 5 ID 2 5 100 2 5 1,000 2 5 10,000
FREOUENCY (Hz)
HEAVY
SS2 WIND
SPEED
10 KTS
RAIN
V a r i a t i o n of the acouatic energy spectrum
level aa a function of frequency for a fiberoptic
presaure-gradient hydrophore with
other noise levels in a sea subsurface environment.
P
PA- -
I
The calculated reaults shown in Fig. 5.9 is
for the case of the aound wave propagating parallel to
the line joining the two sensors. The sensitivity of
a Preasure gradient sensor to a sound wave propagating
perpendicular to this direction ia zero because both
sensors are then aubjected to the aame pressure. The
directivity is dipole-like aa shown in Fig. 5.10(a).
The cardioid directional responae shown in Fig. 5.10(b)
can be obtained by combining the dipole output with
that of an omnidirectional hydrophore with sensitivity
equal to that exhibited by the dipole at e = OO. The
Fig. 5.8
The pressure distribution aa a function of
distance from the zero-preasure point of a
single pressure wave.
instantaneous acoustic preasure, P, is given by:
p = pAsiI’i (2~/ka)x (5.10)
where pA is the acoustic amplitude, as is the sound
wavelength, and x is distance in the same units as ~.
The pressure amplitude at x = O and x = S (S

Since neutral bouyancy is required, m/AS = maaa per unit
volume = 1 and Eq. (5.13) becomes:
tin = (2T/k~)pA (5.14)
Thus, once the sound frequency (wavelength, 1s) and
pressure level are chosen, the acceleration can be
determined. For f = 100 Hz (As = 1460 cm) and PA = 50
dB re 1 micropascal, corresponding to the 118-met r
curve that waa shown in Fig.
= 1.67 -3
X 10 g
(1.6 gal). This requires an5;1;r~%Ny sensitive accelerometer.
The two-fiber accelerometer described
below exhibits the required sensitivity.
5.1.3 Fiberoptic Magnetic Sensors
Yariv and Winsor (See Ref. 7) suggested that
an optical fiber could be used to measure the change
in length of a magnetostrictive material subjected to
a magnetic field. The resulting optical phase change
is linearly related to the magnetic field. Jarzynski,
et.al. (See Ref. 8 in Subsection 5.1.7) developed expressions
for the strain induced in a magnetostrictively-jacketed
fiber subjected to a weak axial magnetic
field. These expressions were obtained as a function
of jacket thickness for a variety of magnetostrictive
materials as shown in Fig. 5.11. The magnetooptic
J
10 100 1,000 10,000
FREQUENCY (HZ)
Fig. 5.12 The magnetooptic coupling coefficient versus
frequency for an optical fiberwound
nickel toroid with walls 0.038 cm thick.
After J. Cole et al., Opt. Lett. ~, 216 (1981).
\ /-WINDING
.
10.0
t
4.5% CO.95.5% Ni
-TOROIDAL
WINDING
8.0 -
70
-1
*j
aXO
6.0 -
4.0 -
2.0 -
2V-PERMENDUR
HOUSING
Fig. 5.13 Optical fiber wound on a magnetostrictive
nickel toroid (wall thickneas 0.038 cm) for
use in meaauring the magnetooptic coupling
coefficient.
After J. Cole et al., Opt. Lett. ~, 216 (1981).
I , , # 1 # 1 , 1
0 5 IO 15 20 25 30 35 40
METAL JACKET THICKNESS (pm)
Fig. 5.11 Magnetic sensitivity of magnetostrictive
metal-jacketed optical fiber as a function
of jacket thickness for various magnetostrictive
metals.
Adapted from J. Jarzynski et al., Appl. Opt. ~, 3746
(1980).
coupling coefficient as shown in Fig. 5.12 was measured
for nickel by Cole, et.al. (See Ref. 9 in Subsection
5.1.7) using a nickel cylinder around which the optical
fiber in one arm of the interferometer was wound as
shown in Fig. 5.13). The relevant theory has been compared
with magnetooptical experimental data taken at
low frequency (< 1 kHz) and msgnetomechanical data
taken at frequencies greater than several tens of kilohertz.
Thia study demonstrated that the piezomagnetic
atrain coefficient remains constant from low frequency
up to the frequency at which eddy currents become important.
Therefore, the low frequency measurement reaults
may be uaed to design magnetic sensors that will
operate at high frequencies, i.e., to the eddy current
limit.
Magnetoatrictive materials have been used extensively
as acoustic transducers for the production or
detection of sound. In the preaent application these
materiala are used to detect magnetic fields by measuring
the reaulting atrain produced. The most atraight
forward and sensitive technique for such measurements
involvea uaing an optical fiber in one arm of a Mach-
Zehnder interferometer. The fiber is either jacketed
with the magnetostrictive material or wound around a
magnetostrictive mandrel. The resulting change in optical
path is due to changes in both the refractive
index and the length of the optical fiber core. This
leads to a phase ahift A+ given by Eq. (5.5) in Subsection
5.1.2.1. An expression for S11 can be obtained
from the effective piezomagnetic strain constant dT defined
by the expression:
dT = 4n(3S11/aH)T (5.15)
where T is the streaa.
yields:
Integrating this expression
Sll = (1/41r) a ‘b dTdH (5.16)
where the limits a and b are Ho-Hi/2 and Ho+H1/2, respectively,
H. is the dc bias field choaen to ~ximize
dT, and HI is a small excursion about that point. For
5-5

nickel H. = 3.6 oersteds and for a small excursi n
about the maximum, dT r~~ains constant at 8 x 10 -8 .
Therefore, S1l = 6.4 x 10 HI and:
Using this technique a
1o-8 A/m waa measured
to 5000 Hz.
minimum electric current
over the frequency range
of 3 x
100 Hz
@/kLHl = 8.6 X 10 -7 oersteda -1 (5.17)
is the magnetooptic coupling coefficient. This agreea
quite well with the value of coupling coefficient between
7 and 8 x 10-7 measured by Cole et.al. (See Fig.
5.12 and Ref. 9 in Subsection 5.1.7). The value of dT
used in Eq. (5.16) was measured at approximately 30 kHz
and has been shown to be valid up to the frequency at
which eddy current limitations occur.
Using the measured magnetooptic coupling coefficient
shown in Fig. 5.12, the minimum detectable
magnetic field (oersteds) per meter of nickel-jacketed
optical fiber can be calculated. From Fig. 5.12, for
A$ = 7.5 x 10I7 kLH, and using k = 7.4 x 10-4 (for 0.85
micron optical radiation), L = 102 cm, and 10-6 radians
minimum detectable phase shift, the minimum detectable
magnetic field for 1 meter of nickel-jacketed optical
fiber is 1.8 x 10-7 oersteds (1.8 x 10-2 gamma). Recently
a minimum detectable magnetic field of 5 x 10-9
oersted per meter of fiber waa measured using optical
fiber jacketed with an amorphous magnetostrlctlve material
(See Ref. 10). Extrapolating to 1 km of such metallic
glass-jacketed fiber leads to the prediction
that magnetic fields as amall as 5 x 10-12 oersteds may
be detected by this means. On the other hand a one cm
length of such jacketed fiber should permit the measurement
of a magnetic field as small as 5 x 10-7 oersted
(0.05 gamma).
The sensitivities of pressure, magnetic, and
temperature fiberoptic sensors is summarized in Fig.
5.14. The cross section configuration of the various
jacketed optical fiber is shown in the middle column.
The predicted sensitivities corresponding to one mlcroradian
phase shift for one meter of jacketed fiber is
shown in the last column.
FIBER
a
FIBER
I
ALUMINUM
TUBING
\“
Fig. 5.15 Fiberoptic senaors for measuring electrical
currents.
After A. Dandridge et al., Electron. Lett. ~, 524
(1981).
The second technique, also shown in Fig. 5.15,
depends on the resistive heating that occurs in a section
of aluminum jacketed optical fiber as a result of
passing the electric current to be measured through the
jacket. Using this technique aminimum detectable electric
current of 1.3 x 10-5 A/m was measured at 1 Hz.
5.1.5 Fiberoptic Spectrophones
Spectrophones are used to determine the preaence
of trace vapors by means of the acoustic signal
produced by the temperature increase associated with
the absorption by the vapor of a pulsed laser output.
Conventional microphones are used to detect the acoustic
signal. The schematic of a fiberoptic spectrophone
(See Ref. 12 in Subsection 5.1.7) is shown in Fig. 5.16.
SENSOR TYPES
CONFIGURATIONS
FI?EDICTED PERFORMANCES
A~-W-6RAD, lMETER FISER)
op,Geo~
339u”ItleNe
LASER
PRESSURE
Si02
P~NX 60dS re #Pa
LASTOMER
MAGNETIC
aSiO*,0e02
SiO*
MAGNETO–
STRICTIVE
HMNZ 5xlo”90ERsTED
(METALLIC GLASS)
06328 ”. H?Ne
LAsER@
TEMPERATURE
SiO~
Si02, GeO~
e METAL
ATMNZ FTSC”
Fig. 5.14 Fiberoptic sensor performance parameters
(coefficients) for several fiber jackets.
5.1.4 Fiberoptic Electric Current Sensors
Two techniques for measuring electric currents
are shown in Fig. 5.15 (See Ref. 11 in Subjection
5.1.7). In the first, a section of nickel-jacketed
fiber is located in the center of a solenoid energized
by the current being meaaured. By measuring the magne -
tic field intensity, the electric current is determined.
Fig. 5.16 A fiberoptic spectrophone for detecting the
pressence of trace vapors.
After D. Leslie et al., Electron. Lett. ~, 581 (1981).
The frequency of the excitation laser is equal to an
excitation frequency in the absorption spectrum of the
trace vapor being detected. The absorption cell consists
of a thin walled cylinder around which is wound
a fiberoptic coil to form one arm of a Mach-Zehnder
interferometer. The fiber coil serves as the microphone.
It has the advantage of not requiring electri-
5-6

cal leads in the vicinity of the vapor. The chopper
is operated at a frequency at which the acoustic aenaitivity
of the absorportion cell is high.
The light from the excitation laser excites
a characteristic absorption line in the molecular spectrum
of the vapor being detected. When the excited
molecules return to equilibrium the temperature of the
vapor Is increased resulting in a preaaure increase.
By chopping (interrupting) the light at a given rate
(frequency), the resultant fluctuation in preasure Is
detected as aound of the same frequency. Even more
desirable 1S to make use of a variable frequency laaer
aa the excitation source. The absorption coefficients
vs. frequency of ambient atmosphere and of methane
whose concentration 1S five times ambient are shown in
Figs. 5.17 and 5.18.
measure strains, electric fields, temperature, acceleration,
and rate of rotation. They differ from the
acoustic and magnetic senaors discussed above that rely
on specialized jacketa and utilize a Mach-Zehnder interferometer.
The electric current and trace vapor sensors
are secondary devices relying on the measurement
of the magnetic field or the temperature in the former
case and the aound associated with the absorption of
light in the latter case.
5.1.7 References
1.
2.
3.
D. Jackson, A. Dandridge, and S. Sheem, Opt. Lett.
~, 139 (1980).
B. Budiansky, D. Drucker, G. Rino, and J. Rice,
APP1. Opt. ~, 4085 (1979).
G. Hocker, Opt. Soc. Am. ~, 320 (1979).
lo”~
WAVELENGTH
Fig. 5.17 The absorption coefficient of ambient atmosphere
aa a function of wavelength.
Provide by D. Leslie, U.S. Naval Reaearch Laboratory.
4.
5.
6.
7.
8.
9.
10.
11.
N. Lagakos and J. Bucaro, Appl. Opt. — 20, 2716
(1981).
N. Lagakos, T. Hickman, J. Cole and J. Bucaro,
Opt. Lett. ~, 443 (1981).
N. Lagakos, private communication.
A. Yariv and H. Winsor, Opt. Lett. ~, 87 (1980).
J. Jarzynski, J. Cole, J. Bucaro and C. Davia,
Appl. Opt. ~, 3746 (1980).
J. Cole, N. Lagakos, J. Jarzynski, and J. Bucaro,
Opt. Lett. ~, 216 (1981).
K. Koo and G. Sigel, Technical Digest, Optical Fiber
Communication Meeting, Phoenix, Arizona (1982)
p. 72.
A. Dandridge, A. Tveten, and T. Giallorenzi, Electron.
Lett. ~, 523 (1981).
ABSORBERS
TYPE (TORR)
H20 14.260
C02 0,251
03 2.3x lC”5
~’”i
N20 2.1 X1 O-4
co 5.7 x10-5 I
CH4 12’1 0-31 1II I
159627
02
1~ II
WAVELENGTH
22.9°C
JJ
760 TORR
Fig. 5.18 The absorption coefficient of methane gas
as a function of wavelength for a concentration
of 7.6 x 10-3 torr (5 x ambient).
Provide by D. Leslie, U.S. Naval Research Laboratory.
12.
5.2
D. Lealie, G. Trusty, A. Dandridge and T. Giallorenzi,
Electron. Lett. ~, 581 (1981).
5.2.1 General
INTENSITY MODULATED FIBEROPTIC SENSORS
The second type of fiberoptic sensor to be
diacusaed is referred to as an intensity-modulated aensor.
Ita basic configuration is sketched in block diagram
form in Fig. 5-19. The output lightwave from an
OPTICAL
SOURCE
+ l~”T
SENSOR
OPTICAL
DETECTOR
.
‘OUT
5.1.6 Summary
The acoustic and magnetic field sensors described
above represent primary measurement devices.
Other primary measurement devices include sensors to
TIME
TIME
TIME
Fig. 5.19 A generalized intensity-type fiberoptic
senaing system.
5-7

optical source of constant intensity IIN (shown at the
lower left) is injected into the sensing element. This
element, acted on by an external force field (baseband
signal), represented in the figure as an incident ainusoidally-varying
quantity, alters the intensity of the
light transmitted through the sensor. The modulation
envelope of the output intensity, IOUT, matches that of
the input force field (signal). In turn, the time varying
output optical intensity, incident on the photodetector,
similarly modulates the output voltage, eo~.
The intensity-modulation sensor shown in Fig.
5.19 employs relatively simple optica and circuitry. An
incoherent optical source, such as an LED, or a highintensity
incandescent source, may be used, together
with multimode fibers as links between the sensing element
and the source and detector. The sensor itaelf
typically consists of one or two multimode fibers or
some mechanooptic, electrooptic or other atraight forward
transduction element. Achievable sensitivities,
expresaed in terms of minimum detectable displacements
for intensity-type mechanical motion detectors, lie in
the ran e 10-10 to 10-7 m, as compared to a lower limit
of 10-1 fm achievable with interferometric type fiberoptic
sensors.
5.2.2 Evanescent-Field Fiberoptic Sensor
To illustrate the various types of intenaity
modulation transduction mechanisms currently under investigation,
consider first the evanescent field transducer
(see Ref. 1 in Subsection 5.2.6) outlined in Fig.
5.20. It consists of a pair of single or multimode op-
L .
:;cm;
OPTICAL
DETECTOR
I
CORE
CLADDING ‘2
CLADDING
FIBER
SENSOR
\’
—MIRRORED
Fig. 5.21 A critical-angle intensity-type fiberoptic
sensor.
After R. Phillips, Opt. Lett. ~, 318 (1980).
in the optical reflection coefficient (See Ref. 2 in
Subsection 5.2.6) at the right hand tip of the fiber.
Referring to the upper portion of Fig. 5.21, light injected
into the core at the left end of the fiber is
partially reflected back along the length of the fiber
and then directed to the photodetector using a beam
splitter. As indicated in the lower expanded view of
the right end of the fiber, two reflecting facets are
lapped on the end of the fiber. The lower facet is
coated so that it ia totally reflecting. By carefully
controlling the angle of the upper facet so that the
beam in the core is incident at an angle larger than
the critical angle, the light in the core will be partially
transmitted into the medium of refractive index
n3 in contact with the end of the core. Slight variations
in n3, induced by changea of pressure or temperature,
for example, will change the intensity of the
reflected beam. One can thus envisage a probe or catheter-type
presaure transducer, of active area equal to
that of the end of the core, i.e., effectively a point
pressure probe, that could be superior in many ways to
some of the more conventional types that are in use
today.
d -CORE SPACING
L- INTERACTION LENGTH
OPTICAL
DETECTOR
5.2.4 Moving Grating Fiberoptic Sensor
A conceptually simple intensity-type aensor
is the moving grating transducer shown in Fig. 5.22
(See Ref. 3 in Subjection 5.2.6). Two fibers are sep-
Fig. 5.20 .An evanescent-field intensity-type fiberoptic
sensor.
MOVABLE
GRATING
STATIONARY
~GRATING
tical fibers. In the transduction element itself the
cladding is reduced In thickness, or entirely removed,
so that the distance, d, between the cores is small
enough to permit evanescent field coupling between the
two fibers over some small interaction length L. Coupling
may be enhanced by potting the interaction response
in a fluid or flexible elastomer of refractive index,
nz, the same as that of the cladding. Slight variations
of the spacing, d, the interaction length, L, or
the refractive index, n2, induced by the particular
force field of interest may produce substantial changes
of the light coupled into the lower or pick-up fiber.
Promising results have been reported on two hydrophonetype
applications of this modulation mechanism. Further
studies are in progress.
Fig. 5.22
H
A moving-grating
senaor.
1
I
CORE
TO
DETECTOR—
I
1nCLADDING
intensity-type fiberoptic
5.2.3
shown in
Reflection Coefficient Fiberoptic Sensor
A second intensity-type fiberoptic sensor is
Fig. 5.21. Its operation is based on changea
5-8

arated by a small gap in which is placed a pair of gratings,
consisting of a cyclic grid of totally transmissive
and totally reflecting (opaque) parallel line elements
of equal width. When the gratings are moved relative
to one another there is a change In the transmitted
intensity. This type of transducer has been employed
in a hydrophore, as sketched in Fig. 5.23. Here one
DIAPHRAGM
n \ n
L
r
HYDROPHORE
/HOUSING
/
be seen that the sensitivity will be greatest when the
quiescent or bias point is set at a relative displacement
of 2.5 pm, 7.5 pm, 12.5 pm, etc. In addition, decreasing
the width of the grating elements will increase
the sensitivity but decrease the dynamic range.
5.2.5 Microbend Fiberoptic Sensor
The intensity-type sensors to be considered
last are based on microbend-induced ejection of light
from the core of a fiber into the cladding (See Ref. 4
in Subsection 5.2.6). Referring to Fig. 5.25, the
transduction element in this type of sensor consists
of a deforming device such as a pair of toothed or serated
plates that introduce small bends in a fiber. As
FIBER
\
I
F
I
DEFORMER
F
I
I , I
OPPOSED GRATING
Fig. 5.23 A moving grating intensity-type fiberoptic
sensor used in a hydrophore.
Adapted from W. Spillman, Appl. Opt. ~, 465 (1981).
of the gratings is shown mounted on the rigid base
plate of the housing while the other is attached to a
flexible diaphragm. The diverging lightbeam from the
input fiber on the left is collimated using a short
graded-index self-focusing (Selfocc) lens and then partially
transmitted through the gratings as a parallel
(collimated) beam that is focused into the output fiber
using a second self-focuaing (Selfocc) lens. Assuming
the two gratings each consist of 5 pm-wide grating elements
that are spaced 5 Bm apart, the transmitted light
intensity will vary cyclically as sketched in Fig. 5.24,
passing through successive maxima each time the grating
displacement changes by 10 ~m. From this graph it may
1.0
MODE1:
E1-sin(LJt-~lz)
MODE2: E2-sin(Ut–~2z)
COUPLING CONDITION: L=— 13;:132
Fig. 5.25 A microbend intensity-type
ser.
fiberoptic senahowo
in the figure, the distance L between adjacent
teeth defines the apatial frequency of the deformer. By
increasing the force, F, applied to the plates the amplitude
of the deformations can be increased. In the
earlier brief discussion of attenuation mechanisms in
fibera, it was shown that random bends in fibers can
cause light to be ejected from the core into the cladding.
Thia process is illustrated in the enlargement
of the deformer shown in Fig. 5.26. Rays propagating
~

in a straight section of the fiber at an angle less
than the critical angle may have their angle of incidence
on the core-cladding interface increased by the
bends and thus be partially transmitted into the cladding.
A more detailed wave theory analysis of periodic
bend-induced coupling indicates that the level of coupling
between modes, including non-attenuating core modes
as well as attenuating core and cladding modes, is
strongest when the difference between the effective
propagation constants of a pair of modes, (Bi - Bj), is
equal to 2 /1..
range 0.5N < F > 1.5 N. In the latter caae, 9“ corresponded
closely to the critical incidence angle, thus
the light waa injected mainly into the highest order
propagating modes and therefore was more eaaily ejected
from the core into the cladding.
loofiT_..-
,_L
1::::-,-
1 I 1 I I I I I I I I I I
T – - * — - 0 - - 1
A number of studies of this phenomenon have
been conducted. For example, the system shown in Fig.
5.27 was used at the Hughes Research Laboratories. As
EO
~ —
L
I
FIBER
DETECTOR MODE DEFORMER
STRIPPER
Fig. 5.27 A microbend intensity-type
sor system developed by the
Laboratories.
fiberoptic sen-
Hughes Research
indicated in the figure, light was injected into a
multimode step-index fiber which was passed through a
deformer element. In this case the intensity of the
core light reaching the end of the fiber was monitored.
By using a helium-neon laser with a well-collimated
beam it was possible to vary the incidence angle of
light into the fiber and thus inject light into a fairly
well defined set of propagating core modes. On sections
of the cladding, just before and just after the
deformer, mode strippers were employed. These elements,
which in their simplest form might consist of black
paint applied to a few centimeters of the outer surface
of the cladding, absorb almost all of the light that
my be propagating in the cladding of the fiber. The
use of cladding mode strippers first insured that only
core light reached the section of fiber in the deformer
and then that any core light ejected into the cladding
by the deformer was absorbed so that it did not reach
the photodetector.
Uaing the system outlined in Fig. 5.27, the
Hughes’ inveatigatora measured the transmitted optical
intensity as a function of the force applied to the
transducer (microbend deformer). This was done for
several different angles of incidence of the input light
and the reaulting data la preaented in Fig. 5.28. Aa
shown in that figure, when the input incidence angle
was set at 0°, i.e., for light injected along the axis
of the fiber, the output intensity decreased by about
twenty percent as the force applied to the deformer increaaed
from O to 2 newtons. On the other hand, for
light incident at 9°, the transmitted intensity decreased
to approximately 40 percent of the input when the
applied force waa again increased to 2 N. In addition,
the slope of the transmission intensity, I, veraus applied
force, F, curve was nearly conatant over the
1
r
r
——— O.ODEG .
20
----- 7.ODEG 0
-“---”- 8.ODEG ❑ 1
} ------- 9.0 DEG ●
4
oo~
0.5 1.0 1.5
FORCE N
Fig. 5.28 The percent transmission of core input
light obtained at the output as a function
of applied force in a microbend intensitytype
fiberoptic sensor.
After J. Fields, et al., J. Acouat. Soc. Am. ~, 816
(1980).
Using the results of this and aimilar experiments,
the Hughes investigatora, in cooperation with
the Physical Acouatica Branch of the U.S. Naval Reaearch
Labora~ory, deaigned and teated a hydrophore employing
such a microbend deformer as the transducer element.
Their first prototype unit ia aketched in Fig. 5.29
DIAPH
/-- FIBERLEADS
/
Fig. 5.29 A microbend intenaity-type fiberoptic sensor
hydrophore developed by the Hughes Research
Laboratories and the U.S. Naval Research
Laboratory.
After Fields and Cole, Appl. Opt. ~, 3265 (1980),
(See Ref. 5 in Subsection 5.2.6). One deformer plate
was rigidly mounted to the cylindrical ahell of the
hydrophore while the other was attached to a thin diapragm.
In addition to the through-put fiber, a second
inactive fiber was included to insure that the deformer
plates remain parallel during operation.
At this point it would be uaeful to review
some of the basic acoustical levels and unita of meaaure.
Referring to Fig. 5.30, one frequently encountered
acoustic reference pressure level encountered in air
acouatics is 0.0002 dynea/cm2. This is the accepted
5-1o

AIR ACOUSTICS
REFERENCE LEVEL –––
I
UNDERWATER ACOUSTICS
REFERENCE LEVEL . . . . . . - 1 -
Fig. 5.30
TT71 NEWTONIMETER 2
~0 ~B 1 PASCAL (Pa)
1 DYNE/CENTlMETER2
DYNEICENTIMETER2
20 MICRONEWTON/METER2
4’0.0C02
20 MICROPASCAL
26 dB
1 MlCRONEWTONfMETER2
1 MKROPASCAL (#Pa)
Pressure levels and units for comparison of
underwater acoustic pressure reference
levels.
average minimum detectable sound pressure for humans at
1000 Hz. Another is the currently accepted 1 m.lcronewton/m2
or 1 micropascal (1 ~Pa) reference pressure for
underwater acoustics. To compare these on a decibel
scale, recall first that for a pressure ratio, P1/P2,
the number of decibels, N, in dB, is defined by:
N = 20 loglo P1/P2 (5.18)
Since 0.0002 dynes/cm 2 is equl to 26 upa, the air
acoustic reference pressure is 26 dB above the underwater
reference pressure. Similarl as indicated in
Fig. 5.30, a pressure of 1 dyne/cm J’ is at a level of
74 dB re 0.0002 dyne/cm2 and at a level of 100 dB re
1 pPa. Finally, a pressure of 1 Pa corresponds to 120
dB re 1 pPa and 20 dBre 1 dyne/cm2. The table presented
in Fig. 5.30 is an aid in interpreting hydrophore
characteristics and in performing comparisons presented
here and in later sections.
Returning to the consideration of the Hughes-
NRL microbend hydrophore, an experimental evaluation of
the acoustic characteristic of their initial prototype
was conducted at NRL. As indicated in Fig. 5.31, the
hydrophone was placed in an acoustic test tank and measurements
were made of its sensitivity and frequency response
over a frequency range of 200 Hz to 2000 Hz. The
H
~
MODE STRIPPER
u \
results are shown in graphical form in the lower por–
tion of the figure. The minimum detectable pressure,
in a 1 Hz band and at a unity signal-to-noise ratio,
was approximately 100 dB re 1 ma. The 10 dB fluctuations
about this value were attributed to resonances in
the outer case and deformer mount. It should be possible
to eliminate these resonances without much difficulty.
In addition, a significant increase in sensitivity
was achieved in later designs by employing speciallydesigned
graded-index fibers. This was to be expected
since the fiber employed in the initial prototype was
a readily available standard communications step-index
fiber. Such optical fiber has been designed to have
low microbend sensitivity to reduce losses due to bending
introduced in cabling and other field use distortions.
By employing graded-index fibers with enhanced
microbend effects, sensitivity increases of more than
40 dB have been achieved. Thus, these improved microbend
transducers are comparable to many of the more
conventional hydrophores currently in use.
It should be emphasized that with the microbend
transducers discussed above, attempts are made to
detect a very small change in the intensity of a relatively
intense optical beam. This type of sensor is
referred to as a brightfield microbend transducer. A
second type of microbend device, a so called darkfield
transducer, was proposed initially by a group at Catholic
University and currently is under investigation by
several different groups. The sensor is shown in Fig.
5.32. Beginning at the left, it is quite similar in
OPTICAL
SOURCE
Fig. 5.32
FIBER
DEFORMER
MODE
STRIPPER
The microbend darkfield intensity-type fiberoptic
sensor system.
arrangement to the brightfield transducer up to and including
the deformer. As with the brightfield transducer
described above, light, possibly from a broadband
incoherent source, is introduced into a multimode
fiber. Care ia taken to remove cladding light prior to
the deformer. The darkfield transducer differs from
the brightfield transducer in that the light ejected
from the core into the cladding is used to generate the
output signal.
Fig. 5.31 Test arrangement and sensitivity level of
the Hughes Research Laboratories and U.S.
Naval Research Laboratory microbend intensity-type
fiberoptic senaor hydrophore.
After Fields and Cole, APP1. Opt. ~, 3265 (1980)0
5.1 1
As indicated in Fig. 5.32, the Catholic University
group used a more elaborate mode-stripper on
the output section of the fiber (see Ref. 6 in Subsection
5.2.6). The fiber was stripped of ita outer coating
and passed through a small chamber filled with a
refractive-index matching fluid. A number of photodetectors
mounted in the walls of the chamber responded
to changes in the intensity of the core-to-cladding
ejected light. In contrast with brightfield, the darkfield
case has a relatively low level of background
light that is modulated by changes in displacement of
the deformer. The degree” of modulation
-
may be quite
large and thus a very high sensitivity
may be employed without overdriving it.
detectable signals should, in principle,
in the brightfield case. This has been
recent studies.
photodetector
The minimum
be lower than
confirmed in

A simplified design of the cladding light
monitor is indicated in Fig. 5.33. The pick-up fiber
STRIPPER
I o-
SOURCE FIBER
DEFORMER
transducer outputs could also be accomplished prior to
photodetection. The optical outputs may be combined
with appropriate time delays determined by the transducer
spacings and coupler fiber lengths. On the other
hand, by employing a pulse modulated optical source, it
is possible to employ a single return bus fiber into
which the optical output pulses from the various transducers
could be fed. Time domain multiplexing schemes
could then be used to identify and process the signal
from the individual sensors. These and other various
types of fiberoptic sensor arrays and the telemetering
of their outputs are discussed in detail in Chapter 6.
Fig. 5.33
FIBER-FIBER
COUPLER
DETECTOR FIBER
kAI
A darkfield microbend intensity-type fiberoptic
sensor with a fiber-fiber coupler
following the deformer (microbender) developed
by the Catholic University.
is directly coupled to the outer surface of the cladding
of the through-put fiber. Recent studies of this
technique have ha~ p~omising results.
darkfield
The design and operation of a linear array of
microbend sensors is shown in Fig. 5.34. Each
This brief description of various intensity
type sensors is not exhaustive. The discussion is aimed
at introducing some basic concepts regarding their overall
design and behavior. Many other fiberoptic intensity
transducers are currently under investigation such
as sensors employing fibers with temperature sensitive
absorptive dopants, and several displacement and pressure
transducers employing strain-induced birefringence
as an intensity transduction mechanism. All of these
have the advantage of being much simpler in design and
operation, but they are less sensitive than interferometric
fiberoptic sensors. Further improvements, including
increases in sensitivity, are expected for the
intensity-type fiberoptic sensors.
5.2.6
1.
2.
3.
s.
R.
w.
References
Sheem and J. Cole, Opt. Lett. ~, 322 (1979).
Phillips, Opt. Lett. ~, 318 (1980).
Spillman, Appl. Opt. ~, 465 (1981).
STR!-R
DEFORMER
SOURCE FIBER
STRIPPER
,~fi \.- .
----
\
---
-
DEFORMER
K /’
FIBER-FIBER
COUPLERS
%T
)
Fig. 5.34
A series of deformers used to control the
intensity of light tapped from an optical
fiber bus.
sensor is an assembly consisting of a cladding-mode
stripper, a microbend deformer (transducer), and a fiber-to-fiber
coupler. Many of these assemblies may be
mounted in series on a single optical fiber bus. The
cladding-mode stripper removes any residual light in
the cladding just prior to the microbend deformer. The
deformer causes light from the core to enter the cladding
according to the baseband (information-bearing
force, pressure, or sound) signal. Following the deformer,
the coupler removes the light (baseband signal)
from the claddlng and dispatches it to a photodetector.
A number of different multiplexing schemes
could be used in the detection portion of the array.
The moat direct, would be to feed each cladding light
pick-up fiber to a separate photodetector. Temporal
and spatial averaging of a number of closely spaced
5-12
4.
5.
6.
5.3
J.
J.
J.
N.
R.
Fields, C. Asawa, O. Ramer, and M. Barnoski,
Acoust. SOC. Am. Z, 816 (1980).
Fields and J. Cole, Appl. Opt. ~, 3265 (1980).
Lagakos, T. Litovitz, P. Macedo, R. Mohr, and
Meister, Appl. Opt. ~, 167 (1981).
FIBEROPTIC LINRAR ACCELEROMETERS
The operation of interferometric fiberoptic
sensors described in Section 5.1 depends primarily on
phase changes associated with force-field-induced mechanical
strains. Similarly the two-fiber optical accelerometer
described in this section makes use of the
change in fiber length due to a force resulting from
the acceleration of a mass suspended between two fibers.
The effect is to increase the tensile stress in the fiber
in one arm of an interferometer and decrease the
tensile stresa in the fiber in the other arm. The device
for accomplishing this is shown in Fig. 5.35. A
section of the fiber in one arm of the interferometer
is attached both to the upper end of the case and to
the mass. A similar section of fiber in the other arm
of the interferometer is attached to the mass and to
the lower end of the case. Thus, the mass, m, is suspended
between the two fiber sections which effectively
serve as springs. If the accelerometer case is given
an acceleration, a, vertically upward, the upper fiber
elongates by AL and the lower fiber shortens by the
same amount in providing the force F required to accelerate
the mass. This may be written as
F=2AAT=ma (5.19)

Fig. 5.35
SIGNAL
ELECTRICAL
REBALANCE
UPPER
~1 lppoRT
IER
MASS
DIODE
LASER
3dB COUPLER
iii=
CASE
DIAPHRAGMS
LOWER SUPPORT
lkFIBER
)1‘t’ /u
m1
s
3dB COUPLER
PHOTODIODES
A two-fiber phase-change interferometric
fiberoptic accelerometer.
where A is the cross sectional area of the fiber, AT is
the magnitude of the change of the tensile stress in
each fiber, and the 2 is due to the presence of two fibers.
The resulting strain AS = .4L/L is given by:
AS = AT/Y = ma/2YA (5.20)
attached to a spring with a spring constant k, the resonant
frequency is given by:
combining Eqs. (5.26) and (5.27) there is obtain-
Thus,
ed:
fr = (1/2n)(k/m)112. (5.27)
fr = (1/2n)(2YA/Lm)l/2 (5.28)
As above, A = m(d/2)2. To further emphasize the dependence
of the resonant frequency, fr, on the fiber parameters,
Eq. (5.28) may be written as:
fr = [Yd2/8mLm]1/2 (5.29)
Comparing Eqs. (5.25) and (5.29) we see that the optical
fiber physical parameters appear in the form Yd2/
Lm. Therefore, if the expression d2/Lm in Eq. (5.25)
is decreased in order to decrease ~in, the value
of fr given by Eq. (5.28) is also decreased. The minimum
detectable acceleration (a~n) and longitudinal
resonant frequency are shown in Figs. 5.36 and 5.37 as
functions of m and d. In each case the length of fibe
L is taken to be one cm and the value of A is 10 -5
radian. Alternately, if a mass of one gram % ~ chosen,
the mass in grams on the abscissa in both Figs. 5.36
and 5.37 can be replaced by the length in centimeters.
3.0 t.
where Y is Young’s modulus for the fiber.
Consider next an optical beam propagating in
one of*the fibers. Its phase shift, $ , in traveling
the length L, as given in Subsection 4.2.1 and Eqs.
(4.7) and (4.8), is:
4 = zn~~l~o (5.21)
where h. is the optical wavelength in vacuum and n is
the fiber core’s refractive index. The’ quantity Aoln
is the wavelength of the light in the fiber core. In
general, the change in @ per fiber (twice this for two
fibers) may be written as it was in Eq. (5.1), namely:
A+ = 2m(nAL + LAn)/Ao (5.22)
with the wave number k = 2iI/lo. For the case of a tensile
strain, however, the AL term dominates and one may
write:
A+ = 2nnAL/~o = 2nnLAS/lo (5.23)
Fig. 5.36
10.0
10 2.0 3.0
MASS (grams)
The variation of sensitivity in micrograms
as a function of the mass in grams in a
fiberoptic accelerometer for different
sizes of fibers.
Substituting into Eq. (5.23) from Eq. (5.20) and because
A - n(d/2)2:
A~ = 4nLma/Y~d2 (5.24)
where d is the fiber diameter.
- h
-$
d
m -1-
Solving Eq. (5.24) for ~n in terms of A$~n yields:
amin = AoYd2A$tin/4nLm (5.25)
Referring to Fig. 5.35, the effective spring
force F, required to displace the mass m a distance z,
along the axis of the fiber, is given by:
F = -2YAz/L = -kz (5.26)
from which it follows that 2YA/L = k, where k is the
effective spring constant. However, when a mass m is
.--— ------.-----
I 1 1 1
10 2.0 3.0
MASS(grams)
Fig. 5.37 The variation of resonant frequency as a
function of the mass in a fiberoptic accelerometer
for different sizes of fibers.
5-13

Referring once more to Fig. 5.35, if the mass
is given a transverse (cross axis) acceleration, both
optical fibers are strained the same amount. Thus, the
interferometer remains balanced and to first order this
device is insensitive to transverse accelerations.
Cross axis coupling will occur if simultaneously there
are components of acceleration that has components
parallel and perpendicular to the longitudinal axis of
the fiber. The diaphragms indicated in Fig. 5.35 are
provided to essentially eliminate cross-axis coupling.
Tveten et.al. (See Ref. 1 of Subsection 5.3.1)
investigated a single fiber version of this device. The
sensitivity in radians/g versus frequency is shown in
Fig. 5.38 and the value of amin versus frequency in
Fig. 5.39.
100or
y 100 -
v
: 10 -
~
> ~-----
&l -
:
~ 0.1 1
0 100 200 300 400 500
5.4 FIBEROPTIC ROTATION-Fb+TE SENSORS
5.4.1 Introduction
The measurement of rotation is of considerable
interest in a number of areaa. For example, inertial
navigation systems as used in aircraft and spacecraft
depend critically on accurate inertial rotation
sensors. The allowable errors in rotation sensor performance
depend on the particular application. Typical
requirements for aircraft navigation lie between 0.01
and 0.001 degreeslhour. In terms of earth rotatio
rate, flE = 15 degrees/hour, this becomes 10-3 to 10 -2
!lE. Fig. 5.40 lists several other applications of rotation
sensors, such as surveying, where the accurate
determination of azimuth and geodetic latitude is important
(see Ref. 1, Subsection 5.4.20). In this case
-6 ~ or less iS needed.
performance of 10
Geophysics
applications include 2t e determination of astronondcal
latitude, and the monitoring of polar motion caused by
wobble, rotation, precession and wandering effects (see
Ref. 1, Subsection 5.4.20). A highly precise rotation
sensor may be used to measure any changes in the length
of the day and to detect torsional oscillation in the
earth caused by earthquakes. Finally, ultraprecise
sensors may find applications in relativity-related
experiments such as the determination of the preferred
frame and dragging of inertial frames (see Ref. 2,
Subsection 5.4.20).
FREQUENCY HZ
Fig. 5.38 The sensitivity in radianslg (g = 9.8m/s2)
of a single-fiber fiberoptic accelerometer
as a function of frequency. The low-frequency
theoretical sensitivity is shown by
the horizontal line.
After A. Tveten et al., Electron Lett., — 16, 854 (1980),
●
●
●
●
NAVIGATION WQESIO –3
SURVEYING
AZIMUTH, GEODETIC LATITUDE N

● ANGULAR MOMENTUM CRYOSCOPES
MECHANICAL - ROTATING WHEELIBALL
NUCLEAR - SPINNING NUCLEI
● SAGNAC EFFECT “GYROSCOPES”
E.M. WAVES
MAITER WAVES
● DISTANT-STARS TRACKERS
Fig. 5.41
SIMPLE STAR TRACKERS
LONG-BASELINE STELL4R INTERFEROMETRY
Various rotation-rate sensor devices.
5.4.3 Interest in Optical Rotation Sensors
The main advantages of optical “gyroscopes”
over mechanical ones are briefly outlined in Fig. 5.42.
However, it is the promise of the projected low cost of
the optical devices that is driving their development.
where A is the area enclosed by the path, i.e., A = ~R2
and c ia the velocity of light in a vacuum.
The rigorous derivation of this formula is
based on the propagation of light in a rotating frame
(see Ref. 5, Subsection 5.4.20) i.e., an accelerating
frame of reference, where the general theory of relativity
must be used to perform the calculation. However,
a simple way of explaining the formula in Eq.
(5.30) iS given in Fig. 5.43. Again, consider the disc
D ----------- % 1
i’R,,@j
,’ .
2
‘1 ,,, ,’
‘., ,/’
‘.
..- --
,,
------
Lcw=2mR+R~tcw= Ccwtcw
{
Lccw=27rR-R~tccw= Cc,-wtccw
>tcw= ~c::RRQ
~At=tcw–tccw= ‘wR
IN A VACUUM CCW=CCCW=C
2*R
: tccw = Cccw + RQ
[2R~ - (Ccw - Cccw)]
Ccw ccc.
Fig- 5.42
● NO MOVING PARTS
● No wARM-UPTIME
● NO G-SENSITIVITY
. LARGE DYNAMIC RANGE
● DIGITAL READOUT
● LOW COST
● SMALL SIZE
● USES LIGHT
Potential advantages of optical rotationrate
sensors (gyroscopes).
In this section we will give a brief and
ple derivation of the Sagnac effect in vacuum and
in a medium; discuss techniques of implementing
simalso
the
Sagnac effect for the measurement of rotation together
with the fundamental limits on sensitivity in each case.
The basic principle of fiberoptic rotation aensors will
then be considered with emphasis on techniques, problem
areas, and recently achieved performance.
5.4.4 Sagnac Effect in a Vacuum
AH the optical rotation sensors under development
are based on the Sagnac effect (ace Ref. 5,
Subsection 5.4.20) which generatea an optical path difference
AL that is proportional to a rotation rate fl.
For example, if we have a diac of radius R that is
rotating with angular velocity Q, as shown in Fig. 5.43,
the optical path difference AL experienced by light
propagating along opposite directions along the perimeter
is given by:
~ At = ‘TR ~ O = %() ; ~ AL= LCW– LCCW. ~C)
Fig. 5.43 A demonstration of the Sagnac relationships
for the vacuum case.
of radius R rotating with an angular velocity !l about
an axis perpendicular to the plane of the disc. At a
given point on the perimeter, designated by 1 in Fig.
5.43, identical photons are sent in clockwise and counterclockwise
directions along the perimeter. If Q = o,
the photons, which travel at the speed of light in a
vacuum, will arrive at the starting point 1 after covering
an identical distance 2?TR in a time t = 2nR/c. Now
in the presence of a disc rotation $2, the ccw photon
will arrive at the starting point on the disc, which is
now located at position 2, after covering a distance
Lccw which iS shorter than the perimeter 2TR given by:
L Ccw
= 2TR - l?iltccw = cccwtccw (5.31)
where Ri2 is the tangential velocity of the disc and
tccw is the time taken to cover the distance Lccw. I n
addition, Lccw is also given by the product of the
velocity of light Cccw in the ccw direction and tccw.
For propagation in a vacuum Cccw = C. Similarly, the
photons propagating in the cw direction experience a
larger perimeter Lcw given by:
Using Eqs. (5.31)
tccw as given In
between clockwise
comes:
LCw = 2TR + R!ltcw = ccwtcw (5.32)
At = tcw - tccw
and (5.32) we can solve for tcw and
Fig. 5.43 so that the difference At
and counterclockwise propagation be-
. (21TR)(2Rf0/C2 =
(5.33)
AL = (4A/c)$l (5.30)
4TR2nlc2 =
(4A/c2)sl
5-15

The path length AL traveled by light in a time At is
therefore given by:
AL = cAt = (4A/c)fl (5.34)
5.4.5 Sagnac Effect in a Medium
In the case of light propagation in a medium
(see Ref. 5, Subsection 5.4.20) of refractive index n,
(Fig. 5.44) the velocity of propagation must take into
consideration the relativistic addition of the velocity
of light in the medium, i.e., c/n and the tangential
velocity of the medium, i.e., Rfl so that Ccw becomes:
Ccw = (c/n + R.Q)/(l + RQ/nc) =
c/n+RQ(l- l/n2 + ...)
(5.35)
This
given
corresponds to a nonreciprocal phase shift A$,
by:
A$ = 2~Atc/Ao = 2rAt/(A/V)
= (8.AN/aoC)c?
(5.40)
where A = A./n and v = c/n are the wavelength and sc.eed
“.
of light in the medium (n is the refractive index of
the fiber core), respectively. In terms of path length
difference:
AL = A4A012T = (4AN/c)!l (5.41)
For a fiber of length L wound in a coil of diameter D:
A = TD2/4 and N = L/nD so that:
AL = (4~/c)n = (LD/c)n (5.42)
to first
order in VIC.
Similarly Cccw,
is given by:
or:
CCCW = (c/n - IW)/(1 - RQ/nc) =
c/n-RQ(l - l/n2 + ...)
IN A MEDIUM. REFRACTIVE INDEX n
~
c
+RO
c . Cw = ~ +RQ (l– ~)+..
1+% “2
c
Ti- – R()
C&w = —
,–~
=
nc
c
7i-
–Rfl (1-~)+
(5.36)
AI$ = (2TTLD/aoC)Q (5.43)
5.4.6 The Magnitude of the Sagnac Effect
In order to get a feel for the magnitude of
AL, (Fig. 5.45) assume an area A = 100 au2 and a rota-
~~:~orate of 10-3 ~ (i.e., 0.015°/hr or 7 x 10-8 radl
For a single-turn fiber loop enclosing such an
area we get AL . 10-15 cm. This is not a very large
effect considering the diameter of a hydrogen atom is
about IO-8 cm. Clearly, a large number of turns N is
necessary to increase the magnitude of AL.
~Ccw-Cccw=2RQ (1-;)
r
~A, ~2wR[2R &(Ccw-Cccw)l ~ 2rR12R0-2R62(l-p)j
Ccwcccw
C2
“2
THESAME ASIN AVACUUM
‘EE1
Fig. 5.44 A demonstration of the Sagnac relationships
for the rotating single-loop optical fiber.
A=100cm2; Q .CiE * 10-4 rad/sec
~ AL*10-12cm
W. ‘DIAMETER- OF HYDROGEN ATOM- lo-8cm
FoR n = 10-3nE = 10-7 radlsec
Fig. 5.45 Computation of the change in effective optical
length (Sagnac effect) in a rotating
single-loop of optical fiber.
Therefore, At in a medium becomes:
At = tcw - tccw
= 21rR[2Ro - (Ccw - cccw)l/[cc#ccwl
(5.37)
UPon substitution for Ccw - Cccw from above, there is
obtained:
At = 21TR[2RQ - 2RQ(I - l/n2]/[c2/n2]
. 21TR(2RQ/C2) = (4A/c2)Q
(5.38)
which is idential to that in a vacuum. If the medium
is an optical fiber wound in a coil of N turns, then At
becomes:
At = (4AN/c2)fl (5.39)
5.4.7 Methods of Optical Rotation Sensin&
For the sake of completeness, Fig. 5.46 shows
the various schemes for the measurement of AL. On the
extreme right is the multiturn fiber interferometer
method (see Ref. 7, Subsection 5.4.20) mentioned above.
On the extreme left is the ring laser approach (see
Ref. 6, Subsection 5.4.20) and in the middle is the
passive resonator approach (see Ref. 8, Subsection
5.4.20). In both the active and the passive reaonator
approach, a nonreciprocal path length difference AL due
to the Sagnac effect becomes a nonreciprocal change in
the resonance frequency, Af, of the cavity for CW and
ccw propagation where:
Af = (4A/ioP)$l (5.44)
5-16

1
1
I
where P is the optical perimater of tha path. In the
active resonator (i.e., ring laser) approach the cw and
ccw outputs of the laser have a frequency difference
Af which IS auto~tically generated when the laser is
JIL
subjected to a rotation. In the case of the passive
resonator, Af has to be measured by means of lasers
external to the cavity (see Refs. 8 and 9, Subsection
5.4.20).
SAGNAC EFFECT I
1
I
I
ACTIVE APPROACH
PASSIVE APPROACH
[ r {
RING LASER RESONATOR
II INTERFEROMETER
PHOTON SHOT NOISE
c ~0/2
‘jf]MFG= LD ~
~
Fig. 5.48
Photon shot-noise computation for a multiturn
fiberoptic gyroscope utilizing the
Sagnac effect.
fcw
H
Fig. 5.46
fccw
I-7 d
( AL=!$N,,
&@=bA N,,
A. & -
AL
Methods of measuring the change in effective
optical length ( Sagnac ef feet).
5.4.8 Fundamental Limits in Optical Rotation
Sensors
Figs. 5.47 and 5.48 show a comparison without
derivation of the quantum noise limit for all three
cases. For the ring laser (RL) , the quantum limit comes
from spontaneous emission in the gain (see Ref. 10, Subsection
5.4. 20) medium and gives an uncertainty 6!l in
the measurement of Sl given by:
where r. is the linewidth of the ring laser cavity with
no gain; nph Is the number of photons/see in the laser
beam and T is the averaging time. For the passive resonator
(PR) case the limit is determined by photon shot
noise and is given by:
6nPR
= (kop/4A)(rc/(nphTl~T )1’2) (5.46)
where q D is the quantum efficiency of the photodetector.
As can be seen, the passive and active resonator approaches
give approximately the same limit. For the
multiturn fiberoptic (FO) interferometer ( see Ref. 11,
Subsection 5.4. 20) the photon shot noise limit is given
by:
M-lFo = (c/LD) (ko/2(nph~JjT )1/2) (5.47)
where nph is a number of photons/see leaving the interf
erometer. Al these limits are compare -# in Fig. 5.49
for A = 100 cm i ; P = 60 cm; 10 = 6 x 10 =3X
1015 photons/see corresponding to 1 mW; L =c~bOn~h(i. e. ,
N = L/P = 1000); rc = 300 kHz; IID = O. 3; and T = 1 sec.
We notice tha the uncertainty d~ in this example is
about 5 x 10
-t ,E or O. 008°/hr for all three cases.
6% x oioP/4A)(rc/(nphT) l’2) (5.45) RING LASER PASSIVE RESONATOR FIBER
● RING LASER GYRO
J-------+
1
I
1
! SPONTANEOUS
EMISSION
,
\-~:;.+.w- fccw
i
fcw
● PASSIVE RESONATOR GYRO
t+
+- + ~+
4 4
I
fccw
fcw
,\cJ P I ‘~
,)!! x — —
RLG 4A ~
~2
EXAMPLE: A = 77
P = To
L = NP
= 100 cm 2 ; Ao= 6x1O cm
c AOI 2
LD j=
= 40 cm ; n ~h = 3x1015Isec = lmW
= 400 m ; T * 1 sec
rc x 300 kHz 70 = 0.3
El
PHOTON
SHOT NOISE
-t
Fig. 5.47
I
Computation of quantum noise limits in fiberoptic
rotation-rate sensors.
I
Fig. 5.49
&f)= 4.10–4QE 7XI0 “QE 5X1O–4 f)E
0.006 “/hr 0.01 “Ihr 0.008 O/hr
Computation and comparison of the shot-noise
limits for various types of rotation-rate
sensors utilizing the Sagnac ef feet.
5-17

5.4.9 Fiberoptic Rotation-Rate Sensors
A simple configuration of a multiturn fiberoptic
rotation-rate aensor (see Ref. 7, Subsection
5.4.20) is shown in Fig. 5.50. Light from a laser or
some other suitable light source ia divided into two
beams by a 50-50 (3 dB) beamsplitter and then coupled
into the two ends of a multiturn (multlloop) singlemode
fiber coil. The light emerging from the two fiber
ends is combined by the beamsplitter and detected in a
photodetector. In the abaence of rotation, the two
emerging beams interfere either destructively or constructively
depending on the type of beamsplitter used.
For a 50-50 (3 dB) lossless beamsplitter the emerging
beams, as shown in Fig. 5.50, interfere destructively.
Fig. 5.50
d
DETECTOR
L –L~cw=~NQ
Cw
c
n
e,g. N=1000:A=100cm2: Q=f)E
=AL~16gcm
-5A
=2X1O
A$=8mANQs10-4 RAD
Aoc
NTURNS
Computation of the phaae change for a multiturn
fiberoptic interferometric rotationrate
sensor.
However, the emerging beams that return back to the
light source interfere constructively, i.e., at the peak
of a fringe. In the presence of a rotation rate $2, a
AL will be generated given by:
Typically, for a fiber attenuation rate of 1 dB/km, the
optimum length is several km.
5.4.10 Photon Shot-Noise Limit
Earlier a proof was given of a comparison of
the basic limits to the rotation measurement using the
three techniques outlined in Fig. 5.46. In this section
we will derive an approximate formula for the limit in
a fiberoptic rotation-rate sensor.
Fig. 5.51 shows a plot of intensity I or detector
output current iD versus nonreciprocal phase
shift A+ . In this case, the peak intensity, due to constructive
interference, is shown centered on A$ = O for
a zero rotation rate. In the presence of a rotation,
A+ shifts from zero and therefore a change in detection
current iD occurs. The greatest change in iD for a
given small change in A$ clearly occurs at the point on
the fringe with the maximum slope, i.e., where A$ = +
~12. Therefore, by applying a fixed nonreciprocal bia~
of T/2, the operating point can be maintained where the
sensitivity to rotation is a maximum. In this way, an
applied rotation causes a A$ which in turn generates a
change in the light intensity at the detector that is
proportional to the rotation. A problem arises when the
1
&I D
,)
;1
,1 i
,1
,1
INTENSITY NOISE
-w OY?$7
)
A+
8(A+)
- PHOTON
/ SHOT NOISE
N O I S E - -
8( AIP)s-= — iD/~ - iD/IT
T
7r
*LS .—
SIN iDm m
*OC ~=87AN
BUT A@=* —Q AOC
AL = Lcw - Lccw = (4Atf/c)n = (LDIc)Q (5.48)
where A, N, L, D have been defined earlier. This AL
will therefore cause a fringe shift Az given by:
or a phase shift of:
AZ = (LD/ioC)n (5.49)
A$ = (21TWaoC) (5.50)
For A = ~D2/4 = 100 cm2 and N = L/rD = 1000 (i.e., D
‘11.3 cm and Lx 355 meters) and if i. = 0.63 ~m and
n= 1.5, we get a phase shift of 3.0 rad for a rotation
rate of 1 rad/sec. Therefore, to detect the full earth
rotation, we must measure a phase shift of 9.1 x 10-5
radians and for typical navigation applicat ons (10-3
~) the phase ahift reduces to about 10 -{ radians.
For a given size sensor, i.e., a fixed coil
diameter D, the sensitivity may be enhanced by increasing
the length of the fiber L by adding more turns. Unfortunately
L cannot be increased indefinitely because
of the finite attenuation of optical power in the fiber.
Fig. 5.51
The optical intensity (power) or photodetector
output current as a function of
phase change and photon shot-noise computation
in a fiberoptic rotation-rate sensor.
intensity of the light source varies since this cannot
be distinguished from a change in intensity due to a
rotation. Therefore, the uncertainty in the measurement
of a given rotation rate, i.e., a given A$, must
be influenced by the intensity noise in the light. M-
though there are many ways of compensating for intensity
variations of the light source, it is not, however,
possible to reduce the effect of photon shot noise (see
Ref. 12, Subsection 5.4.20) because it is a random proceas.
Therefore under ideal conditions the uncertainty
in the measurement of A$ ia limited only by the photon
ahot noise (see Ref. 12, Subsection 5.4.20). This uncertainty
6(A$) is therefore given by:
6(A$) = (photon shot noise)/(fringe alope) (5.51)
5-18

This is a minimum where the fringe slope is a maximum.
In other words:
15(A$) z n(2eiDB) qiD .
iT(nph~DT )1’2/nph~DT
(5.52)
where e iS the electron charge; B is the bandwidth of
the detection system; nph is the number of photonsfsec
falling on the detector; ~ is the quantum efficiency of
the detector; and T is the averaging time = l/2B. Since
Eq. (5.50) iS:
A+ = 2nLD/loc
the uncertainty in the measurement of ~, i.e., 6$2, becomes:
62 = Aoc&(A41)/21rLD
Fig. 5.53
JtL
o ‘ $7 A#J—
I/
iii-
-7r 0 r 4#J—
Two DC methods for measurement of phase
change, LO, in a fiberoptic rotation-rate
sensor.
which : s the same expression given earlier.
5.4.11
= (C/LD)(lo/2)/(nphtlT)l’2 = (5.53)
cio/2LD(iD/2eB)112
Ideal Performance
The ideal performance of a fiberoptic “gyro”
may be summarized as shown in Fig. 5.52. The random
drift : s limited by photon shot noise and there should
not be any aource of bias or drift in the absence of
rotation. For a given rotation, the stability of the
scale factor, i.e., 2nLD/aoc, which related !2 to Ah
must be limited by the stability of L, D and ~o.
A much better method is to use an a.c. modulation
scheme employing nonreciprocal phase dither (see
Ref. 11, Subsection 5.4.20) as shown in Fig. 5.54. The
requirements for optimum operation are that the amplitude
of the phase modulation should be + r/2 and the
rate of the modulation should be high enou~h so that the
detector noise is dominated by photon shot noise. Fig.
5.55 is a sketch of a typical noise spectrum of a laser
showing the large “l/f” noise component at low frequencies.
The start of the ahot-noise-limited region depends
on the particular light source and can be any
where from a few kHz to a few hundred kHz. Using such
●
RANDOM DRIFT IS LIMITED BY PHOTON SHOT NOISE
.MODULATION METHODS
●
●
Fig. 5.52
5.4.12
NO BIAS OR DRIFT WHEN!! =0
SCALE FACTOR STABILITY IS LIMITED BY STABILITY OFL,D
ANDAO
Ideal performance features of a fiberoptic
rotation-rate sensor (L = coil length, D =
diameter, and i. = source wavelength).
Measurement of Nonreciprocal Phase Shift
In order to reach the ideal performance disthe
previous section, a number of problems
cussed in
must be overcome. The measurement of nonreciprocal
phase shift A@ with an uncertainty that is limited only
by the photon shot noise will now be described.
A simple way of measuring A$ is illustrated
in Fig. 5.53, where a T/2 bias is applied so as to operate
at the point of maximum slope. In thia way an increase
in intensity correaponda to a negative A$ and
vice veraa. Among the disadvantages of this method is
the stability of the bias and the need to compensate for
laser intensity fluctuations. A better method might be
to employ a differential scheme in which two detectors
are placed astride a fringe as ahown in the lower diagram
of Fig. 5.53. l%is scheme has twice the sensitivity
of the first, and better discrimination againat
intensity variations. However, it still suffers from
the instability of the operating points and requires
high common mode rejection.
Fig. 5.54
I
I
‘D
\,& .+
REQUIREMENTS:
-w ; o : w
● AMPLITuDE*r/2
e~NONRECIPROCAL
PHASE MODULATION
cRATE – HIGH ENOUGH TO GIVE SHOT-NOISE LIMIT
AC measurement of phase change, A$, in a
fiberoptic rotation-rate sensor.
It
INTENSITY
NOISE
PHOTON 1 ——-—-——
SHOT —
NOISE
o f—
Fig. 5.55
Atypical intensity-noise spectrum of a
laser showing inverae frequency (l/f) and
phase noise.
5-19

a modulation scheme, the output of the photodetector is
demodulated in a phase-sensitive demodulator followed
by a low-pass filter. In this way a zero output is obtained
at A$ . 0, a positive voltage for A+< O and a
negative voltag e
for A$ > 0. The main advantages of the
modulation method are that the peak of the interference
pattern is used as the reference point (i.e., no need
for external offset) and that the null point is independent
of intensity fluctuations as long as the modulation
rate 1S high enough as mentioned above.
5.4.13 Methods of Nonreciprocal Phase Modulation
The various possibilities for achieving nonreciprocal
phase modulation at high rates will now be
described. The phase shift $ that light experiences in
propagating along a single-mode fiber of length L and
refractive index n (Fig. 5.56) given by:
~ = 2~fnL/c (5.54)
where f 1S the frequency of the light in Hz and c is
the velocity of light in a vacuum. It should be noted
that the magnitude of $ does not depend on the direction
of propagation so that $Cw = $Ccw = $. This implies
that if L, n, or f is varied, a nonreciprocal phase
shift cannot be generated.
Therefore, in order to generate a nonreciprocal
phase shift, either Lcw ~ Lccw or ncw $ nccw or fcw
+f Ccw”
c
but suffers from the fact that orthogonally polarized
beams propagating in the fiber do not experience the
aame index thus generating a temperature dependent bias.
Another method of making ncw # nccw makes use
of the Faraday effect either in the main fiber coil or
In a separate length of fiber. By applying a longitudinal
magnetic field to the fiber it is possible to cause
the index for right circularly polarized light to be
different from that for left circularly polarized light.
Even though the Verdet constant, i.e., the constant of
proportionality between magnetic field strength and index
difference, is small, it can be enhanced considerably
by using a longer length of fiber. Again, this
scheme has been demonstrated recently (see Ref. 14, Subsection
5.4.20).
Yet another nonreciprocal index scheme that
has enjoyed much popularity is the time delay modulation
method (see Ref. 15, 16, 17, and 18, Subsection
5.4.20), illustrated in Fig. 5.57. In this case advantage
is taken of the comparatively long time the photons
spend in the fiber. A typical scheme would be to
A /
“ @~w - 4CCW = ~ fn (Lcw – Lccw)
* ‘/’
OUTPUT
‘D
2T fL (ncw – ‘Ccw)
● 4CW - @ccw ‘ ~
14’ Cw – $Ccw ~ 2$0 SIN (2T fm ~)
I
“ 4CW - 4CCW = gn Ufcw - fccw)
Fig. 5.56 Various possibilities
phase modulation.
for nonreciprocal
One possibility of making Lcw ~ Lccw whether
In a medium or in a vacuum is to mechanically dither the
interferometer at a high angular rate so that the Sagnac
ef feet itself resulting from this motion can provide the
necessary nonreciprocal phase ahift. This method has in
fact been used in early fiber gyros (see Ref. 13, Subsection
5.4. 20) but is clearly not very desirable in
general.
In order to generate a nonreciprocal refractive
index, i.e. , ncw # n ccw there me a number of methods
that could be used. A simple scheme would be to
make the polarization of, say, the cw beam orthogonal
to the polarization of ccw beam and then use an electrooptic
(E/0) phase modulator to generate a polarizationdependent
refractive index. Such a scheme has been discussed
and demonstrated ( see Ref. 11, Subsection 5.4. 20)
Fig. 5.57
AMPLITUDE OF
PHASE MODULATION
‘f FOR fm = &
The time-delay modulation method for a nonreciprocal
fiberoptic rotation-rate sensor.
pla~e a phase modulator near the beamsplitter as shown
in Fig. 5.57. The phase modulator can be constructed
in many ways, such as an electrooptic crystal, or a fiber
wound around a PZT. Now if the phase modulator is
driven at a frequency fm it is then possible to generate
a nonreciprocal phase shift given by ( see Ref. 18,
Subjection 5.4.20):
r$cw - $Ccw . 2@05in(2nfmTD/2) (5.55)
where $0 is the magnitude of the reciprocal phase shift
generated by the phaae modulation and T ~ is the delay
time in the fiber which is given by nL/c. To maximize
the nonreciprocal phase shift it is necessary to make
the argument of the sin function = n/2 i.e. , by choosing
fm = 112 ~. If fm is less than l/2TD, $0 has to be
increased to achieve the appropriate amplitude of the
nonreciprocal phase shift. For a 1 km fiber the optimum
f m is about 100 kHz.
5-20

The generation of nonreciprocal phase modulation
by the frequency method will now be described (see
Refs. 11 and 18, Subsection 5.4.20). In this scheme
fcw is made different from fccw so that:
@ Cw -0 Ccw
= (2nnL/c)(fcw - fccw) (5.56)
A simple way of implementing this method is by employing
two acoustooptic (A/0) frequency shifters placed
symmetrically on either side of the beamsplitter within
the interferometer. By driving the A/O with independent
oscillators it is possible to generate both nonreciprocal
phaae modulation as well as fixed nonreciprocal
phase shifts. For example, In a 1 km fiber a frequency
difference fcw - f ccw of 50 kHz generates a nonreciprocal
phase shift of T/2.
Related frequency methods have also been investigated
(see Refs. 19 and 20, Subsection 5.4.20).
5.4.14 Open Loop and Closed Loop Operation
The open loop sensor system is shown in Fig.
5.58 where a nonreciprocal phase modulator (NRPM) is
placed near one fiber end and driven at fm. The output
of the photodetector is then demodulated at fm in
a phase senaitive demodulator. After low pass filtering
the demodulator output is a sinusoidal function of
At as illustrated in Fig. 5.58. For any given A$, a
d.c. voltage output is obtained which is proportional
to A$. The disadvantages of the open loop system include
(a) the calibration of the demodulator output
since this depends on the gains of the various amplifiers
that precede it as well as on the intensity of
the light source and (b) the nonlinear behavior of the
demodu~ator output with A$.
1,
T
II
NRPT
LIGHT NRPM I
1. — A II
I
w fm
l--cl
~ETEcToRL A —
Fig. 5.59
I
/
NULL
DEMOD
OUTPUT
-u Smo
*
Closed-loop nonreciprocal phase modulation
in a fiberoptic rotation-rate sensor.
‘She advantages of the closed loop system over
the open loop system include (a) the output is independent
of light source intensity variations since the system
ia always operated at null (the modulation frequency
must be high enough to reach the photon shot noise);
(b) the output is independent of the gains of individual
components in the measurement system as long as a very
high open-loop gain is maintained; and (c) the output
linearity and stability depends only on the NRPT.
The NRPT could, for example, be a Faraday effect
device or an acoustooptic frequency shifter. If a
Faraday device is used, then the stability depends on
the stability of the length of the fiber and the atability
of the magnetic-field/phase-shift transfer function.
However, if the NRPT is an acoustooptic crystal,
then a frequency difference Af = fcw - fccw is generated
to offset a A$ = (21TLD/loC)n caused by a rotation.
Therefore:
A+
LIGHT
SOURCE
DETECTOR
OUTPUT I
wAIP
which implies that:
A+ = 2rAfnL/c = (21TLD/aoC)il (5.57)
Af = (D/nAo)!2 (5.58)
Eq. (5.58) indicates that the scale factor stability
depends on the coil diameter D, n, and ~. If the numerator
and denominator of Eq. (5.58) is multiplied by
nD/4, then:
Fig. 5.58
Open-loop nonreciprocal phase modulation in
a fiberoptic rotation-rate sensor.
In the closed loop system (see Refs. 11 and
18, Subsection 5.4.20), shown in Fig. 5.59, the output
of the demodulator is passed through a servo amplifier
which then drives a nonreciprocal phase transducer
(NRPT) placed within the fiber interferometer. In this
way, the sensor is always operated at null, i.e., at
A+ = O by generating a suitable nonreciprocal phase
shift in the NRPT that is equal to but opposite in sign
to that generated by a rotation 0. The output of the
system ia then the output of the NRFT. Therefore, the
NRFT becomes a critical element.
Af = [(nD2/4)/(nlomD/4)]~ = (4A/XoP)fl (5.59)
where P is the optical perimeter = nTD of the fiber
coil. It should be noted that Eq. (5.59) is identical
with Eq. (5.44) for either the ring laser or the passive
reaonator approach.
5.4.15 Problems in Fiberoptic Rotation Sensors
So far the basic principles of fiber rotationrate
sensors with emphasis on the measurement of small
nonreciprocal phase shift in a multiturn fiber interferometer
have been described. A number of error aources
that can influence the performance of the fiber gyro
will now be described briefly.
5-21

Fig. 5.60 lists several sources of error that
must be dealt with in order to achieve the predicted
performance. Perhapa the major source of noise is backscattering
within the fiber (see Ref. 21, Subsection
5.4.20) and at interfaces, particularly in a setup that
employs discrete components. To overcome this problem,
researchers have used broadband lasers (see Ref. 17 and
22, Subjection 5.4.20), frequency jittered lasers (see
Ref. 18, Subsection 5.4.20), phase modulators, (see Ref.
23, Subsection 5.4.20), and even light-emitting diodes
(LED) (see Ref. 24, Subsection 5.4.20). By destroying
the temporal coherence of the light source the detection
system becomes sensitive only to the interference be-
5.4.16 Integrated Fiber “Gyros”
Although the early investigation of fiberoptic
“gyros” employed (see Refs. 19, 30, 32 and 33, Subsection
5.4.20) discrete optical components for convenience,
it is clear that if fiber gyros are to make a
large impact an integrated (see Ref. 34, Subsection
5.4.20) optical system (Fig. 5.61) with a semiconductor
laser/LED as a light source must be uaed. Beamsplitters
can be replaced by either waveguide or fiber 3-dB couplers
(see Ref. 17, Subsection 5.4.20). Nonreciprocal
RAYLEIGH SCAITERING IN FIBER
SCAITERING FROM INTERFACES
POLARIZATION EFFECTS
PRESENCE OF HIGHER ORDER MODES
TEMPERATURE GRADIENTS
NONIDEAL MODULATORS
NONIDEAL POLARIZERS
INTENSITY DEPENDENT NONRECIPROCITY
LIGHT SOURCE PROBLEMS
MEASUREMENT SYSTEM PROBLEMS
STRESS INDUCED EFFECTS
MAGNETIC FIELD EFFECT
Fig. 5.60 Sources of noise and errors that must be
considered in the design of a fiberoptic
rotation-rate sensor.
tween waves that followed identical counter-propagating
paths. Thus, interference due to backacattering will,
in principle, average to zero.
The problem that has received much attention
both theoretically (see Refs. 25 and 26, Subsection
5.4.20) and experimentally (see Ref. 17, Subsection
5.4.20) is the error due to the polarization behavior
of the optical fiber. By uaing polarizers to establish
the axis of polarization (see Ref. 26, Subsection
5.4.20) in the long-fiber interferometer, it has been
possible to reduce polarization-dependent errors. The
use of the now available single-mode polarization-preserving
fibers (see Ref. 27, Subsection 5.4.20) may
turn out to be a convenient solution.
4I
Fig. 5.61
I
Q=POuTpuT
f~
NR MODULATOR
An open-loop integrated fiberoptic rotation-rate
sensor employing a phase transducer.
phase modulators may employ a short length of fiber
wound around a PZT, the Faraday ef feet, an integrated
Bragg cell, or other features.
Integrated polarizers (see Ref. 17, Subsection
5.4. 20) and polarization controllers (see Ref. 17,
Subsection 5.4. 20) are also feasible. In the closed
loop approach shown in Fig. 5.62 the nonreciprocal
phaae transducer could be a Bragg cell, a Faraday effect
device, or other device. In other words various
possibilities exist for constructing a solid-state fiber
gyro. An all-optical-fiber open-loop system has
already been demonstrated with a very promising performance
(see Ref. 17, Subsection 5.4.20).
All the fiber gyros under study so far have
used single mode fibers. Care has to be taken to insure
that higher order transverse modes are highly attenuated.
A number of error sources are related to temperature
gradients, (see Ref. 28, Subsection 5.4.20)
non-ideal polarizers, (see Ref. 29, Subsection 5.4.20)
non-ideal modulators, stress induced effects, external
magnetic field effects (see Ref. 30, Subsection 5.4.20)
and electronics problems in the measurement system.
A very basic source of nonreciprocal phase
shift has been uncovered, namely that due to unequal
intensities propagating along opposite directions in
the fiber (see Ref. 31, Subsection 5.4.20). This is a
nonlinear optical effect based on four-wave mixing that
takes place in a fiber having a third order nonlinear
susceptibility. Such an intensity-induced nonreciprocity
may be reduced by maintaining equal intensities
in the counterpropagating beam.
5-22
Fig. 5.62
I
SERVO
DETECTOR
f~
A closed-loop integrated fiberoptic rotaa
tion-rate sensor employing
phase trans-
ducer.

5.4.17~
Once the various noise mechanisms in fiber
gyros were uncovered and understood, published performance
data began to improve rapidly. Fiber gyros employing
several hundred meters of fiber wound around a coil
of 15 to 20 cm in diameter have demonstrated short term
drifts in the range of 0.1 - O.01”/hr for averaging
times of about 10 seconds (see Refs. 17 and 18, Subsection
5.4.20). Long term drift of O.lO/hr for more than
one hour has also been demonstrated (see Refs. 17 and
18, Subsection 5.4.20).
5.4.18 Summary of Rotation-Rate Sensors
In summary, fiberoptic rotation sensors have
demonstrated promising preliminary performance. However
most of the causes of short term noise are understood,
the causes of long term drift need further study. Clearly,
the emphasis must now be placed on integrated device
development.
5.4.19 General Conclusions Regarding Fiberoptic
Sensors
It may be concluded for this entire chapter
that fiberoptic sensors demonstrate tremendous potential
for application in any area that requires the sensing
of physical parameters, including electric fields,
magnetic fields, forces, temperature, pressure, linear
and rotation displacements, velocities, and accelerations.
Application areas include navigation, medical
engineering, surveying, transportation, telemetry (communication),
in fact, any area in which measurements
are to be made.
5.4.20 References
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
D.H. Eckhardt, Proc. Soc. Photo-Opt. Instru. Eng.
~, 172 (1978).
M.O. Scully, in Proc. of the Fifth International
Conf. on Laser Spectroscopy, H. Walther and K.
Rothe, eds. (Springer-Verlag, Berlin, 1979); M.P.
Haugan, M.O. Scully, and K. Just, Phys. Lett. ~,
88 (1980).
J.H. Simpson, Astron. & Aeron. ~, #10, 42 (1964).
G. Sagnac, Compt. Rend=, 708 (1913).
E.J. Post, Rev. Mod. Phys. 39, 475 (1967). —
A.H. Rosenthal, J. Opt. Soc. Am. ~, 1143 (1962).
V. Vali and R.W. Shorthill, Appl. Opt. ~, 1099
(1976).
S. Ezekiel and S.R. Balsamo, Apply Phys. Lett. 30, —
478 (1977).
G.A. Sanders, M.G. Prentiss and S. Ezekiel, Opt.
Lett. ~, 569 (1981).
T.A. Dorschner, H.A. Haus, M. HoIz, I.W. Smith,
and H. Stata, IEEE. J. Quant. Electron, QE-16,
1376 (1980).
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
32.
33.
34.
G. Pircher, M. Lacombat and H. Lefevre, Proc. Soc.
Photo-Opt. Instrum. Eng. 157, 212 (1978). —
W.C. Davis, W.L. Pondrom and D.E. Thompson, Proc.
of International Conf. on Fiberoptic Rotation Sensors,
M.I.T., (Nov. 1981), Springer-Verlag (to be
published).
H. Arditty, M. Papuchon, K. Thyagarapan, and C.
Puech in Digest or Topical Meeting on Integrated
and Giroled-Wave Optics, O.S.A. Meeting, Washington,
D.C. (1980).
R. Ulrich, Opt. Lett. ~, 173 (1980).
R.A. Bergh, H.C. Lefevre and H.J. Shaw, Opt. Lett.
~, 502 (1981).
J.L. Davis and S. Ezekiel, opt. Lett. g, 505
(1981).
D.E. Thompaon, D.B. Anderson, S.K. Yao and B.R.
youmans, Appl. Phys. Lett. — 33, 940 (1978).
R.F. Cahill and E. Udd, Opt. Lett. ~, 93 (1979).
C.C. Cutler, S.A. Newton, and H.J. Shaw, Opt. Lett.
~, 488 (1980).
R. Ulrich, Opt. Lett. ~, 173 (1980).
K. Bohm, P. Ruaser, E. Weidel and R. Ulrich, Opt.
Lett. ~, 64 (1981).
K. Bohm, P. Marten, K. Petermann, E. Weidel and
R. Ulrich, Electon. Lett. ~, 352 (1981).
R. Ulrich, Proc. of International Conf. on Fiberoptic
Rotation Sensors, M.I.T. (November, 1981),
Springer-Verlag (to be published).
G. Schiffner, W.R. Leeb, H. Krammer and J. Wittmsn,
Appl. Opt. 18, 2096 (1979). —
I.p. Kaminow, J. Quant. Elect. Q.E.-17, 15 (1981).
D.M. Shupe, Appl. Opt. 19, 654 (1980). —
E.C. Kintner, Opt. Lett. ~, 154 (1981).
K. Bohm, K. Petermann and E. Weidel, Opt. Lett. ~,
180 (1982).
S. Ezekiel, J.L. Davis and R. Hellwarth, Proc. of
International Conf. on Fiberoptic Rotation Sensors,
M.I.T. (Nov. 1981), Springer-Verlag (to be
published).
R. Goldstein and W.C. Rnss, Proc. Soc. Photo-Opt.
Instrum. Eng. 157, 122 (1978).
M.N. McLandrich and H.F. Rast, Proc. Soc. Photo-
Opt. Instrum. Eng. ~, 127 (1978).
M. Papuchon and C. Puech, Proc. Soc. Photo-Opt.
Instrum. Eng. 157, 218 (1978). —
11.
12.
J.L. Davis and S. Ezekiel, Proc. Soc. Photo-Opt.
Instrum. Eng. 157, 172 (1978). —
A. Yariv, “Introduction to Optical Electronics”,
Holt, Rinehart, & Winston, (1976).
5-23

CHAPTER 6
FIBEROPTIC SENSOR ARRAYS
AND TELEMETRY SYSTEMS
Ease of multiplexing and modulation and the
fundamental properties of lightwaves and optical fibers
make them suitable for use in multisensory uniform and
random arrays for many different applications. This
chapter will cover the important characteristics of sensor
arrays, their connection into telemetry systems for
transmission of baseband data within the array, and the
characteristics of fiberoptic transmission lines for
telecommunication systems.
6.1 FIBEROPTIC SENSOR ARRAYS
6.1.1 Fiberoptic Sensor Array Design
Considerations
6.1.1.1 General Design Considerations
The sensor system selected for a particular
application will depend on many considerations. For
example, the individual sensors that are selected depend
on the parameter to be sensed, the sensitivity re -
quired, the dynamic range of the parameter to be sensed,
the baseband frequencies, and the noise and Power
levels. The geographic distribution of the sensors in
an array will be governed by the distribution of locationa
at which parameters are to be aenaed. Other
variables to be selected are the modulation scheme and
whether an analog or a digital form will be used for a
particular application. These and other considerations
may be summarized as follows:
used, and the telemetry methods that are used. Design
aspects differ from one basic configuration to another,
therefore detailed design aspects will be discussed in
the next subsection, Fiberoptic Sensor Array Basic Configurations.
6.1.2~
The method of energizing an array and the
type of fiberoptic sensors used in the array are often
interrelated. For example, suppose an array of baseband-modulated
darkfield microbend sensors are each
sequentially mounted on a single fiber and each is preceded
by a mode-stripper in such a manner that each
microbend sensor of the baseband signal causes an amount
of light proportional to the baseband signal amplitude
to enter the cladding. Following each microbender is
a tap designed to remove this baseband signal from the
cladding and send it via the tap (coupler) to a common
return bus. The return bus output signals may be
photodetected as shown in Fig. 6.1. If the array is
PULSED
LIGHT
SOURCE
(LASER) 1
MODE STRIPPER
MODE STRIPPER
FIBEROPTIC SENSOR ARRAY DESIGN CONSIDERATIONS
SENSOR TYPE
Intensity Modulation
Phase Modulation
Frequency Modulation
Polarization Modulation
Wavelength Modulation
DISTANCE BETWEEN SENSOR ELEMENTS
ANALOG VS DIGITAL TRANSMISSION
SIMPLEX, DUPLEX, MULTIPLEX, OR COMBINATION
SIGNAL PROCESSING REQUIREMENTS
SENSOR/LINR CALIBRATION REQUIREMENTS
POWER LEVELS
SYSTEM NOISE
NUMEER OF SENSOR CHANNELS
MAXIMUM FREQUENCY OF SIGNAL INFORMATION
OPERATIONAL NOISE ENVIRONMENT
SIGNAL DYNAMIC RANGE
SENSOR LEAD LENGTHS
DESIRED TRANSMISSION SCHEME
DESIRED MULTIPLEXING
6.1.1.2 Specific Design Considerations
Detailed design considerations for a fiberoptic
sensor array and associated telemetry depend on
the method of energizing the array, the type of sensor
6-1
DETECTOR
Fig. 6.1
TAP TAP TAP
BUS COUPLERS
A fiberoptic darkfield microbend sensor array
telemetry system with single return bus.
a linear array of equally spaced sensors and the optical
feed bus is pulsed, the pulses on the return bus
will be automatically time-division multiplexed for
the return telemetry. If the sensors are not equally
spaced and the amount of fiber required to create
equal spacing is excessive, the arrangement shown in
Fig. 6.2 can be used. The source output is continuous
in this case. Each microbend cladding mode stripper
output is fed to a separate photodetector via an independent
optical fiber as shown in Fig. 6.2. Return
telemetry for both of these arrangements is discussed
below in greater detail. Both of these arrangements
make use of darkfield sensing.

CONTINUOUS
LIGHT
MODE
STRIPPER
. .
: : . .
MICROBEND SENSOR ARRAY
MODE STRIPPER
STRIPPER
,
energized and either the return optical cables are each
returned to a photodetector in an array, or the return
bus may be a single optical cable with time-division
multiplexed signals from equally-spaced sensors fed to
a single photodetector as discussed earlier.
The sensor array can also consist of an array
of optical grating sensors that modulate the output of
individually-coupled light sources (LEDs) powered by
light pulses on a common electrical bus as shown in
Fig. 6.5. The grating outputs are individually coupl-
Fig. 6.2
A fiberoptic darkfield microbend sensor array
telemetry system with multiple cable
return.
ELECTRICAL POWER BUS
>
I
Brightfield sensing can also be accomplished
in a fiberoptic sensor array as shown in Fig. 6.3. A
STAR COUPLER
I
.
CONTINUOUS \ .)
:
fl “ ‘
PHOTODETECTOR
ARRAY
Fig. 6.5
))
A fiberoptic optical grating electricalbua-fed
senaor array telemetry system.
Fig. 6.3
DETECTOR
ARRAY
)
: MICROBEND BRIGHTFIELD
SENSOR ARRAY
A fiberoptic microbend brightfield starcoupler-fed
sensor array telemetry system.
star coupler is fed by a continuous light source, e.g.,
a laser or an LED. Each output of the star-coupler is
fed to a baseband-modulated microbend fiberoptic brightfield
sensor. The output signal of each fiberoptic
sensor in the array is separately fed to an array of
photodetectors for further processing and transmission.
~so, an electrical power bus to a light source (LED)
at each sensor can be used to energize the basebandmodulated
microbend fiberoptic brightfield sensor as
shown in Fig. 6.4. The electrical bus is continuously
LIGHT SOURCE
ELECTRICAL POWER BUS
)
‘“Ḟ .
I
(LED) (LED) (LED)
. ● MICROBEND SENSOR
.
. ARRAY
.
.
.
.
/
Fig.
DETECTOR ARRAY
6.4 A fiberoptic microbend brightfield electrical-bus-fed
sensor array telemetry system.
6-2
ed to photodetectors in an array via fiberoptic cables.
Some of the performance features of these and other
fiberoptic sensor array configurations will now be
discussed in some detail.
An array of sensors may be used to beam-form
or to signal average. In the former case it is necesaary
to distinguish, i.e. maintain separation of, the
output signals from the individual sensors. In the
latter case the signals from a number of sensors are
summed (OR-gated). For example, beam forming is used
in echo ranging, while averaging can be used to discriminate
between signals that arrive normal (perpendicular,
transverse) to a linear array and those that
arrive parallel (longitudinal) to the array. Thus,
very often the spatial distribution of an array of
fiberoptic sensors can be used to accomplish the multiplexing,
mixing, or summing, of signals from the array.
Although the principle of operation of only a linear
array of sensors will be discussed, the same principles
can be applied to multidimensional arrays.
A linear array of fiberoptic sensors may be
energized by means of a common bus. The bus may be an
electrical conductor, fed by a direct-current power
source or an alternating-current power source, or the
bus may be an optical fiber fed by a relatively highpowered
optical continuous-output source, such as a
laser. Alternatively, in each of these situations, the
power source output can be pulsed rather than be continuous,
giving rise to four posaible arrangements,
namely continuous electrical, continuous optical,
pulsed electrical, and pulsed optical power. In any
caae, the fiberoptic sensors (transducer, modulators)
in the linear array may be either directly connected
to the optical bus by means of a fiberoptic coupler,
or a light source at each sensor may be connected to
the electrical bus. The selection of the appropriate

method of sensor energization will depend on the power
budget, risetime budget, distances to and within the
array, and other matters related to the specific application.
For the pulsed-bus method of energization of
an equally-spaced linear array of sensors, spatial distribution
of the sensors will cause the baaeband-modulated
output signal pulse from each sensor of the array
to occur at a different time according to the time it
takes for a pulse to propagate from one sensor to an -
other. If these signals are all fed into a single
common return bus, they will be automatically timedivision
multiplexed on that bus. This arrangement is
shown in Fig. 6.6. Assume a pulse of light is dis-
‘Warray = l/t = c(m - 1)/2nL (6.2) length of the array, c is the velocity of light in a
For 50 sensors in a linear array, an optical
fiber bus core refractive index of 1.5, a linear array
500 meters long, Eq. (6.1) indicates that the time between
the leading edges of array output pulses is:
to=(2)( l.5)(500)/3(108) (49)=102 ns (6.3)
The corresponding pulse repetition rate, PRR, is:
PRR = l/t. = 1/102(10-9) = 9.8 kfPPS. (6.4)
Thus, the input feed bus pulses cannot be
wider than to. This is the rate at which the basebandsignal
modulated pulses will emerge from the input-output
end of the array. Also, some time should be allowed
between pulses for random variations of sensor spacing,
delays through sensor leads from and to the busses, and
pulse risetimes. Therefore, the pulse length should
not exceed 0.9to or about 90 ns for the above example.
If they are wider, they are liable to overlap in the
return bus. They can be narrower. The pulses will ar -
rive as a train of pulses at the photodetector. The
pulses in the train will come from and be in the same
sequence as the sensors are positioned in the linear
array. These events occur each time the feed bus is
pulsed and as many pulses will be in each array output
pulse train as there are sensors in the array. The
photodetector must be capable of responding to about
10 Mpps for the above example. If any analog-to-digital
(A-D) conversion is to take place in a single A-D
PHOTO– PULSED
OETECTOR SOURCE
converter fed by the return bus, the length of the
pulses must be long enough to allow for analog to digital
conversion. The repetition rate of the pulses in
I r PULSED SOURCE OPTICAL FEEO BUSwlTH M. l
LENGTHL~
the train can be reduced by placing additional fiber
)J LINEAR ARRAY between the sensors or by using a fiber with a higher
refractive index, as indicated by Eq. (6.2).
SPACEDINTENSITY-
. . .
MODULATION
{r
)J
Various methods can be used to telemeter the
sensor-modulated signals from the sensor array to a
EQUALLY-SPACEO PULSES IN AN OPTICAL RETURN SUS
photodetector. For example, the detector could be an
A fiberoptic darkfield optical-bus-fed sensor
array telemetry system with single op-
is required, or the output of the photodetector could
optical repeater if long distance optical transmission
tical return bus.
be transmitted electrically, via a wire line, coaxial
cable, or radio-link. The radio frequency carrier
could be modulated by the detected analog pulses or by
A coupler at each sensor an analog-to-digital converter output. The above discussion
applies each time a single light pulse is sent
along the fiber bus. The maximum safe pulse duration
was shown to be, from Eq. (6.1) and allowing a 10%
The modulated pulse travels via the return bus safety margin:
‘msx = 1.8nL/c(m - 1) (6.5)
The maximum rate at which the pulses can be
dispatched down the optical fiber feed bus is limited
The distance between sensors is by the overall length of the array. Each pulse must
travel twice the full length of the array and clear the
The wave has to travel first sensor before the next pulse can be applied to
the array. This maximum pulse rate is the maximum rate
at which the baseband signal inputs to the fiberoptic
aensors can be sampled. The minimum time between leading
edges of feed bus pulses is twice the time length
of the array, plus the pulse length (maximum possible
The time pulse width is assumed) plus a safety margin for risetime
and settling time. Therefore, these considerations
the time between leading edges of output pulses
will yield a minimum sampling period ts of:
to=2[L/(m-1)] /(c/n)=2nL/c(m-1) (6.1)
t+ = 2nL/c + 1.8nL/c(m - 1) + tr
(6.6)
ts = [2 + 1.8/(m - l)]nL/c + tr
where m is the number of aenaors in the linear array, n
is the refractive index of the fiber busses, L is the
The physical parameter variation (baseband)
to be sensed, such as a sound wave, a magnetic field
variation, a pressure wave, or a force variation, will
modulate the optical input to the fiberoptic sensor,
thus producing an optical baseband-modulated signal output.
This sensor output signal can be telemetered to a
distant location (for detection and processing) in any
of a number of different ways depending on spatial,
timing, compositional, and other factors.
Fig. 6.6
patched along the feed bus.
location taps a fraction of the light from the bus.
The pulse of light enters each sensor in turn where it
is modulated by the baseband signal imposed by the sensor.
bsck to the photodetector for further processing. The
minimum time that can be allowed for the spacing between
the leading edges of pulses in the return bus is
the propagation time between a given sensor location
and the next sensor in the array and return to the given
sensor location.
L/(m - 1), where L is the length of the linear array
and m is the number of sensors.
the distance between aensors in the feed bus and in the
return bus, therefore the travel distance is 2L/(m - 1).
The speed of propagation of a lightwave in the bus is
c/n, where c is the speed of light in a vacuum and n
is the refractive index of the core. It iS assumed the
refractive index is the same for both busses.
of propagation is the distance divided by the speed,
thus,
is:
The pulse repetition rate (PRR) of the pulses emanating
from the linear senaor array is given by:
6-3

vacuum, and t= is the overall risetime to be calculated
later in this chapter. This value of ta can be reduced
to the extent that the pulse width can be reduced.
If there are only a few sensors in the array the
second term in bracketa in Eq. (6.6) is significant.
As the number of sensors is increased, the second term
in Eq. (6.6) becomes less significant. Eq. (6.6) does
not apply to one senaor because then L = O, the second
term in brackets becomes indeterminate, and in fact
there is no array. In this case, only the risetime
requirement will place a limit on the sampling period.
The maximum permissible sampling rate PR~s is:
requirement for any specific spatial relationship among
the sensors. The minimum sampling period for each sensor
tssen in the array will be:
‘asen
= mtad (6.9)
where m is the number of sensors in the array and tad
is the analog-to-digital conversion time. This presumes
a photodetector for each sensor output, a multiplexer
(for polling each photodetector output), and a
aingle A-D converter with its sample-and-hold and other
associated circuitry aa shown in Fig. 6.8.
Pluqs.= l/ts (6.7)
where ts is defined in Eq. (6.6). The sampling rate
can be arbitrarily reduced, but should not be less than
twice the highest significant frequency component in
the baseband signal in order to obtain reproduction of
the baseband signal without significant distortion
(Nyquist criterion).
Another method for energizing an array of sensors
is to connect the array to a pulsed electrical bus
as shown in Fig. 6.7, rather than the pulsed optical
>#
I
l--+-l
EEk5?ltlzl
‘1
LENGTH L-~
WLSSDELECTRICALF
7’I w ,
EWAUY-SPACEDPJSES NANOFTCAL REluRssus SENSORS
L-RARRAY
OFMEWY
SPACEDSENZORS
WITNLSOAND
INTSN.91v-M~L4T10N
Fig. 6.8
A fiberoptic star-coupler-fed sensor random
array telemetry system with multiple and
single cable returns.
Fig. 6.7
A fiberoptic lightfield pulsed
bus-fed sensor array telemetry
single optical return bus.
electricalsystem
with
The random array of fiberoptic sensors may be
energized instead by a direct-current electrical bus
as shown in Fig. 6.9. In this case, there is a contin-
bus just described. A light source, such as an LED, is
optically connected to each sensor. Thia is the brightfield
form of senaor energization. The return bus can
be the same, as was shown in Fig. 6.6, and the analysis
above still applies except that the propagation time
in the electrical bus will be different. In this case,
the electrical sampling pulae period will be:
CONTFWOUS (DC) ELECTRICAL FEED BUS
telec=l/2 [ts+[2+l.8/(m-l)]L/v+trc] (6.8)
where the variables are as in Equation (6.6), v is the
velocity of propagation in the electrical bus, and trc
is the combined electrical and optical risetimes that
will be discussed later in this chapter.
Another configuration for energizing a randomly-distributed
(non-linear) array of fiberoptic aensors
is shown in Fig. 6.8. A continuous source of
light (laser) energizes a star coupler that may be
placed at the center of the array to reduce fiber requirements.
The output of the coupler is fed to each
fiberoptic sensor where it is modulated by the baseband
signal. The senaor outputs are individually fed to an
arrayof photodetector (PDs). In the arrangement
shown in Fig. 6.8, the inputs to the photodetector (PD)
array (one PD for each sensor) are time-division multiplexed,
sampled, digitized, and telemetered as a digital
data bit stream via a fiberoptic cable to another
location for exploitation. In this case, there ia no
6-4
Fig. 6.9
A fiberoptic electrical direct-current busfed
sensor array telemetry aystem with
multiple and single cable return.
uous-output light source (LED) for each sensor. The
baseband-modulated optical output of each sensor is
separately cabled to a photodetector array and processed
there in a manner similar to the preceding arrangement
that had the continuous optical feed as was shown
in Fig. 6.8.
J

1
The preceding discussion applied primarily to
intensity-modulated lightfield and darkfield sensors.
The outputs of arrays of other tYPes of sensors can
also be telemetered to locations distant from the sensors.
An interferometer sensor array configuration is
shown in Fig. 6.10. The optical outputs of all fiber-
(REPEAT OF
R,G”T S,DE,
Fig. 6.10
OPTICAL BuS
mL——...-.!
\
I
COUPLERS
ELECTROOPTIC PHOTODETECTORS
INTEGRATED CHIP DETECTIONIFEEDBACK
DIGITIZATION(MULTIPLEXER
LED
CLOCK
L
A fiberoptic interferometric star-couplerfed
sensor array telemetry system with optical
multiple cable and single cable return
and integrated optical circuit chip.
. . .
There are many other variations and combinations
of the basic fiberoptic sensor-array telemetry
schemes shown here. The basic options include the
selection of the type of telemetry link (to and from
the sensor array, electrical, optical, or electrooptical);
the type of fiber optic sensor (interferometric,
intensity, phase, darkfield, brightfield); the type of
coupling (star, tapped bus); the type of light sources
(laser-powered or LED-powered bus, LED at each sensor);
signal types (analog, discrete); multiplexing schemes;
and many others. Each of these options will incur a
different set of technical problems that require solution,
a different set of costs, and a different set of
performance characteristics. For example, frequencydivision
multiplexing of fiberoptic sensor outputs can
also be applied by energizing the common feed bus of
the equally-spaced-sensor arrays discussed earlier with
a constantly-changing-frequency pulse (frequency ramp).
Thus, each fiberoptic sensor in the linear equallyspaced
array will be fed a different frequency to be
modulated by the baseband signal. The outputs can be
demultiplexed with appropriate narrowband filters.
6.1.3 Fiberoptic Sensor Array Budgets
Fiberoptic aensor array budgets may be prepared
in much the same manner as for the telemetry budgeta
to be described in Subsection 6.2.3. Risetime,
power, cost, and other budgets for fiberoptic sensor
arrays depend on the same set of factors as for the
entire sensor-telemetry system. tin optical power budget
for the sensor array shown in Fig. 6.20 is as
follows:
optic sensors are brought to a common point, an electrooptic
chip. The integrated optical chips are not
yet commercially available, however, they are under
development. A single optical fiber is used to conduct
the output of the electrooptic chip to a distant location.
Ml signal processing is done at the array location
on the chip. The output of each senaor is sent
to the single integrated fiberoptic chip for processing
via a separate fiber. If It should prove desirable to
use less fiber, use can be made of the spatial separation
between sensors and the outputs can be automatically
time-division multiplexed provided the signal processing
can be accomplished at each interferometric
sensor as ahown in Fig. 6.11. In this arrangement, a
single optical return bus is used to telemeter the outputs
to a distant location.
T!+AE Owwm MULTIPLEXER
Fig. 6.11
0 ~-–
LASER 1
I
REFEREW3EARM ‘
II
II
POWER>
ELECTRCAL BUS :
L--—-.——
...__._J
ELECTROOPTCCH!P
Tlt.lEDIvISlON
MULTIPLEXER
A fiberoptic interferornetric star-couplerfed
equally spaced sensor array telemetry
system with electrical outputs to a single
electrical return bus.
6-5
SENSOR ARRAY POWER BUDGET
OUTPUT POWER
Laser output power
Coupling loas in fiber
pigtail (78% Coupling)
AVERAGE POWER OUTPUT
SYSTEM LOSS
Star coupler insertion loss
Star coupler splitting loss (1:60)
Coupler insertion loss (2, ldB each)
3 dB coupler aplitting loss
Fiber loss (300 m, 5 dB/km)
Splicing loss (6, 0.5 dB each)
TOTAL
TOTAL
POWEṚ
6.2
SYSTEM LOSS
AVAILABLE MARGIN 37.3 - 29.3 =
MARGIN AT EACH DETECTOR
Antilog of 0.80 =
FIBEROPTIC TELEMETRY SYSTEMS
7 mW = 38.5 dB VW
- 1.2 dB
37.3 dB UW
2.0 dB
17.8
2.0
3.0
1.5
3.0
29.3 dB
8.0 dB VW
6.3 UW
The properties of optical fibers and fibersensors
have been discussed in detail in prior
optic
chapters where particular attention was given to construction
(materials and geometry), principles of operation
(light transmission properties of fibers), and
relative advantages of fiberoptic sensors over other
types of sensors. Various ways were discussed in which
fiberoptic sensors can be designed to measure absolute
magnitudes or relative changes of a physical parameter,
develop an output signal that is a function of these
absolute or relative values, and emit this signal in a
form suitable for subsequent processing and transmission.
In essence, the fiberoptic aensor is a transducer;
it provides the transform that enables an on-

site measurement of a physical parameter to be represented
in a form (baseband signal) that can be directly
and immediately processed and transmitted to another
location, where it can be further processed and exploited
for any desired use or application. Most, if
not all, applications will require that the signal from
a sensor be telemetered to a location other than the
point of its generation. There are virtually no limits
on the range of telemetering distances that may be required.
llus, many fiberoptic sensors permit direct
optical data transmission without conversion to electrical
signals until photodetection. This section will
be devoted to the configuration and use of fiberoptic
sensor arrays, the telemetering of their outputs to
other locations, and the reconversion of these signals
to useful forms. Topics include system considerations,
sensor systems, data transmission, data link analysis,
repeater design, cable and connector design, and the
budgeting of time, power and cost in telemetry systems.
These topics may be summarized as:
FIBEROPTIC:
TELEMETRY SYSTEMS
SYSTEN GENERAL CONSIDEIbiTIONS
LINR ANALYSIS: RISETINE, POWER,
AND COST BUDGETS
SENSOR SYSTEMS
REPEATER DESIGN
CABLE AND CONNECTOR DESIGN
END-TERMINAL RECEIVER CONSIDERATIONS
The basic components of a telemetry system, from the
sensors of the variations of a physical parameter to
the instruments for displaying, recording, or simply
using a representation of the variation at some destination
user location are shown in Fig. 6.12.
P
?
PHYSICAL
PARAMETER
0TRANSDUCER
I
El
s-f(p)
ENCODER
MOOULATOR
MULTIPLEXER
CONVERTER
TRANSMITTER
SOURCE
YEND INSTRUMENT
DISPLAY
SOUND
RECORD
COMPUTE
E@
TRANSMISSION
I
SINK
Fig. 6.12 Basic components of a fiberoptic array
telemetry system.
6.2.2 Fiberoptic Telemetry System Basic
Configurations
Perhaps the most general telemetry system
configuration is the multisource (sensor array), multiuser
(user-array) general communication network-connected
system shown in Fig. 6.13. The simplest system
ARRAY
SOURCE
FIBEROPTIC
CABLES
1
m------
Fig. 6.13
FIBEROPTIC, RADIO,
OR WIRE
L
TRANS-
MISSION
SYSTEM
-----El .
---b
Generalized fiberoptic telemetry system.
is a single sensor connected to a single output device
via a single channel. Many variations are poasible,
for example the multisource, multiplexed, single user,
fiberoptic data link configuration shown in Fig. 6.14.
El-
1
FIBEROPTIC
CABLES
SIGNAL
CONDl-
4 TIONER
I 1’
. . .
‘B-J
5
ṅ
Fig. 6.14
FOCABLE
USER END INSTRUMENTS
RECORDER
DISPLAY DEVICE
LOUDSPEAKER
COMPUTER
TRANSMITTER
0
photodetector
AND DEMUX
A multisource multiplexed single-uaer fiberoptic
sensor array telemetry system.
6.2.1 Fiberoptic Telemetry System Design OptiOnS
Mny options are open to the designer of a
fiberoptic telemetry system. These include the determination
of the overall system configuration; the design
and selection of fiberoptic senaors, cables, and
connectors; the design and selection of transmitters
and receivers; and the specification of system parameters,
such as signal-to-noise ratios, distortion
limits, permissible bit error-rates, multiplexing
schemes, modulation methods, and the coding, sensing,
and detection arrangements.
6-6
Various arrangements for the transmission of
signals from a fiberoptic sensor array to many users
via different types of fiberoptic data links are ahown
in Fig. 6.15. The simplex, half-duplex, full-duplex,
and multiplex schemes illustrated in Fig. 6.15 describe
various system configurations with different capabilities.
These configurations may be connected to operate
as one-way-at-a-time, two-way alternate, or two-way
simultaneous systems. For example, two simplex channels
could be associated for operating a two-way simultaneous
data link.

SIMPLEX FIBEROPTIC TRANSMITTER FIBEROPTIC RECEIVER
I
%T21
FIBEROPTIC SPLICE
I
G
DUPLEX
T,
cl-l
w —
R2
m RI
m T2
3+! -’,
‘\ \’
FIBEROPTIC CONNECTOR
FIBEROPTIC CABiE
Fig. 6.16
A fiberoptic data link.
m 4’ E
‘“’’’’”x Km7dl
Fig. 6.15
6.2.3 Telemetry System Budgets
Generalized transmission schemes.
Each telemetry system component interacts
with other components within many time and space constraints.
This gives rise to many different ways of
aPPIYing the constraints. Each component may provide
useful power, consume available power, occupy limited
space, contribute to overall weight, poasesa a useful
life, require maintenance, has an acquisition and connection
cost, or has other features that affect the
whole system. Thus, each component makes a contribution
to, or imposes a liability on, the whole system
in each of these areas. If there are limits to resources
or characteristics that are imposed on the
whole system, there will be a requirement to budget
them. h obvious example is to place a limit on system
cost, space, and weight and then aelect a aet of components
whose total cost, space, and weight do not
exceed theae limits. Budgeting of time, power, and cost
will be discussed for fiberoptic telemetry systems.
6.2.3.1 Rise Time Budget Analysis
Distortion, length of lines, attenuation,
signaling (pulse-repetition) rates, and dispersion will
place a limit on the length of time that can be allowed
for a step or pulse input to a fiberoptic transmitter
to reach the 90% of maximum signal level at the output
terminal of the receiver. This risetime is distributed
over the electrical and optical serially-connected
(tandem connected) components of the link on the basis
of an approximated Gaussian “distribution in which the
combined risetime of the components in tandem is the
square root of the sum of the squares (RMS) of all the
risetimes of the serially-connected components. Normally
the total link risetime is the root-meansquare of
the transmitter, cable, and receiver risetimes. However,
these components themselves may have serial
elements each with individual risetimes. For example,
the transmitter may have an electronic risetime and a
fiberoptic pigtail and coupler risetime. The cable
may have splices or repeaters. All the risetimes of
these are combined on the same RMS basis. A schematic
diagram of a simple fiberoptic link ia shown in Fig.
6.16. The elements that comprise the risetime of the
fiberoptic link are as follows:
TRANSMITTER RISETIME, tr(xmtr., primarily due to the
—————
the light source and driver e ectronics.
———
FIBER RISETI~-, tr(cable), due to the modal dispersion
(variation in group delay between fiber modes)
and .— material dispersion (nonlinear variation of the
refractive index, or as a function of wavelength).
Modal dispersion in an optical fiber is a
combination of —-— intramodal — dia~ersion and intermodal
dispersion. Intramodal ~ is pulse broadening
in an optical fiber. It is primarily a function of
the spectral bandwidth of the source and the material
dispersion, to be discussed later. The intramodal
dispersion, Sintram, of an optical fiber is given by:
s intram
= (SAL/c)d2n/d21 (6.10)
where S = Spectral bandwidth of source
k = Wavelength of source, midband
L = Length of fiber
= Speed of light in a vacuum
d2n/di~ = Material dispersion, in which n is the core
refractive index and 1 is the source wavelength
The only deaign option for reducing intramodal dispersion
at a given source wavelength and length of fiber
is to reduce the source spectral bandwidth. The spectral
bandwidth of a typical LED is of the order of
0.05 Vm whereaa that of a typical laser is 0.002 pm.
Intermodal dispersion is pulse broadening due
to differences in propagation velocity, and hence propagation
time, among the various modes. Proper shaping
of the refractive index profile of an optical fiber
can reduce intermodal dispersion to a minimum. Intermodal
dispersion, Sinterm, is given by:
Sintem = (LnA/2c)pi (6.11)
where L = Length of fiber
n = Refractive index at center of fiber
A = (nl-n2)/nl, where nl and n2 are the maximum
and minimum refractive indices , respectively.
It is called the index difference parameter
c = Speed of light in a vacuum
p i
= Refractive index profile parameter, ideally
equal to 2.25, based on zero intermodal dispersion
The individual contributions to dispersion within modes
and among modes in a given optical fiber follow a Gaussian
distribution. Therefore, if Eq. (6.10) and (6.11)
are squared, added, and the length, L, factored, and
the square root of the sum of the squares is taken, the
6-7

following is obtained:
L-BWP= [(SX/c)d2n/dA2]2+[(nA/*c)pi]2
[ 1 1’2 (6.12)
where L-BWP is the optical fiber length-bandwidth product.
Many of theae parameters are fixed by the optical
fiber manufacturer. In addition, the modal dispersion
caused by a fiber can be expressed in terms of the
risetime for a step input optical signal. This can be
empirically determined for typical high performance
commercially available optical fiber. The parameters
given in Eqa. (6.10) and (6.11), and therefore (6.12),
contribute to the fiber riaetime modal dispersion coefficient
used in Eq. (6.13) below.
The portion of the fiber risetime due to
modal dispersion (intramodal and intermodal) ia given
empirically for a typical high-performance commercially
available optical fiber, as:
where L-BWPO =
FIBER RISETIME DUE TO MODAL DISPERSION
L-BWP =
L eff =
where L=
530 =
trmo(cable) = 530/L-BWpo ‘s (6.13)
(L-Bwp)/Leff = Optical 3-dB bandwidth of
the fiber.
Length-bandwidth product, MRz-km.
L x = Effective length of fiber.
Actual length of fiber.
0.5 < x < 1
Short lengtha, < 1 km, x = 1
Long lengths, x = 0.7 or 0.8.
Fiber risetime modal dispersion coefficient
for typical high-performance commercially
available optical fiber.
The portion of the fiber risetime due to
material dispersion is given aa:
where
FIBER RISETIME DUE TO MATERIAL DISPERSION
‘rma(cable) = 1.1 MSL (6.14)
M = Material dispersion coefficient, given
in nslnm-km and as shown in Fig. 6.17.
S = Spectral bandwidth of source, nm
L = Link length, km
A typical curve for the value of M, the material
dispersion coefficient, as a function of wavelength
for two specific glasses is shown in Fig. 6.17.
RECEIVER RISETIME, tr(rcvr), due to the photodetector
and its aaaociated electrical circuits. The
receiver risetime la normally given by the manufacturer
or can be constructed or eatimated from
the manufacturer’s data.
Normally a Gauasian distribution of the risetimes
is assumed, and thus for a set of sequential
components the overall risetime for the system is
given as:
‘r(sya) = [t2*(xmtr) +
2
‘r ma(cable) + ‘r(rcvr)
2
r mo(cable) +
1/2
(6.15)
However, the total risetime for the link,
‘r(sys)~ cannot exceed the maximum allowable risetime
for the link. In digital systems, the allowable risetime
is limited by the requirement to prevent the bit
error rate (BER) due to interaymbol (interpulse) interference
from exceeding a prescribed value. In analog
systems the frequency response at high frequencies must
be sufficient to prevent distortion of the base band
aignals. For example, in the nonreturn-to-zero (NRZ)
method of signal representation (code), ‘he ‘r(sys)
must be less than 0.7 times the bit interval, expressed
as the reciprocal of the bit rate. If the bit rate
ia 7.0 Mb/see, the maximum value tr(sys) can have ia
is 100 nsec for NRZ coding. For return-to-zero (RZ)
coding the factor is 0.5, in which case, for the same
bit rate of 7.0 Mb/see, the maximum allowable tr(sya)
is 71.4 ns.
The following is given as an example of a
riaetime budget for a typical fiberoptic link:
LINR
DESCRIPTION
FIBEROPTIC LINK RISETIME BUDGET
Data rate, Rw
Link length, L
Length-bandwidth-product, L-BWF
Light source
Operating wavelength,a
Light source spectral width, S
COMPONENT RISETIMES
Transmitter [tr(xmtr)] (Manufacturer) *O ns
Fiber modal dispersion risetime [trmo(cable)]
7.0 Mb/see
1.5 km
50 MHz-km
LED
0.830 Pm
0.020 pm
0.25
(L-BWo) =
(L-BWP)/Lx = 50/1.5°”8 = 36.1 MRz-km
015
010
‘rmo(cable)
= 530/(L-BWPo) = 530/36.1 = 14.7 ns
Fiber material dispersion risetime
M = 75 ns/m-km (Manufacturer)
[t_(cable)]
‘rma(cable)=l- lMsL=( 101)(75)(0”02)(1-5)=2”5ns
Receiver risetime [tr(rcvr)] (Manufacturer)
0.05
0
/00 900 1100 1: )
WAVELENGTH(nm)
Fig. 6.17 The material dispersion coefficient versus
wavelength for two types of glasses.
6-8
‘r(rcvr)
LINR RISETIME
= 375/Belec = 375/50 = 7.5 ns 56.3
Substituting the above risetimes in Eq. (6.15) the
overall system (link) risetime is calculated to be
26 ns.

MAXIMUM ALLOWABLE RISETIME = 0.7/RN~ = 100 nS FIBEROPTIC LINR OPTICAL POWER BUDGET
(Fig. 6.16)
RISETIME BUD(ZT MARGIN = 7fI ns
LINK DESCRIPTION
The 74 ns margin between the maximum allowable
risetime based on the required signaling rate and
Link length, L
1.5km
Data Rate, R
7.0 Mblsec
the system risetime for all the components can be used
Operating wavelength
0.830 nm
in many ways. For example, the cable could be made
longer, the signaling rate could be increased, or a
cheaper cable with a greater material or modal dispersion
per unit length could be used. However, other
budgets, such as the power budget, may place limits on
theae changes. Perhaps the one single fact to remember
in regard to risetime is that it represents reciprocal
dollars, i.e., the longer the risetime, the cheaper
the component. Therefore, except for a power safety
margin, all allowable risetime should be used up for
the performance requirement in a given application.
6.2.3.2 Optical Power Budget Analysis
The optical power requirement of a given
fiberoptic telemetry system is also a matter of distribution
of power over a serial or a parallel set of
fiberoptic channels. For example, if there are star
couplers, there must be sufficient input power to satisfy
the input power requirement for each parallel output
channel. Serially connected components, such as
cables, splices, and couplers, will each have an inser -
tion loss. Repeaters will insert a gain. The losses
and gains are added to obtain the source-to-receiver
overall loss. The optical power dissipation that can
be allowed is the difference between the sum of the
transmitter and repeater optical power outputs and the
required receiver (photodetector) optical power input
in order to keep the bit error rate (BER) below, or
signal-to-noise ratio (S/N) above, a specified value.
A typical allowable optical power loss between transmitter
and receiver for various data rates at an allowable
BER of 10-9 is shown in Fig. 6.18. Normally one
TRANSMITTER POWER, pT
Light source type
Average source optical power
Fiber coupling loss
Average launched optical power,
REQUIRED RECEIVER POWRR, pREQ
Detector type
Required bit error rate, BER
Receiver bandwidth
Receiver sensitivity
Link margin
‘REQ
ALLOWABLE LINK LOSS OVER MARGIN, PAL
pm = PT - PmQ = -14 -(-48) = 34 dB
LINR LOSS COMPUTATION
LED 0.1 mW
-10 dBm
-4 dB
-14 dBm
PIN-FET
1(3-9
50 MHz
-55 dBm
+ 7 dB
-48 dllm
Contributor Unit Quantity Total
Recr coupling 3.0 dB 1 3.0 dB
Connectors 2.0 2 4.0
Splices 0.5 4 2.0
Cable 5.0 dB/km 1.5 km 7.5
Splitters
Margin 2.0 dB 2.0
Total link loss
18.5 dB
REMAINING POWER MARGIN
(Allowable - Total link loss) = 34- 18.5
= 15.5 dB
=
II
g
n
Fig. 6.18
o
-lo
-20
-30
-40
-50
-60
-70
t
LASER-LAUNCHED
POWER RANGE
LED-LAUNCHED
--..POWER RANGE _______ -14
I
-80
-901 1 1 1
1 10 100 1000
DATA RATE (Mb/s)
BER =10-9
optical power loss versus data rates for
the fiberoptic data link used in the optical
power budget analysis in Section 6.1.3.
would not use up all the available power, but maintain
a safety margin of a few dB to insure satisfactory performance.
The allowable loss is then distributed over
the fiberoptic link components as shown in Fig. 6.16
and given in the following example:
Since a link margin of 7 dB and a link loss
computation margin of 2 dB have already been allowed,
the entire 34 dB may be used up. The loss in the link
of the given design is 18.5 dB. Therefore, there is an
excess total available optical power margin of 15.5 dB.
It may be cheaper to use up this excess margin by
selecting cheaper cable components with greater losses
or it may be cheaper to choose a lower-power source.
Link power is like dollars, it is best to get by with
the least power, low power sources being cheaper. However,
link loss is more like reciprocal dollars, the
greater the power loss, the cheaper the components.
Therefore, there is a trade-off to be made in order to
minimize the overall cost of a fiberoptic link.
6.2.3.3 Cost Budget Analysis
The cost of a fiberoptic telemetry system
will be based on judicious maximal use of available
risetime and minimal use of power as well as many other
factors. Fiberoptic cable designs, repeater spacing,
multiplexing schemes, allowable BERs, cable routings,
the use of overhead versus subterranean cables, availability
of components, simplicity of design and fabrication,
and ease of maintenance, are just a few of the
many factors that will enter into the overall cost of
the system.
6.2.4 Fiberoptic Telemetry System Specific
Configurations
An example of a set of the final design para-
6-9

meters for the field tested fiberoptic long-haul telemetry
system shown in Fig. 6.19 is as follows:
LONG HAUL FIBEROPTIC LINR PERFORMANCE DATA
PROCESSING STATION TRANSMISSION PARALLEL SENSOR ARRAY
LINK
,—
SYSTEM LENGTH
REPEATER SPACING
NUMBER OF REPEATERS
Diameter
Length
Weight
OPEIUiTING DEPTH
CABLE DIAMETER
CABLE STRENGTH
DATA FORMAT
FULL DUPLEX
WAVELENGTHS
HIGH BIT RATE CHANNEL
Bit Error Rate (BER)
Low Bit Rate
Bit Error Rate (BER)
70 km
6.8 to 8 km
8
2.9 cm
30.5 cm
< 400 g
1000 m
2.4mm
60 kg (0.8% Strain)
Digital PCM
1 Fiber
0.83 and 1.06 pm
22 Mb/s
< 10-9
43 kb/s
< 10-7
2+
DEMODU-
LATOR
SIGNAL
PROCESSOR
DISPLAY
i
LASER
OR LED \
: FIBEROPTIC
RECEIVER
t-1
PHOTODETECTOR [
CONNECTOR
Fig. 6.20 An example of a fiberoptic sensor array
multimode intensity modulated telemetry
system.
h
The above system is the Naval Ocean Systems
Center and the International Telephone and Telegraph
(NOSC/ITT) Undersea Single Fiber Multirepeater Full
Duplex Electrooptical Data Link, a schematic diagram of
which was shown in Fig. 6.19.
PROCESSING STATION TRANSMISSION LINEARSENSOR ARRAY
LINK
HBR RCVR
LBRXMTR
)
_HBR(22 MBISEC)
LBR (43KBISEC)C
SPACING: 8km BTWN REPEATERS
Al= .83pm LASER
A2=106#mLED
SENSOR
STRING
liBRXMTR
LBRRCVR
EOREP1
LBR
I I
liBR
EOREP2
-
HBR(A1) ~ EOREP8
_LBR(A2)
I
1
1
,
t
[.
DEMODU
LATOR
SIGNAL
PROCESSOR
DISPLAY
8
Fig. 6.21
q J J 1
: FIBER
; COUPLERS
AII example of a fiberoptic sensor array
multimode intensity modulated telemetry
system.
Fig. 6.19
The Naval Oceans Systems Center and the International
Telephone and Telegraph (NOSC/
ITT) undersea single fiber multirePeater
full duplex electrooptical data link.
There probably is no limit to the number of
different fiberoptic sensor array system configurations
that can be designed, considering the number of energization
methods, types of sensors, and return telemetry
methods that can be uaed. Four specific fiberoptic
telemetry system and sensor array configurations are
shown in Figs. 6.20 through 6.23. Specific design
aspects of basic configurations will be discussed in
following subsections.
PROCESSING
STATION
c=
TIMING
D
FIBEROPTC
RECEIVER
cl
DEMOCY.JLATOR
aSIGNAL
PROCESSOR
DSPLAY
I
TRANSMISSION
LINK
ELECTRICAL FOWER
-
FIBEROPTIC CASLE
I
ARRAY
Fig. 6.22 An example of a fiberoptic interferornetric
sensor array telemetry system.
6-10

PROCESSING STATION TRANSMISSION wAVELENGTHM ULTIPLEXED
LINK
ARRAY
BDEMODU-
LATOR
SfGNAL
PROCESSOR
c1
OISPLAY
[
i
BROAD
s:::~::M
RECEIVER
IQ
FIBEROPTIC
CONNECTOR
Ld
;DIFFRACTION
: GRATING
; ~A’&
Fig. 6.23 An example of a fiberoptic diffraction
grating senaor array telemetry system.
n
For m parallel channels with equal pulse intervals,
this reduces to:
RE = (m/T) log2 n. (6.17)
For two condition modulation, this reduces to m/T.
For a single channel, RT reduces to (l/T) log2n,
and with 2 conditions, I/T, i.e., the baud rate
for one channel. Each of the multiplexed fiberoptic
channels can be used as an analog (voice,
sound, continuous signal) or as a digital (pulse
coded) channel.
6.3.2 Transmission Line Specific Parameters
The construction features of a fiberoptic or
electrooptic transmission line (cable) depend on many
environmental factors. Some of these are as follows:
6.3 FIBEROPTIC SENSOR ARRAY TELEMETRY TRANSMIS-
SION LINE PARAMETERS
6.3.1 Transmission Line General Parameters
Fiberoptic array data transmission line designs
include a large but manageable number of options
and variables. A few of these are as follows:
GENERAL FIBEROPTIC TRANSMISSION LINE DESIGN PARAMETERS
SIGNAL MODE
Analog, digital, hybrid, discrete
MODULATION SCHEME
Phase, frequency, intensity, polarization, wave -
length
CHANNEL CAPABILITY
Simplex, duplex, half-duplex, diplex, multiPlex
OPERATIONAL MODE
One way, one way at a time, two way simultaneous
CABLE DESIGN
Fibers, strength members, conductors, jacket,
filling, insulation, buffering, spacing type,
spacing
FAIL-SAFE
Redundancy, power margin, tolerance to breaks
ATTENUATION
Absorption, scattering, insertion loss, bit error
rate (BER)
DISPERSION
Bit error rate (BER), distortion, signal-noise
ratio
RELIABILITY
Failure rates, failure modes
OVERALL CHANNEL SIGNALING RATE
In digital systems the number of transmission
lines or channels will be determined by the total
data signaling rate requirements and the multiplexing
schemes that are used. For example, assume
many channels with different signaling rates and
different digital pulsing schemes connect two stations.
Then, the total data aignaling rate (capacity
between the stations, or as an output capacity
from one to many stations) for a group of m parallel
channels in which Ti is the minimum interval
in seconds between signal transitions for the i-th
channel and ni is the number of significant conditions
of modulation, is given by:
m
RT = ~ (1/Ti) log2 ni (6.16)
1=1
6-11
FIBEROPTIC CABLE DESIGN PAMMETERS AND
ENVIRONMENTAL FACTORS
PHYSICAL STRENGTH PARAMETERS
Tensile Strength
Radial Compression Strength
Flex Resistance
Bend Resistance
Abrasion Resistance
Vibration Resistance
Strength Member Location
Strength Member Materials
ENVIRONMENTAL FACTORS
Operating Temperature
Operating Pressure
Moisture/Chemical/Other Resistance
OPTICAL FIBER PARAMETERS
Multimode or Single Mode
Glass or Plastic
Refractive Index Profile
Core Concentricity
Cladding Outer Diameter
Numerical Aperture
Fiber Jacket Material
Fiber Jacket Thickness
Dispersion (Modal and Material Multimode
vs Singlemode)
Attenuation Per Unit Length
Lose and Bandwidth Stability
Costings on Fibers
Number of Fibers
Ease of Joining
Size of Fibers
CABLE PARAMETERS
Size of Cable
Bend Radii
Sheathing
Location of Fibers
Armor Requirements
ELECTRICAL FEATURES
Electrical Heating
Wire Size
Number of Conductors
Shielding
h example of an electrooptic cable crosssection
is shown in Fig. 6.24. The need for built-in-

55/125 pm, F.4uI-TIMODE,
Gl, OPTICAL FIBER \
EL BUFFER TO
D. OF 1.02 mm
‘r
4
15 CU-CLAD-STEE
WIRES – EACH 0.
0. D. – AS HELIX
;KET TO 2.54 mm
Fig . 6.24 A cross section of one of a large number of
different electrooptic cable designs.
cable fiberoptic repeaters is determined by the risetime
and power budgets, which in turn, depend on attenuation
and cable length-between-repeaters. An example
of a fiberoptic electrooptic repeater is shown in Fig.
6.25. This repeater handles a high bit-rate in one di-
24
Fig. 6.27
~
01 1000
FREQUENCY (MHz)
The optical power loss per hertz for one
kilometer lengtha of several types of cables
at various frequencies.
6.3.3 Multiplexing with Optical Fibers
Multiplexing may be accomplished with optical
fibers in the following ways:
HBR(A,)
TOPROCESSING— OPTCAL
— STATION — DuPLEXER
Fig. 6.25
+=+
LSR(A2)
OPTICAL
DU~ER —
LSR
H=?HSR
OTHER REKATERS
h example of a fiberoptic full duplex repeater.
rection for user data and a low bit-rate in the other
direction for control and supervisory data in a single
fiberoptic cable. An arrangement for the optical duplexers
that was shown in Fig. 6.25 is sho~ in Fig.
6.26.
FREQUENCY -DIVISION MULTIPLEXING (FDM)
Modulate a single optical wavelength with a different
carrier frequency for each channel.
WAVELENGTH-DIVISION MULTIPLEXING (WDM)
Use two or more optical sources each with a different
wavelength for each channel.
TIME-DIVISION MULTIPLEXING (TDM)
Different time-slot for each channel.
sPAcE-DIvxsIoN MULTIPLEXING (fiDM)
Different fiber for each channel.
POLARIZATION
Different form of polarization for each channel.
The multiplexing scheme that is used for a
given application depends on the number of channels required
and the cost factors for each scheme. A typical
multiplexing arrangement is shown in Fig. 6.28. In
TOHSR
RCVR
Fig. 6.26
. . ()
. ---
_HSR
6 Q A, .
_LSR
A2 Q
‘
----
~.
p
AZFROM
--- LSRXMTR
‘- ‘- ““-~%1:
DICHROIC
FILTER
An arrangement for a fiberoptic duplexer.
m
2
1
$
Fig. 6.28
SENSOR
ARRAY
TRANSMl~ER
IJULILS,GNAL / \ ( /
-’45-J ‘RECE’VER
AQQ.. nlln
An example of a fiberoptic sensor lineararray
telemetry system with single optical
repeatered cable return.
tin indication of the power-loss-per-hertz
versus frequency for an optical fiber, compared to wire
pairs and coaxial cables, iS sbo~ in Fig. 6.27. Note
that in the graded-index fiber the loss-per-hertz is
almost independent of frequency for frequencies up to
almost one gigahertz.
this figure, the signals from the sensor array are
multiplexed on a time-division multiplexing (TDM) basis
so that only one series of repeaters is required for a
single fiber. This basic fiberoptic link consists of
a fiberoptic transmitter (modulated light source), a
6-12

fiberoptic cable (optical cable), and a fiberoptic
receiver (photodetector). Electrical-to-optical and
optical-to-electrical conversion (transduction) is presumed
at each end, though such presumption is not always
true for all fiberoptic links. For example, the
receiving end may consist of a fiberscope (display device)
or simply a flashing light indicator of on-off
conditions.
6.3.4 Connector Parameters
There are many performance requirements and
design considerations that enter into the choice of
suitable connectors for fiberoptic cables. In addition
to the optical insertion loss introduced by the connector,
other optical features such as axial misalignment,
axial offset, and spacing between fibers must be considered,
as was indicated in Chapter 3. Some of the
connector physical features and design considerations
are as follows:
After a physical parameter, such as a sound
wave or a varying magnetic field, has been sensed and
transformed by a fiberoptic sensor into modulated light
that is then transmitted to a point of use via a fiberoptic
telemetry system, the modulated light has to be
demodulated in order to recover the information-bearing
signal. One or more photodetectors may be required to
obtain an electrical signal that may be used as is or
further processed by electrical circuits. Demultiplexing
may be required to obtain the separate signals that
were originally generated or transmitted. For digital
data, decoding will be necessary to convert the pulse
codes to analog form or to recover alphanumeric data.
In some cases, the incoming signals need not be converted
to electrical signals, but ULSY be directly displayed
as light signals, such as for signaling on-off
conditions or for telemetering images received via a
multifiber coherent optical cable connected directly
to the faceplate of a fiberscope. Thus, the type of
processing that must be performed on incoming lightwave
signals at an end terminal depends on the specific
application.
6.5 SUMMARY
The topics that were covered in this chapter
included fiberoptic telemetry system configuration;
system risetime, power and cost budgeting; sensor array
design and construction; and fiberoptic transmission
considerations, including multiplexing and fiberoptic
cable, repeater, and connector design considerations.
CONNECTOR DESIGN CONSIDERATIONS
NUMEER OF ELECTRICAL LEADS AND SIZE
NUMBER OF OPTICAL FIBERS AND SIZE
OPERATING TEMFERiTURR AND PHESSURE
MOISTURE AND DIRT RESISTANCE
FIELD MATABILITY
STRAIN RELIEF DESIGN
An example of a ruggedized connector is shown
in Fig. 6.29.
ACHlEVED2.8dS LOSS WHEN COUPLING
50#m CORE0.2 NAGRAOEDINOEX FIBER
Fig. 6.29
A ruggedized fiberoptic cable connector.
Courtesy Standard Telecommunications Laboratories
Limited, Harlow, Essex, England;
and ITT Cannon, Basingstoke, Hampshire,
England.
6.4 END-TEHMINa (RECEIVER) C0N51DEWT10N
6-13

APPENDIX
FIBEROPTIC SENSORS GLOSSARY
This Glossary on fiberoptic aensors is intended to
provide definitions of the terms used in this Handbook
and to provide supplementary information directly related
to the topics discussed. Many topics that were
introduced in the various chapters are developed in
further detail in thia Glossary. l%is approach was used
to avoid burdening the reader with details and explanations
of terms aa topics were covered. For example,
Maxwell’s equations, solid state electronics, electrooptic
effects, electromagnetic theory, multiplexing
and modulation methods, and various coefficient for
transmission, reflection and attenuation are covered
in this Gloasary.
The definitions in this Glossary are consistent
with international, national, Federal, military, and
technical society atandards. Many were taken from the
more comprehensive Fiberoptic and Lightwave Communications
Standard Dictionary, Illustrated, 284 pages;
and from the Communications Standard Dictionary,
Illustrated. 1045 Dazes. .-. by . Martin H. Weik, Van
Nostrand Reinhold Company, 135 W. 50th Street, New
York, New York, 10020.
A
absorption. The transference of some or all of the
energy contained in an electromagnetic wave to the
substance or medium in which it ia propagating or
upon which is is incident. Abaorbed energy from
incident or transmitted lightwaves is converted into
energy of other forms, usually heat, within the
transmission medium, with the resultant attenuation
of the intensity. See intrinsic absorption.
acceptance angle. The maximum angle, measured from the
longitudinal axis or centerline of an optical fiber
to an incident ray, within which the incident ray
will be accepted for transmission along the fiber,
that is, total internal reflection of the incident
ray occurs. If the acceptance angle for the fiber
is exceeded, total internal reflection will not occur
and the incident ray will be lost by leakage,
scattering, diffuaion, or absorption in the cladding.
The acceptance angle is dependent upon the
refractive indicea of the two media that determine
the critical angle. For a cladded fiber in air,
the sine of the acceptance angle is given by the
square root of the difference of the squares of the
indices of refraction of the fiber core and ~he cla -
ding. In mathematical notation, sine= (n -n
7
where 0 ia the acceptance angle, n, is tiie r~~l~c~
tive index of the core, and n2 is the refractive
index of the cladding. Synonymous with acceptance
one-half angle.
acceptance cone. A solid angle whose included apex
angle is equal to twice the acceptance angle. Rays
of light within the acceptance cone can be coupled
into the end of an optical fiber and still maintain
total internal reflection for all the rays in the
cone. Typically, an acceptance cone is 40°.
acceptance one-half angle.
angle.
Synonym for acceptance
acceptor. In an intrinaic semiconducting material (such
as galium arsenide), a dopant (such as germanium
that has nearly the same electronic bonding structure
as the intrinsic material, but with one less
electron among its valence electrons than that required
to complete the intrinsic bonding structural
pattern. This pattern leaves a “space” or “hole”
for one electron for each dopant atom in the structure.
The dopant atoms are relatively few and are
far apart and hence to not interfere with the electrical
conductivity of the intrinsic material. An
electron from a neighboring intrinsic material atom
can fill the hole at the dopant site, leaving a hole
from whence it came; thus, the hole can appear to
move or wander about, although with less mobility
than the electrons that are free and exceas to donor
atoms. Also see donor; electron; hole.
acoustooptic effect. The changes in diffraction gratings
or phase patterns produced in a transm.lssion
medium conducting a lightwave when the medium is
subjected to a sound (acoustic) wave, due to the
photoelaatic changes that occur. The acoustic waves
might be created by a force developed by an impinging
sound wave, the piezoelectric effect, or magnetostriction.
The effect can be used to modulate a
light beam in a material since many properties,
such as lightconducting velocities, reflection and
transmission coefficients at interfaces, acceptance
angles, critical angles, and transmission modes,
are dependent upon the diffractive changes that
occur. The effect includea the phase transduction
mechanism used in fiberoptic sensors, i.e., t h e
change in phase that occurs due to the change in
length and refractive index caused by the acoustic
presaure. Also see electrooptic effect.
acoustooptics. The study and application of the interrelation
of acoustics and optics. Synonymous with
optoacoustics.
amplification by stimulated emission of radiation
(laser). See light amplification by stimulated emission
of radiation (laser).
amplitude modulation (AM). The modulation of the amplitude
of a wave serving as a carrier, by another wave
serving as the modulating signal. The amplitude excursions
of the carrier are made proportional to a
parameter of the modulating signal that bears the
information to be transmitted.
A-1

angstrom. A unit of length equal to 10-10 meter, 10-1
nanometer, and 10-4 micron.
aperture. See numerical aperture (N. A. ).
array.
See sensor array.
attenuation. The decrease in power of a signal, light
beam, or lightwave, either absolutely or as a fraction
of a reference value. The decrease usually
occurs as a result of absorption, reflection, diffusion,
scattering, deflection, or dispersion from
an original level and usually not as a result of
geometric spreading, i.e., the inverse sqwre of
the distance. In an optical fiber, attenuation Is
undesirable for transmission purposes but desirable
for prevention of leakage or clandestine detection.
Optical fibers have been classified as high-loss
(over 100 dB/km), medium loss (20 to 100 db/km),
and 10W1OSS (less than 20 dB/km).
band.
B
See conduction band; energy band; valence band.
bandwidth. 1. A range of frequencies, usually specifying
the number of hertz of the band or the upper
and lower limiting frequencies. 2. The range of
. frequencies that a device is capable of generating,
handling, passing, or allowing, usually the range
of frequencies in which the response is not reduced
greater than 3 dB from the maximum response.
baseband. The band of frequencies associated with or
comprising an original signal from a modulated
source. In the process of modulation, the baseband
is occupied by the aggregate of the transmitted signals
used to modulate a carrier. In demodulation,
it is the recovered aggregate of the transmitted
signals. The termis commonly applied to cases where
the ratio of the upper to the lower limit of the
frequency band is large compared to unity.
beam splitter. h optical device for dividing a light
beam into two separated beams. One simple beam
splitter consists of a plane parallel plate, with
one surface coated with a dielectric or metallic
coating that reflects a portion and transmits a portion
of the incident beam; i.e., part of the light
is deviated through an angle of 90°, and part iS
unchanged in direction. A beam splitter may also
be made by coating the hypotenuse face of a 45°-90”
prism and cementing it to the hypotenuse face of
another. The thickness of the metallic beam splitting
interface will determine the proportions of the
light reflected and transmitted. In metallic beam
splitters, an appreciable amount of light is lost by
absorption in the metal. It may also be necessary
to match the reflected and transmitted beam for
brightness and for color. In these cases, it is
necessary to use a material at the interface that
gives the same color of light by transmission and
reflection. Nhere color matching at the surface or
interface cannot be accomplished, a correcting color
filter may be placed in one of the beams. In a
fiber-to-fiber beam splitter, evanescent coupling
can be used to transfer optical energy from one
fiber to another.
birefringence. The splitting of a light beam into two
divergent components upon passage through a doublyrefracting
transmission medium, with the two components
propagating at different velocities in the
medium. In an optical fiber, birefringence is related
to the strain in the fiber which causes the
fiber to be a single polarization transmission
medium.
Bragg cell. An acoustooptlc device that accepts fixed
frequency monochromatic light and that has a baseband
vibrating element capable of modulating the input
lightwaves producing an output lightwave with a
frequency equal to the frequency of the input lightwave
plus the frequency of the baseband input signal.
The Bragg cell has application as part of an interferometer
in which heterodyne detection is used.
Brewster angle. The angle, measured with respect to
the normal, at which an electromagnetic wave incident
upon an interface surface between two dielectric
media of different refractive indices is totally
transmitted into the second medium. The magnetic
component of the incident wave must be parallel to
the interface surfa~~l The Brewster angle is given
by: tan B = (~2/E1)
, where B is the Brewster angle,
c1 is the electric permittivity of the incident
medium, and e2 is the electric permittivity of the
transmitted medium. The Brewster angle is a convenient
angle to transmit all the energy in an optical
fiber to an outside detector. There is no Brewster
angle, for which there is total transmission and
therefore zero reflection, when the electric field
component is parallel to the interface, except when
the permittivities are equal, in which case there
is no interface. Mso, for entry into a more dense
medium, such as from air into an optical fiber: tan
B = (n2/nl), and from a more dense medium into a
less dense medium, such as fiber to air: tan B =
(nl/n2), where nl and n2 are the refractive indices
of the air and fiber, respectively.
brightfield sensor. In fiberoptic, a sensor in which
the optical power modulated by the sensor is all or
a large fraction of the total optical power fed to
or available to the sensor. Synonymous with lightfield
sensor. Contrast with darkfield sensor.
budget. See optical power budget; power budget; risetime
budget.
bulk coupler. In fiberoptic, a coupler that has one
input and many outputs.
bundle jacket. The outer protective covering applied
over a bundle of optical fibers.
bus. 1. One or more conductors that serve as a common
connection for a related group of devices. 2. One
or more conductors used for transmitting optical or
electrical power or signals.
bend.
See ordinary bend.
bend loss.
See microbend loss.
A-2

c
cable. 1. A jacketed bundle or jacketed fiber in a
form that can be terminated. 2. A group of conductors
that are bound together, usually with a protective
sheath, a strength member, and insulation
between individual conductors and for the entire
group. See fiberoptic cable.
cable jacket. The outer protective covering applied
over the internal cable elements.
carrier. 1. In communications, a wave, pulse train,
or other signal suitable for modulation by an information-bearing
signal to be transmitted over a communication
system. 2. h unmodulated emission. A
carrier is usually a sinusoidal wave, a recurring
series of pulses, or a direct-current (DC) signal.
See charge carrier.
cavity.
See resonant cavity.
charge carrier. tin atomic or molecular particle that
possesses an electric charge and is capable of moving
under the influence of an electric or magnetic
field. For example, an electron, a hole, or an ion.
cladding. An optical transparent material, with a refractive
index lower than that of the core, placed
over or outside the core material of an optical
waveguide that serves to reflect or refract lightwaves
in order to confine them to the core. The
cladding also serves to protect the core.
cladding mode stripper. 1. A material applied to optical
fiber cladding to allow light energy being
transmitted in the cladding to leave the cladding of
the fiber. 2. A piece of optical material or an
optical component that can support only certain electromagnetic
wave propagation modes. In particular,
it does not support the propagation modes in the
cladding of a cladded optical fiber, slab dielectric
waveguide, or integrated optical circuit. The stripper
effectively removes the cladding modes without
disturbing the core-supported propagation modes.
close-confinement junction. A synonym for single heterojunction.
CMos.
coating.
See combined metal oxide semiconductor.
See optical fiber coating.
coherence length. The coherence time of a light beam
multiplied by the velocity of the light, namely
(1/cAv)c = l/Av. AI.SO see coherence time.
coherence time. In beam of light propagating in a vacuum,
the time obtained from the expression l/cAv,
where c is the velocity of light in a vacuum, v is
the reciprocal of the wavelength, and Avis the variation
or spread of v over time for the beam. In
material media, the c is replaced by c/n, where n is
the refractive index. Also see coherence length.
coherent bundle. A bundle of optical fibers in which
the spatial coordinates of each fiber are the same
or bear the same spatial relationship to each other
at the two ends of the bundle. Synonymous with
aligned bundle.
coherent light. Light of which all parameters are predictable
and correlated at any point in time or
space, particularly over an area in a plane perpendicular
to the direction of propagation or over time
at a particular point in space. Contrast with
incoherent light.
collection angle.
Synonym for acceptance angle.
combined metal oxide semiconductor. A metal oxide semiconductor
that consists of both positively-doped and
negatively-doped material.
common-mode. 1. Pertaining to any uncompensated combination
of generator or receiver ground potential
difference (voltage), generator common return offset
voltage, and longitudinally-coupled peak random
noise voltage measured between the receiver circuit
ground and receiver cable with the generator ends
of the cable short-circuited to ground. 2. The
algebraic mean of the two voltages appearing at the
receiver input terminals with respect to the receiver
circuit ground. 3. Pertaining to the relative
optical intensity fluctuations between two coherent
electromagnetic (light) waves.
common-mode rejection ratio (CMRR). The ratio of the
common-mode interference voltage or optical intensity
at the input of a circuit to the interference
voltage or optical intensity at the output of the
circuit.
conduction band. In a semiconductor, the range of electron
energy, higher than that of the valence band,
possessed by electrons sufficient to make them free
to move from atom to atom. When they leave the
valence band, they are free to move under the influence
of an applied electric field and thus they
constitute an electric current.
conductor. 1. In fiberoptic, a transparent medium
that is capable of transmitting or conveying lightwaves
a useful distance. 2. In electric circuits,
a material that readily permits a flow of electrons
through itself upon application of an electric field.
Electrical conductors include copper, aluminum,
lead, gold, silver, and platinum. The conductivity
is specified by: J = aE, where J is the current
density in amperes/square meter for S1 units, E is
the applied electric field in volts/meter, and o is
the conductivity in reciprocal ohms/meter. Also see
dielectric. Contrast with insulator.
connector. In fiberoptic, a device that permits the
coupling of signals from one optical fiber or cable
to another.
connector insertion loss. The power loss sustained by
a transmission medium, such as a wire, coaxial cable,
optical fiber cable, or integrated optical circuit
component, due to the Insertion of a connector between
two elements, which would not occur if the
media were continuous without the connector i.e.,
if there were no reflected, absorbed, dispersed,
or scattered power.
controllable coupler.
coupler.
See electronically controllable
A-3

core. The central primary light-conducting region of a
material medium, such as an optical fiber, the refractive
index of which must be higher than that of
its cladding in order for the lightwaves to be
totally reflected or refracted. Most of the optical
power is in the core.
coupler. In optical transmission aystems, a component
used to interconnect two or more optical fibera.
Also see connector; bulk coupler; electronic&llycontrollable
coupler; reflective star-coupler; 3-dB
coupler.
coupling. The connection, attachment, or binding of
optical elements, electric circuit elementa, electric
and magnetic fields, propagation modes, or electromagnetic
wave component, such as surface waves
and evanescent waves, to internal waves in waveguides,
dielectric slabs, or other interdependent
associations and interactions of events and materials
in a system. For example, two optical fibers or certain
elements in an integrated optical circuit may
be coupled together in some manner to preserve signal
continuity. See evanescent field coupling.
coupling coefficient. Synonym for coupling ratio.
coupling efficiency. In fiberoptic transmission, the
ratio of the optical power on one side of an interface
to the optical power on the other side. For
example, the ratio of the power developed by a light
aource to the power accepted by a bundle of fibers,
or the power received at the end of a bundle of
fibers to the power that impinges on a photodetector.
For light sources with emitting areas larger than
fiber core diameters, the product of fiber numerical
aperture (N.A.) and core diameter is a good indicator
of maximum coupling efficiency. For other
sources, such as small laser diodes with emitting
areas small than the fiber core diameter, the N.A.
alone is a relevant indicator of coupling efficiency,
usually expresaed as a percentage.
critical angle. The angle, with the normal, at which
an electromagnetic wave incident upon an interface
surface between two dielectric media, at which total
reflection of the incident ray first occurs as the
incident angle with the normal to the incident aurface
is increased from zero, and beyond which total
internal reflection continues to occur although with
increased attenuation at a rate determined not only
by the electromagnetic parameters of the transmission
medium, but also by the frequency and the incidence
angle. The wave is guided along the reflecting
surface with no average transport of energy into
the second medium, and the intensity of the reflected
wave is exactly equal to the intensity of the
incident wave. The wave in an optical fiber will
be confined to the fiber for all incidence angles
greater than the critical angle. The critical angle
is given by sin ec = (~2/~1) 1/2 where 9C is the
critical angle and Cz and c1 are the permittivities
of the transmitted (outside) and incident medium
(inside), respectively, and where El is always greater
than =2; e.g. , the case for an optical fiber (conducting
a wave), and air. In terms of refractive
indices, the critical angle is the incidence angle
from a denser medium, at an interface between the
denser and less dense medium, at which all of the
light is refracted along the interface, i.e., the
angle of refraction is 90°. When the critical
angle is exceeded, the light is totally reflected
back into the denaer medium. The critical angle
varies with the refractive indices of the two media
with the relationship, sin Oc = n2/nl, where n2 is
the index of refraction of the less dense medium, nl
is the refractive index of the denser medium, and 9C
is the critical angle, as above. In terms of total
internal reflection in an optical fiber, the critical
angle is the smallest angle made by a meridional
ray in an optical fiber that can be totally reflected
from the innermost interface and thus determines
the maximum acceptance angle at which a meridional
ray can be accepted for transmission along a fiber.
Also see total internal reflection.
critical radius. The largest radius of curvature of an
optical fiber, containing an axially propagated
electromagnetic wave, at which the field outside the
fiber still detaches itself from the fiber and radiates
into space because the phase-front velocity
must increase to maintain a proper relationship with
the guided wave inside the fiber. Thia velocity cannot
exceed the velocity of light, aa the wavefront
sweeps around the outside of the curved fiber. This
causes attenuation due to a radiation loss. The
field outside the fiber decays exponentially in a
direction transverse to the direction of propagation.
It is the radius of curvature of an optical
fiber at which there is an appreciable propagation
mode conversion loss, due to the abruptness of the
transition from straight to curved. For a radius
of curvature greater than the critical value, the
fields behave essentially as in a straight guide.
For radii smaller than the critical value, considerable
mode conversion takea place.
coupling loss. In a fiberoptic coupling, the optical
power loss caused by the coupling itself, a loss
that would not occur if the optical fiber were continuous
without the coupling.
coupling ratio. The ratio of power on the output side
of a coupling to the power on the input side. The
coupling ratio is always less than unity. Synonymous
with coupling coefficient. Also see 3-dB coupler.
A-4
D
dark current. ~’e current that flows in a photodetector
when there is no radiant energy or luminous flux
incident upon its aensitive surface, i.e., when there
is total darkness. Dark current generally increaaea
with increaaed temperature for most photodetectors.
For example, in a photoemissive photodetector, the
dark current is given by:
Id = AT2eq’$lkT
where A is the surface area constant, T is the absolute
temperature, q is the electron charge, $ ia
the work function of the photoemisaive surface material,
and k is Boltzmann’s constant.
darkfield sensor. In fiberoptic, a sensor in which
the optical power tapped and modulated by the sensor
is a small fraction of the total optical power fed
to or available to the sensor. Contrast with brightfield
sensor.
data. Representation of facts, concepts, or instructions
in a manner suitable for communication, interpretation,
or processing by human, manual, semiautomatic,
or fully-automatic means. The characters
used as data may assume any form or pattern to which
meaning may be assigned in order to represent infor-

mat ion. Data may be transferred or transported from
place to place, auch as from city to city; from position
to position, such as from coordinate poaition
to coordinate position in the display space on the
diaplay surface of a display device as display elements,
display groups, or display images; or from
location to location, such as in computer or buffer
storage as characters or words. Data may be holes
in tapes or cards; magnetized spots on discs, drums,
tapes, cards, or chips; electrical current or voltage
pulses in a wire; or modulated electromagnetic
waves in free space or in optical fibers. Data may
be presented on a CRT screen, a LED or gas panel, a
fiberscope faceplate at the end of a coherent bundle
of optical fibers, or other surface suitable for data
display.
data link. 1. A communication link suitable for transmission
of data. The data link does not include the
data source and the data sink. 2. TWO data stations
and their connecting network, operating in
such a manner that information can be exchanged bedata
tween the stations. See fiberoptic link.
— dB.
dBV.
dBm.
See decibel.
Decibel referred to one volt.
Decibel referred to one milliwatt.
decibel (dB). A gain or attenuation factor measured as
10 times the logarithm to the base 10 of a power or
acoustic energy ratio, or aa 20 timea the logarithm
to the base 10 of the voltage or current ratio with
reference to l-ohm impedance or pressure ratio. The
ratio consists of a reference value as the ratio
denominator and the value to be defined or measured
as the numerator. If the logarithm is positive a
gain is represented by decibels that are positive
and if loss or attenuation is defined or measured,
the decibels are negative. For example, if the ratio
of optical power at the end of an optical to the
power, at the beginning in 0.500, the 10SS iS expressed
as 10 log 0.500 = -3.0103 dB., i.e., 3 dB
down. Since the individual component gain or loss
ratios introduced by serially connected cables, amplifiers,
optical fibers, and other circuit or optical
elements are multiplicative, the decibel gains
and losses need only be added or subtracted according
to sign. Thus, the mathematical relationships
are:
dB = 10 loglO(P1/P2)
If R1=R2, then:
= 10 loglo(E12/Rl)/E22/R2)
= 10 loglo(112R1)/122R2)
dB = 10 loglo(E12/E22) = 10 loglo(112/122)
= 20 log10(E1/E2) = 20 loglo(I1/12)
where P is the electrical or optical power, E is the
electrical voltage, I is the electrical current, and
R is the resistance or like impedance and the subscripts
identify the two pointa of comparison of
power, voltage, or current. The dB is one tenth the
size of a bel, which is too large for convenient use.
decollimation. In a lightwave guide, the spreading or
divergence of light due to internal and end effects.
Such effects include curvature, irregularities of
surfaces, erratic variations in refractive indices,
occlusions, and other blemishes that may cause dispersion,
absorption, scattering, deflection, diffraction,
reflection, and refraction.
defect.
See interstitial defect; vacancy defect.
deflection. 1. A change in the direction of a traveling
particle, usually without loss of particle kinetic
energy, repreaenting a velocity change without
a speed change. 2. A change in the direction of a
wave, beam, or other entity, such as might be accomplished
by an electric or magnetic field rather than
by a prism (refraction), a mirror (reflection), or
optical grating (diffraction).
delay distortion.
See waveguide delay distortion.
demodulation. 1. To undo or reverse the effects of
modulation; i.e., to remove the intelligence-bearing
signal from a modulated carrier or to reconstitute
the aignal that performed the modulation. 2. The
process in which a modulated wave is processed to
derive a wave having substantially the characteristics
of the original modulating wave.
density.
See optical power density.
depletion region. A region near a semiconductor junction
in which there is a reduced concentration of
charge carriers.
detection. See heterodyne detection; homodyne detection;
phase detection.
detector. A device responsive to the presence of a
stimulus. See photodetector.
dielectric. Pertaining to material composed of atoms
whose electrons are so tightly bound to the atomic
nuclei that electric currents are negligible even
under applied high electric fields. That is, scarcely
any electrons of the material are in the conduction
band; most remain in the valence band, even
when high electric fields are applied, thua qualifying
the material to be called an insulator. Conduction
currents in dielectrics are nearly zero. Charges
that might accumulate in one place tend to remain
for relatively long periods of time. Most optical
elements and optical fibers are dielectric. A transient
polarization current occura only when an electric
field is applied or removed, due to dipole
rotation and alignment and polarization. Polarization
and polarization currents are specified in
Maxwell’s equationa by the electric permittivity,
E, of dielectric materials. Also see conductor.
See slab dielectric op-
dielectric optical waveguide.
tical waveguide.
dielectric waveguide.
See alab dielectric waveguide.
A-5

diffraction. 1. The procesa by which the propagation
of radiant waves or lightwaves are modified as the
waves interact with objects or obstacles. Some of
the rays are deviated from their path by diffraction
at the objects, whereaa other rays remain undeviated
by diffraction at the objects. As the objects become
small in comparison with the wavelength, the
concepts of reflection and refraction become useless,
and diffraction plays the dominant role in determining
the redistribution of the rays following incidence
upon the objects. Diffraction results from
the deviation of light from the paths and foci prescribed
by the rectilinear propagation laws of geometrical
optics. Thus, even with a very small, distant
source, some light, in the form of bright and
dark bands, is found within a geometrical shadow
because of the diffraction of the light at the edge
of the object forming the shadow. Diffraction gratings,
with spacings of the order of the wavelength
of the incident light also cause diffraction that
results in the formation of light and dark areas
called “diffraction patterns.” Such gratings can
be ruled grids, spaced spots, or crYstal lattice
structures. 2. The bending of radio, sound, or
lightwaves around an object, barrier, or aperture
edges.
diode. See light-emitting diode (LED).
dispersion. 1. The process by which rays of light of
different wavelength are deviated angularly by different
amounts; e.g. , as with prisms and diffraction
gratings. 2. Phenomena that cause the refractive
index and other optical properties of a transmission
medium to vary with wavelength, also refers to the
frequency dependence of any of several parameters,
for example, in the process by which an electromagnetic
signal is distorted because the various frequency
components of that signal have different propagation
characteristics and paths. Thus, the components
of a complex radiation are dispersed or
separated on the basis of some characteristic. A
prism disperses the components of white light by
deviating each wavelength a different amount. For
example, 2.5 nsec/km might be a maximum allowable
dispersion for an 18.7 Mbit/see pulse repetition
rate with 10 km repeater spacing. 3. The allocation
of circuits between two points over more than
one geographic or physical route. See intermodal
dispersion; intramodal dispersion; material dispersion;
modal dispersion; waveguide dispersion.
distortion.
See waveguide delay distortion.
diversity. See polarization diversity.
donor. In an intrinsic semiconducting material, a dopant
that has nearly the same electronic bonding
structure as the intrinsic material, but with one
more electron among its valence electrons than that
required to complete the intrinsic bonding pattern,
thus leaving one “extra” or “excess” electron for
each impurity (dopant) atom in the structure. The
dopant (i.e., the donor) atoms are relatively few
and far apart and hence to not interfere with the
electrical conductivity of the intrinsic material.
Tin or tellurium can serve as a dopant for galium
arsenide. The extra electron moves or wanders from
atom to atom more freely than the bound electrons
that ar required to complete the bonding structure,
although interchanges actually occur with the bound
electrons. The extra electrons move about more
freely than the holes created by acceptors. Hence,
the electrons are more mobile than the holes. Under
A-6
the influence of electric fields, the electrons and
holes move in the direction of the field according
to their sign, thus constituting an electric current.
Also see acceptor; electron; hole.
E
electromagnetic interference. Interference caused or
generated in a circuit by electromagnetic radiation
energy coupling. The radiation may be lightwaves,
radio waves, gamma rays, high-energy neutrons, x-
rays, or microwaves. Sources include artifical
transmissions and emissions as well as natural
sources, such as cosmic and solar sources. The
phenomenon of interference is considered to occur
when electromagnetic energy causes an unacceptable
or undesirable response, malfunction, degradation,
or interruption of the intended operation or performance
of electronic equipment.
electromagnetic pulse (EMP). A broadband, high-intensity,
short-duration burst of electromagnetic energy,
such as might occur from a nuclear detonation.
In the case of a nuclear detonation, the electromagnetic
pulse (signal) consists of a continuous spectrum
with most of its energy distributed throughout
the lower frequencies between 3 Hz and 30 kHz.
electromagnetic wave (EMW). The effect obtained when a
time-varying electric field and a time-varying magnetic
field interact, causing electrical and msgnetic
energy to be propagated in a direction that is
dependent upon the spatial relationship of the two
interacting fields that are interchanging their energies.
The most common EMU consists of time-varying
electric and magnetic fields that are directed at
right angles to each other, thus defining a plane in
which they both lie, i.e., polarization plane. The
direction of energy propagation is perpendicular to
this plane, and the wave is called plane polarized.
A plane-polarized wave may be linearly, circularly,
or elliptically polarized depending on the phase
relationship between the varying electric and msgnetic
fields. When launched initially, the interacting
and interrelated time-varying electric and magnetic
fields are produced by an electric current,
consisting of moving electric charges that oscillate
in time and space, such as might oscillate In a wire,
called an antenna. If an electric field is made to
vary in time in a conductive medium in order to produce
an oscillating current, an electromagnetic wave
will be launched that can propagate energy through
material media and a vacuum. If the time and spatial
distributions of currents are given, the electromagnetic
field intensities, power flow rates, and energy
densities can be determined everywhere in space, provided
also that the parameters of the material in
the space are known. Lightwaves are electromagnetic
waves that can travel in optical fibers where they
can be trapped and guided, and can be made to energize
photodetectors.
electron. A basic negatively charged particle with a
char e of 1.6021 x 10-19 C and a mass of 9.1091 x
10-3 f kg. It is outside the nucleus of the chemical
elements, exists with different discrete energy
levels in a given chemical element, differentiates
the elements by its population outside the nucleus,
and is the moving matter that contributes the most
to the formation of electric currents and voltages.
Also see acceptor; donor; hole.

electron-hole recombination. The combining of an electron
and a hole resulting in a decrease in electron
energy and the production of a photon.
electronically-controllable coupler. An optical element
that enables other optical elements to be coupled
to, or uncoupled from, each other, in accordance
with an applied electrical signal. For example, two
parallel slab dielectric waveguides with an optical
material between them whose refractive index can be
altered by application of an electronic signal, thus
turning the coupling of the waveguides on or off according
to the signal.
electrooptic coefficient. A measure of the extent to
which the refractive index changes with applied high
electric field, auch as several parts per 10 thousand
for applied fields of the order of 20 V/cm.
Since the phase shift of a lightwave is a function
of the refractive index of the transmission medium
in which it is propagating, the change in index can
be used to phase-modulate the lightwave by shifting
its phase at a particular point along the guide, by
changing propagation time to the point.
electrooptic device. 1. An electronic device that uses
electromagnetic radiation in the visible, infrared,
or ultraviolet regions of the frequency spectrum;
emits or modifies noncoherent or coherent electromagnetic
radiation in these same regions; or uaes
such electromagnetic radiation for its internal operation.
The wavelengths handled by theae devices
range from approximately 0.3 to 30 microns. 2. Electronic
devices associated with light, aerving aa
sources, conductors, or detectors. Synonymous with
optoelectronic device.
electrooptic effect. The change in the refractive index
of a material when subjected to an electric field.
It can be used to modulate a light beam in a mater–
ial since many light propagation properties are dependent
upon the refractive indices of the transmission
medium in which the light travels.
electrostrictive effects. The change in physical dimensions
that occurs to certain materials when they are
placed in an electric field.
EMI.
EMP.
emission.
See electromagnetic interference.
See electromagnetic pulse.
See spontaneous emission.
emission of radiation. See light amplification by stimulated
emiasion of radiation (laser).
energy band. A specified range of energy levels that a
constituent particle or component of a substance may
have. The particles are uaually electrons, protons,
ions, neutrons, atoms, or molecules. Some energy
bands are allowable and some are unallowable for
specific particles. For example, electrons of a
given element at a specific temperature occupy only
certain energy bands. Examples of energy bands are
the higher and lower level ranges of the conduction
and valence bands.
energy gap. The difference in energy level between the
lower limit of the conduction band and the upper
limit of the valence band.
energy level. The discrete precise amount of kinetic
and potential energy possessed by a body, such as an
orbiting electron. A quantum of energy is absorbed
or radiated depending on whether an electron moves
from a lower to a higher energy level or vice versa.
evanescent-field coupling. Coupling between two waveguides,
auch as an optical fiber or an integrated
optical-circuit (IOC), in which the waveguides are
held parallel to each other in the coupling region,
with the evanescent waves on the outside of one of
the waveguides entering the coupled waveguide, bringing
some of the light energy with it into the coupled
waveguide. In optical fibers and planar dielectric
waveguides, close-to-core proximity or fusion
is required. The evanescent field of the core modes
can be made available by etching away the fiber
cladding or locally modifying the refractive index.
evanescent wave. In a waveguide conducting a transverse
electromagnetic wave, the wave on the outside of the
guide. It will radiate away at sharp bends in the
guide if the radiua of the bend is less than the
critical radius. It uaually has a frequency smaller
than the cutoff frequency above which true propagation
occurs and below which the waves decay exponentially
with distance from the guide. Evanescent
wavefronts of constant phase may be perpendicular
or at an angle less than 90” to the surface of the
guide.
extrinsic fiber loss. Optical power loss in an optical
fiber aplice, connector, or coupling caused by end
separation, axial displacement, axial misalignment,
reflection, or other external condition involved in
implementation or use and subject to the control of
the uaer.
F
Fabry-Perot interferometer. A high-resolution multiple-beam
interferometer consisting of two optically
flat and parallel glasa or quartz plates held a short
fixed diatance apart, the adjacent aurfaces of the
platea or interferometer flata being made almoat
totally reflecting by a thin silver film or multilayer
dielectric coating. If one plate is moved with
respect to the other, interference patterns are produced.
If the ends of an optical fiber are made reflective,
moving one end with reapect to the other
will also result in an output signal when monochromatic
light is inserted into the fiber.
Faraday effect.
FDM.
Synonym for magnetooptic effect.
See frequency-division multiplexing.
fiber. See graded-index fiber; low-loss fiber; multimode
fiber; optical fiber; SELFOCc fiber; self-focusing
optical fiber; single-mode fiber; step-index
fiber; optical-fiber coating.
fiber length-bandwidth product. The product of the
length of an optical fiber and the spectral width of
lightwavea propagating within it, usually expressed
in micron-kilometers.
fiber loss. See extrinsic fiber loss; intrinsic fiber
loss; optical fiber loss.
A-7

fiberoptic. Pertaining to optical fibers and the systems
in which they are used, such as sensor, telemetry,
and telecommunication systems.
fiberoptic cable. Optical fibers incorporated into an
assembly of materials that provides tensile strength,
external protection, and handling properties comparable
to those of coaxial cables. Fiberoptic cables
(light guides) are a direct replacement for conventional
coaxial cables and wire pairs. The glassbased
transmission facilities occupy far less physical
volume for an equivalent transmission capacity,
which is a major advantage in crowded underground
ducts. Manufacturing, installation, and maintenance
costs are less. These advantages, with the reduced
use of critical metals, such as copper, is a strong
impetus for the use of fiberoptic cables.
fiberoptic data link. A data link, consisting of a modulated
light source, a fiberoptic cable, and a
photodetector, that can handle signals in the form
of a modulated lightwave. Synonymous with optical
data link.
fiberoptic ribbon.
Synonym for optical fiber ribbon.
fiberoptic (FO). 1. As first defined by Kapany in
1956, the art of the active and passive guidance of
light (rays and waveguide modes) in the ultraviolet,
visible, and infrared regions of the spectrum along
transparent fibers through predetermined paths. 2.
The technology of guidance of optical power, including
rays and waveguide modes of electromagnetic
waves along conductors of electromagnetic waves in
the visible and near-visible region of the frequency
spectrum, specifically when the optical energy is
guided to another location through thin transparent
strands. Techniques include conveying light or
images through a particular configuration of glass
or plastic fibers. Incoherent optical fibers will
transmit light, as a pipe will transmit water, but
not an image. Coherent optical fibers can transmit
an image through small (2-12 microna diameter), clad,
optical fibers that are in a fixed spatial relative
position at both ends. Specialty fiberoptic combine
coherent and incoherent aspects.
fiberoptic sensor. A sensor in which a parameter (property,
characteristic) of an optical waveguide (optical
fiber), or of a lightwave propagating in an
optical fiber, is varied in accordance with an input
baseband signal thus modulating the lightwave in the
waveguide. Synonymous with optical fiber sensor;
optical sensor. Also see sensor.
fiberoptic sheath. An outer protective covering placed
over an optical fiber, bundle, or cable.
fiberoptic splice. A nonseparable junction joining one
optical conductor to another.
fiber ribbon.
See optical fiber ribbon.
fiberscope. A receiving device consisting of an entry
point, at which a bundle of optical fibers can enter,
and a faceplate surface on which the entering fibers
can uniformly terminate, in order to display the optical
image received through the fibers. The bundle
of fibers transmit a full color image that remains
undisturbed when the bundle is bent. By mounting
an objective lens on one end of the bundle and an
eyepiece at the other, the assembly becomes a flexible
fiberscope that can be used to view objects that
are otherwise Inaccessible for direct viewing. The
transmitter is a similar device, except that an image
is focused on it for transmission. The device is
used to transmit images. Also see coherent bundle.
fiber sensor. See fiberoptic sensor.
field coupling.
See evanescent field coupling.
focusing optical fiber. See self-focusing optical
fiber.
frequency-division multiplexing (FDM). Multiplexing in
which the available transmission frequency range is
divided into narrower bands, each used as a separate
channel. When an optical fiber transmits more than
one frequency at the same time, each frequency can
be modulated with a different information-bearing
signal.
frequency modulation. The modulation of the frequency
of an electromagnetic, elastic, sound, or other wave
serving as a carrier, with another wave serving as
the modulating signal, such that the frequency excursions
of the carrier are proportional to a parameter
of the modulating signal bearing the information
to be transmitted. It is a form of angle modulation
in which the instantaneous frequency of a
aine wave carrier is caused to depart from the carrier
frequency by an amount that is proportional to
the instantaneous value of the modulating signal.
Combinations of phase and frequency modulation are
also considered as frequency modulation.
Fresnel equations. See reflection coefficient, transmission
coefficient.
E!-Fl”
See energy gap.
G
geometric spreading. In a wave propagating in a transmission
medium in which there are no sources, the
decrease in power density as a function of distance
in the direction of propagation. As a curved wavefront,
such as for divergent electromagnetic waves,
moves in the direction of propagation, the available
power at one point must be spread over a larger area
at the next point in space; e.g., a point source of
light has its light energy spread over larger and
larger spherical surfaces as the distance from the
source increases.
graded-index fiber. An optical fiber witb a variable
refractive index that is a function of the radial
distance from the fiber axis, the refractive index
getting progressively lower away from the axis. This
characteristic causes the light rays to be continually
refocused by refraction in~o the core. As a
result, there is a designed continuous change in
refractive index between the core and cladding along
a fiber diameter. Synonymous with gradient-index
fiber.
gradient-index fiber. A synonym for graded-index fiber.
A-8

group velocity. The velocity of propagation of the envelope
produced when an electromagnetic wave is modulated
by, i.e., mixed with, another wave of a different
frequency. The group velocity is the velocity
of information propagation and, loosely, of energy
propagation. It is the velocity of transmission
of energy associated with a progressing wave consisting
of a group of sinusoidal components; i.e., the
velocity of a certain feature of the wave envelope,
e.g., the crest. The group velocity differs from
the phase velocity. Only the latter varies with
frequency. In general, the group velocity, representated
as:
is less than the phase velocity, represented as;
‘P “
IJJ/i3
where B is the angular velocity, ( u= 2n’f) and u is
the propagation constant.
guide.
See waveguide.
H
heterodyne detection. In fiberoptic, detection based
on the use or mixing of two or more frequencies.
For example, if a lightwave is fed to a Bragg cell,
it produces an output lightwave frequency that is
the sum of the input lightwave frequency and the
baseband frequency; an interferometer can be used to
recover the baseband frequency.
heterodyning. The mixing of an electromagnetic wave of
one frequency with a wave of another frequency to
produce one or more additional frequencies. Usually
the sum and difference frequencies will be produced
when waves of two different frequencies are combined
in a nonlinear device, such as a nonlinear amplifier.
heterojunction. In a laser diode, a boundary surface
at which a sudden transition occurs in material composition
across the boundary. For example, in a
semiconductor, a change in the refractive index as
well as a change from a positively-doped (p) region
to a negatively-doped (n) region; or a positivelydoped
region with a rapid change in doping level,
i.e., a high concentration gradient of dopant versus
distance. In most heterojunctions, change in geo -
metric cross-section occurs across which a voltage
or voltage barrier exists. Heterojunctions provide a
controlled level and direction of radiation confinement.
There usually is a step in the refractive
index level at each heterojunction. Contrast with
homojunction. See single heterojunction.
hole. In physical electronics and solid-state devices,
a semiconducting material containing a dopant that
has one less electron for each atom than that required
to complete the intrinsic bonding structure,
a site at which an electron is missing to complete
the bonding structure. Initially, the hole is created
by the impurity atoms, but if an electron from a
neighboring atom moves in to “fill” the hole, the
neighboring atom will have a hole; thus, the hole
can be considered to have migrated. Also see acceptor;
donor; electron.
homodyne detection. In fiberoptic, detection based on
the use of only one frequency. For example, a detector
that makes use of a varying-length fiber to achieve
modulation of the phase of the lightwave at
the output end of the fiber; the input baseband signal
modulates the length of the fiber and thus there
is no change in frequency of the lightwave.
homogeneous medium. In optical systems, a transmission
medium whose light-transmission parameters, such as
the parameters of the constitutive relations, are
spatially constant and not a function of space coordinates,
although they may vary as a function of
time, temperature, pressure, humidity, or other parameter
uniformly throughout the medium.
homojunction. In a laser diode, a single junction; i.e.,
a single region of shift in doping from positive to
negative majority carrier regions, or vice versa,
and a change in refractive index, all at one boundary.
Hence one energy-level shift, one barrier, and
one refractive-index shift constitute a aingle homojunction.
Constrast with heterojunction.
I
incident ray. A ray of light that falls upon, or
strikes, the surface of any object. The ray is said
to be incident at the surface.
incoherent light. Light of which not all parameters
are predictable and correlated at any point in time
or space, such as scattered or diffused light.
Contrast with coherent light.
index.
See refractive index.
index profile. See radial refractive index profile.
See refractive-index-pro-
index-profile mismatch loss.
file mismatch loss.
index profile parameter.
parameter.
See refractive index profile
index-matching material. Alight-conducting material
used in intimate contact with optical components
such as optical fibers and lenses, to reduce optical
power losses by using materials with refractive indices
at interfaces that will reduce reflection,
increase transmission, avoid scattering, and reduce
dispersion.
insertion loss. 1. In a communication system, the decrease
in signal level that results from the insertion
of a series component in a transmission circuit.
It is expressed as a percent, in decibels, or as a
per unit coefficient or fraction. The loss may be
positive or negative, that is, greater or less than
unity when expressed as a ratio (per unit fraction
or coefficient). If the insertion loss is negative
it is considered as a gain. When it is expressed
as a fraction, ratio, or per unit, it is the decrease
in signal level caused by the insertion divided by
the signal level before insertion. 2. In an optical
fiber, the optical power loss due to all causes,
usually expressed as decibels/kilometer. Causes of
loss may be absorption, scattering, diffusion, leaky
modes, dispersion, microbending, or other causes or
A-9

methods of coupling power outside the fiber. For
example, in an optical component such as a 3-dB
coupler, the insertion loss is considered as that
in excess of the 3-dB associated with splitting the
light between two fibers. 3. In lightwave transmission
systems, the power lost at the entrance to
a wavegufde due to any and all causes, such as
Fresnel reflection, packing fraction, limited numerical
aperture, axial misalignment, lateral displacement,
initial scattering, or diffusion.
insulator. A substance with a molecular structure in
which all electrons remain in the valence band,
rather than in the conduction band, even under the
influence of high electric field gradients, and
therefore a material that is used to prevent the
flow of electric current when electric fields exist.
tiso see dielectric. Contrast with conductor.
integrated optical circuit (IOC). A circuit, or group
of interconnected circuits, consisting of miniature
solid state optical components. Examples of such
components include light-emitting diodes, optical
filters, photodetectors (active and passive), and
thin-film optical waveguides on semiconductor or dielectric
substrates. Components onan IOC chip might
include semiconductor injection lasers, modulators,
filters, lightguides, switches, couplers, logic
gates, pulse shapers, differential amplifiers, and
optical memories. Synonymous with optical integrated
circuit.
integrated optics. The design, development, and operation
of circuits that apply the technology of integrated
electronic circuits produced by planar masking,
etching, evaporation, and crystal film growth
techniques to microoptical circuits on a single
planar dielectric substrate. Thus, a combination
of electronic circuitry and optical waveguides are
produced for performing various communication,
switching, and logic functions, including amplification,
gating, modulating, light generation, photodetecting,
filtering, multiplexing, signal processing,
coupling, and storing.
intensity.
See luminous intensity.
intensity sensor. In fiberoptic, a fiberoptic sensor
in which the optical intensity of a light ray (beam)
is varied in accordance with a baseband signal by
varying the light propagation properties of an optical
fiber. For example, a microbend sensor.
interference.
See electromagnetic interference.
interferometer. An instrument in which the interference
effects of lightwaves are used for purposes of
measurement, such as the measurement of the accuracy
of optical surfaces by means of Newton’s rings, the
measurement of optical paths, linear and angular
displacements, phase changes due to pressure, rotation,
and temperature effects on the sensing arm as
compared to the reference arm. See Fabry-Perot
interferometer; Mach-Zehnder interferometer; Michelson
interferometer; Sagnac interferometer; _n-
Green interferometer.
interferometric sensor. In fiberoptic, a fiberoptic
sensor that employs the principles of interferornetry
to performa sensing function. For example, aFabry-
Perot interferometer used as a fiberoptic sensor.
Also see interferometer.
interferometry. The scientific discipline devoted to
the study and useful application of interference
among electromagnetic waves.
intermodal disperson. Dispersion (pulse broadening)
that results from propagation time differences among
the various modes in an electromagnetic pulse. Intermodal
dispersion can be reduced by appropriate refractive
index profile shaping.
internal reflection. In an optical element in which an
electromagnetic wave is propagating, a reflection at
an outside surface from the inside such that a wave
that is incident upon the surface is reflected wholly
or partially back into the element itself. Optical
fibers depend on internal reflection for the successful
transmission of lightwaves in order that the
waves do not leave the fiber; namely, the wave energy
is confinded to or bound to the fiber. Also see
total internal reflection.
internal reflection sensor. See near total internal reflection
sensor.
interstitial defect. In the somewhat ordered array of
atoms and molecules in optical fiber material, a
site at which an extra atom or molecule is inserted
in the space between the normal array. The defect
can serve as a scattering center, causing diffusion,
heating, absorption, and resultant attenuation. Also
see vacancy defect.
intrinsic absorption. In lightwave transmission media,
the absorption of light energy from a traveling or
standing wave by the medium itself, causing attenuation
as a function of distance, material properties,
mode, frequency, and other factors. Intrinsic absorption
is primarily due to charge transfer bands
in the ultraviolet region and vibration or multiphonon
bands in the near infrared, particularly if
they extend into the region of wavelengths used in
optical fiber, namely, 0.7 to 1.2 microns.
intramodal dispersion. The dispersion (pulse broadening)
that occurs within one of the modea in an electromagnetic
pulse. Intramodal dispersion in an optical
fiber is a function of the spectral bandwidth
of the light source and the material dispersion
caused by the fiber. It is usually the only type of
dispersion preaent in a monomode fiber.
intrinsic fiber loss. Optical power loss in an optical
fiber or optical fiber splice, connector, or coupling,
caused in the manufacturing process, such as
refractive index profile mismatch, diameter differences,
scattering, absorption, and other causes not
subject to the control of the user.
intrinsic region. In a semiconductor junction, a region
that lies between a positively-doped region and a
negatively-doped region and that does not contain
any dopant. Synonymous with i-region.
inversion.
See population inversion.
Ioc. See integrated optical circuit.
i-region.
Synonym for intrinsic region.
A-10

isotropic material. A substance that exhibits the same
property when tested along an axis in any direction.
For example, a dielectric material with the same
permittivity to electric fields, a glass with the
same refractive index for a lightwave, or the same
conductivity to electric currents, in all directions.
jacket.
See heterojunction; homojunction; p-n junc-
junction.
tion.
See bundle jacket; cable jacket.
J
K
Kerr cell. A substance, usually a liquid, whose refractive
index change is proportional to the square of
an applied electric field. If the substance is configured
to be part of an optical path, the cell can
provide a means of modulating the light in the optical
path.
L
lasing. A phenomenon occurring when resonant frequency
controlled energy is coupled to a specially prepared
material, such as a uniformly-doped semiconductor
crystal that has free-moving or highly mobile loosely-coupled
electrons. AS a result of resonance and
the imparting of energy by collision or close approach,
electrons are raised to highly excited energy
states, which, when they move to lower states, cause
quanta of high-energy electromagnetic radiation to
be released as coherent lightwaves. This action
takes place in a laser.
LED.
length.
See light emitting diode.
See coherence length.
length-bandwidth product.
product.
See fiber length-bandwidth
light. See coherent light; incoherent light; polarized
light.
light amplification by stimulated emission of radiation
(lasers). A coherent-light generator in which molecules
of certain substances absorb incident electromagnetic
energy at specific frequencies, store the
energy for short periods in higher energy-band levels
and then release the energy, upon their return to
the lower energy levels, in the form of light at particular
frequencies in extremely narrow frequency
bands. The release of energy can be controlled in
time and direction so as to generate an intense
highly directional narrow beam of electromagnetic
energy that is coherent, i.e., the electromagnetic
fields at every point in the beam are uniquely and
specifically definable. Diode lasers and heliumneon
lasers make use of a resonant cavity that is
pumped to high energy levels to cause Population
inversion and lasing action.
rate, and the same operational current densities,
but without lasing action. The high current densities
of thousands of amperes per square centimeter
often cause catastrophic and graceful degradation.
Compared to the laser diode, the LED possesses
greater simplicity, tolerance, and ruggedness, and
about 10 times the spectral width. Typical peak
spectral power output for a gallium arsenide LED
occurs at 0.910 pm (microns), with a spectrum about
0.005 pm wide. An aluminum arsenide LED operates at
0.820 pm at a 10-MHz-wide spectrum. Both operate at
roughly l-mW spectral power output and a 50-mA
driving current.
lightfield sensor.
Synonymous with brightfield sensor.
light pipe. 1. An optical element that conducts light
from one place to another, such as an optical fiber
or slab-dielectric waveguide. 2. A hollow tube with
a reflecting inner wall that guides lightwaves in
its hollow center. 3. An optical fiber.
light ray. A line perpendicular to the wave-front of a
lightwave indicating its direction of propagation
and representing the lightwave itself.
light source. A device that produces or emits lightwaves,
such as a light-emitting diode, a laser, or a
lamp.
linear medium. An electromagnetic wave transmission
medium with constitutive parameters, such as electric
permittivity, magnetic permeability, and electric
conductivity (and hence refractive index), that remain
constant under the influence of applied electric
and magnetic fields. For example, in the relations
B=uH, D=cE, andJ=uE, thep, e, a nd u are constant
at a given point even though the fields are
changing.
link. See data link; fiberoptic data link.
lock 100P.
w“
See phase-lock loop.
See phase-lock loop.
loss. See coupling loss; extrinsic fiber loss; insertion
loss; intrinsic fiber 10SS; microbending 10SS;
optical fiber loss; refractive-index-profile mismatch
loss.
low-loss fiber. AII optical fiber having a low energy
loss, due to all causes, per unit length of fiber,
usually measured in decibels/kilometer at a specified
wavelength. Low-loss is usually considered to
be below 20 dB/km. In low-loss fiber, attenuation
of a propagating wave is caused primarily by scattering
due to metal ions, by absorption due to water
in the OH radical form, and by Rayleigh scattering.
Low-loss fiber attenuation rates are approaching 0.01
dB/km.
luminous intensity. The ratio of the luminous flux
emitted by a light source, or an element of the
source, in an infinitesimally small cone about the
given direction, to the solid angle of that cone,
i.e., luminous flux emitted per unit solid angle.
light-emitting diode (LED). A diode that operates sim -
ilar to a laser diode, with the same total output
power level, the same output limiting modulation
A-II

M
Mach-Zehnder interferometer. An interferometer in which
an electromagnetic wave is split, each half traveling
around half a loop in opposite directions, one
via a beam splitter and a fixed mirror, the other
via a movable mirror and a beam splitter, both halves
being recombined at a photodetector where their relative
phase can reinforce or cancel. The moveable
mirror modulates the resultant intensity at the
photodetector.
magnetooptic. Pertaining to the control of lightwaves
by means of magnetic fields, for example by rotating
the magnetic polarization of a lightwave and thus
achieving polarization modulation or by cementing
or coating ferromagnetic material on the outside of
a fiber and using the magnetostrictive effect to
alter the length of a fiber in the sensing arm of
an interferometer thus obtaining a method of converting
magnetic field variations to light intensity
variations. Synonymous with optomagnetic
magnetooptic effect. The rotation of the polarization
plane of lightwaves in a transmission medium brought
about when subjecting the medium to a magnetic field
(Faraday rotation). The effect can be used to modulate
the light beam in a material, since many properties,
such as conducting velocities, reflection
and transmission coefficients at interfaces, acceptance
angles, critical anglea, and transmission
modes, are dependent upon the direction of propagation
at interfaces in the media in which the light
travels. The amount of rotation is given by:
A = aHL
where a is a constant, H is the magnetic field
strength, and L is the propagation distance. The
magnetic field is in the direction of propagation of
the lightwave. Also, by coating or cementing ferroelectric
material to a fiber, the magnetostrictive
effect can be used to alter the length of a fiber in
the sensing arm of an interferometer, thua obtaining
a method of converting magnetic field variations to
light intensity variationa. Synonymous with Faraday
effect.
magnetooptic modulator. A modulator that makes use of
the magnetooptic effect to modulate a lightwave carrier.
magnetostriction. The phenomenon exhibited by some
materials in which dimensional changes occur when
the material is subjected to a magnetic field, usually
becoming longer in the direction of the applied
field. The effect can be used to launch a shock or
sound wave each time the field is applied or changed,
possibly giving rise to phonons that could influence
energy levels in the atoms of certain materials such
as semiconductors and lasers and thereby serve as a
modulation method. Along with photon or electric
field excitation, the phonon energy could provide
threshold energy to cause electron energy level
transitions, causing photon absorption or emission.
The effect can also be used to change the physical
dimensions of an optical fiber that is wrapped
around or cemented to or jacketed by, a magnetostrictive
(ferromagnetic) material and thus modulate a
light beam in the fiber.
margin. See power margin.
material dispersion. 1. The variation in the refractive
index of a transmission medium as a function of
wavelength, in optical transmission media used in
optical waveguides; e.g., optical fibers, slab dielectric
waveguides, and integrated optical circuits.
Material dispersion contributes to group-
-delay distortion, along with waveguide-delay distortion
and multimode group-delay spread, i.e., the
spreading of a pulse. 2. The part of the total
dispersion of an electromagnetic pulse in a waveguide
caused by the changes in properties of the
material with which the waveguide, such as an optical
fiber is made, due to changes in frequency. As
wavelength increasea, and frequency decreases, material
dispersion decreases. At high frequencies, the
rapid interactions of the electromagnetic field with
the waveguide material (optical fiber) renders the
refractive index even more dependent upon frequency.
Maxwell’s equations. A group of basic equations, in
either integral or differential form, that (1) describe
the relationships between the properties of
electric and magnetic fields, their sources, and the
behavior of these fielda at material media interfaces;
(2) express the relations among electric and
magnetic fields that vary in space and time in material
media and free space; and (3) are fundamental to
the propagation of electromagnetic waves in material
media and free space. The equations are the basis
for deriving the wave equation that expresses the
electric and magnetic field vectors in a propagating
electromagnetic wave in a transmission medium such
as a lightwave in an optical fiber. Maxwell’s
equations in differential form are:
vx E = -aBlat
v. H = J + aD/3t
V. B=O
V“ D=o
where E, H, B, and D are the electric field intensity,
the magnetic field intensity, the magnetic
flux density, and the electric flux density (electric
displacement) vectors, respectively, J is the
electric current density, and pis the electric
charge density, the v is the “del- space derivative
operator, expressing differentiation with respect
to all distance coordinates, the VX being the curl
and the v - being the divergence. The partial derivatives
are with respect to time. These equations
are Used in conjunction with the constitutive relations
to obtain useful practical results given actual
sources of charge and current in real media.
These are only valid when the field and current
vectors are single-valued, bounded, continuous functions
of poaition and time, and have continuous
derivatives.
medium. See homogeneous medium; linear medium; sourcefree
medium; transmission medium.
meridional ray. In an optical fiber, a light ray that
passes through the central axis of the fiber, is
internally reflected, and is confined to a single
plane, called the meridian plane. Also see skew ray.
metal oxide semiconductor. A semiconductor composed of
doped metal oxide, such as silicon oxide (Si02). See
combined metal oxide semiconductor.
A-12

Michelson interferometer. b interferometer in which
an electromagnetic wave is split. One half is then
reflected from a fixed mirror and back through the
splitter to a photodetector, the other half is passed
directly through the splitter to a movable mirror
(transducer) that reflects it back to the splitter
where it is reflected to the same photodetector.
The two waves can phase enhance or cancel and thus
modulate the intensity at the photodetector in accordance
with a baseband input signal to the movable
mirror. If an optical fiber is used, the ends of
the fiber form the reflecting surfaces. Moving one
end with respect to the other produces the same effect
as moving the mirror.
microbend. A small bend or induration in the outer
surface of an optical fiber core that causes lightwaves
in the core to penetrate into the cladding
and thus leak from the fiber. Contrast with ordinary
bend.
microbend loss. In an optical fiber, the loss or attenuation
in signal power caused by small bends, kinks,
or abrupt discontinuities in the direction of the
fibers, usually caused by fiber cabling or by wrapping
fibers on drums. Microbending losses usually
result from a coupling or guided modes among themselves
among the radiation modes when light rays
enter the cladding at the microbends or get reflected
at larger than critical angles and hence also enter
the cladding. Use can be made of microbend loss by
creating microbends in number and amplitude in accordance
with a baseband signal and thus modulating
leakage. Contrast with ordinary bend.
microbend sensor. A transducer capable of converting
mechanical mvement, such as displacement actuated
by applied forces or pressures, into a modulated
lightwave in an optical fiber. The microbender
introduces microbends in the fiber thus modulating
the lightwave intensity by causing leakage in accordance
with the information-bearing baseband signal.
micrometer. See micron.
micron (lhn or P). A unit of length in the metric system
equal to one-millionth of a meter, i.e., 10-6
meter. Synonymous with micrometer.
mismatch 10ss. See refractive-index-profile-mismatch
loss.
mixing box.
See optical mixing box.
mixing rod. See optical mixing rod.
modal dispersion. 1. The difference in propagation
time for each of the modes propagating in an optical
fiber, resulting in a broadening of a light pulse.
2. In the propagation of an electromagnetic wave or
pulse in a waveguide, the changes introduced in the
relative magnitudes of the frequency components of
the wave or pulse. The guide is capable of supporting
or introducing only a fixed number of frequencies
depending on its geometry and material parameters,
such aa permeability, permittivity, and conductivity.
where a is the fiber radius, nl and n2 are the refractive
indexes of core and cladding, and 1 is the
wavelength. There are additional degenerate modes
that can be supported, such as polarization and
evanescent modes. 2. In communication systems, a
form or medium for transmission of voice, image,
digital data, or other signala.
mode stripper.
See cladding mode stripper.
mode volume. For a large number of modes, N = fn2/2,
where fn is the V-parameter (normalized frequency or
V-value).
modulation. 1. The variation of a characteristic or
parameter of a wave in accordance with a characteristic
or parameter of another wave. For example, a
variation of the amplitude, frequency, or phase of a
carrier wave in accordance with the wave form that
represents information by means of superposition,
mixing, or transduction. The carrier may be a continuous
direct-current (DC) signal or a continuous
alternating signal such as a sinusoidal wave. The
carrier is used as a means of propagation. The
superimposed or mixed aignal is used as the intelligence-bearing
signal. The variation of the modulated
carrier is detected at the receiver. The information
or intelligence frequencies are normally called
the baseband. 2. In fiberoptic, the variation
of a characteristic or parameter of a lightwave in
order to superimpose an information-bearing signal
on a carrier wave. For example, a variat~on of the
amplitude, frequency, or phase of a lightwave by an
analog or digital baseband signal in a fiberoptic
sensor, transmitted in an optical fiber, and recovered
by a photodetector. The carrier may be a continuous
lightwave when it is not modulated by the sensor.
Contrast with demodulation. See amplitude
modulation; phase modulation; polarization modulation;
frequency modulation.
modulator. A device that accomplishes modulation, that
is, has the capability of varying one signal in accordance
with the variations of another aignal. Thus,
it converts baseband signal into a modulated carrier.
moving grating sensor. A sensor consisting of a fixed
and moveable grating of transparent and opaque areas
such that the intensity of light passing through is
modulated according to the amount that the transparent
areas of both gratings coincide (overlap) aa
the movable grating is moved according to the applied
baseband aignal.
multimode fiber. An optical fiber waveguide that will
allow (support) more than one mode to propagate.
Multimode optical fibers have a much larger core (25
to 75 microns) than aingle-mode fibers (2 to 12
microns diameter) and thus permit nonaxial rays or
modes to propagate through the core.
multiplexing. See frequency-division multiplexing; polarization
multiplexing; space-division multiplexing;
time-division multiplexing (TDM); wavelengthdivision
multiplexing (WDM).
mode. 1. A specific condition or arrangement of electromagnetic
waves in a transmission medium, particularly
in a waveguide. The total number of dimensional
modes that a step-index optical fiber can support,
couple to, or radiate into is given by:
1= ~2a2 (n12-n22)/A2
A-13

N
nanometer. One thousandth of a micron, i.e. , 10-9
met er.
near total internal reflection sensor. In fiberoptic,
a fiberoptic sensor that operates on the principle
of varying the property of an optical fiber in such
a manner that the amount of light that leaks into
the cladding ie altered by varying the critical angle
in accordance with a baseband signal, auch as by
altering the refractive index or the ordinary bend
radius, thus altering the internal reflection.
noise. In a fiberoptic system, the sum of unwanted or
disturbing energy introduced into the system from
natural or man-made sources, such as unwanted lightwaves
coupled into an optical fiber or unwanted modulation
of lightwaves in an optical fiber due to environmental
conditions that alter the propagation or
modulation characteristics of an optical fiber or
fiberoptic sensor.
noise power. The power that is developed by unwanted
electromagnetic waves from all sources in the output
of a device, such as a transmission channel or amplifier.
Noise power is usually the total noise power
of waves with frequencies within the passband of the
system or device. Croastalk, distortion, and lntermodulation
products are usually classed as noise.
normalized frequency.
See V-parameter.
numerical aperture (N.A.). A measure of the light-accepting
property of an optical fiber. For example,
glass; given by:
N.A. = (n12-n22)1/2
i.e., the square root of the difference of the
squares of the refractive indices of the core, nl,
and the cladding, n2. If nl is 1.414 (glass) and n2
is 1.0 (air), the numerical aperture is 1.0 and all
incident rays will be trapped. The numerical aperture
is a measure of the characteristic of an optical
waveguide in terms of its acceptance of impinging
light. The degree of openness, light-gathering
ability, angular acceptance, and acceptance cone are
all terms describing the characteristic. It may be
necesaary to specify that the refractive indices are
for step index fibera and for graded index fibers;
nl is the maximum index in the core and n2 is the
minimum Indexin the cladding. As a number, theN.A.
expresses the Mghtgathering power of a fiber. It
is mathematically equal to the sine of the acceptance
angle. A method of meaauring the N.A. is to excite
the fiber in the visible region and display the light
emerging from the end perpendicularly on a screen
about 10 to 30 cm away. The measured diameter of
the projected circle of light divided by twice the
distance from the fiber end to the screen is the
numerical aperture. The numerical aperture is also
equal to the sine of the half-angle of the widest
bundle of rays capable of entering a lens, multiplied
by the refractive index of the medium containing
that bundle of rays, i.e., the incident medium.
Typical numerical apertures for plastic-clad fused
silica optical fibers range from 0.25 to 0.45.
optic.
optical cable.
See fiberoptic.
optical circuit.
optical data link.
0
See fiberoptic cable.
See integrated optical circuit.
See fiberoptic data link.
optical fiber. A single discrete optical transmission
element or waveguide usually consisting of a fiber
core and a fiber cladding that can guide a lightwave
and is usually cylindrical in shape. It consists
either of a cylinder of transparent dielectric material
of a given refractive index whose walls are in
contact with a second dielectric material of a lower
refractive index; or of a cylinder whose core has a
refractive index that gets progressively lower away
from the center. The length of a fiber is usually
much greater than its diameter. The fiber relies
upon internal reflection to transmit light along its
axial length. Light enters one end of the fiber and
emerges from the opposite end with losses dependent
upon length, absorption, scattering, and other factors.
A lightwave in an optical fiber can be modulated
by changing the light propagation parameters
of the fiber. A bundle of fibers has the ability
to transmit a picture from one of its surfaces to
another, around curves, and into otherwise inaccessible
places with an extremely low losa of definition
and light, by the proceas of total internal reflection.
One optical fiber classification scheme is
to divide them into plastic, glaas, or plastic-clad
fuaed silica fibers; then into step-index multimode,
graded-index multimode, or step-index single mode
fibers. Plastic is less brittle than glass but has
increased attenuation compared to glass. Synonymous
with light pipe. See self-focusing optical fiber.
optical fiber coating. A protective material bonded to
an optical fiber over the cladding to preserve fiber
atrength and inhibit cabling losses by providing protection
againat mechanical damage, protection against
moisture and debilitating environments, compatibility
with fiber and cable manufacture, and compatibility
with the jacketing proceas. Coatings include
fluorpolymers, Teflonc, Kynarc, polyurethane,
and many others. Application methods include dipcoating
(for those in solution), extrusion, spray
coating, and electrostatic coating.
optical fiber jacket. A material used to cover an optical
fiber, whether or not it is cladded or coated.
optical fiber loss. The optical power loss in an optical
fiber, usually expressed in dB/km.
optical fiber preform. Specially-shaped material from
which an optical fiber is made, usually by drawing
or rolling. For example, a solid glass rod made with
a higher refractive index than the tube into which
it is alipped,
into a cladded optical fiber; or
tive-index rods surrounding a
index rod heated and drawn into a
drawing procesa results in fiber
than the preforma.
to be heated and drawn or rolled
four lower-refrachigher-refractivecladded
fiber. The
many times longer
A-14

optical fiber ribbon. A rowof optical fibers laminated
in a flat plastic strip. Synonymous with fiberoptic
ribbon.
optical fiber sensor.
Synonym for fiberoptic sensor.
optical integrated circuit. A synonym for integrated
optical circuit.
optical mixing box. A fiberoptic coupler consisting of
a piece of fiberoptic material that receives several
optical frequencies and that mixes them to produce
dichromatic or polychrometic lightwaves for dispatch
via one or more outputs for transmission elsewhere
and perhaps subsequent separation into the constituent
frequencies to produce the original information
introduced by the modulation of each of the constituent
frequencies. The mixing box usually has reflective
inner surfaces, except at the ports. The
lightwaves entering the box are usually a group of
monochromatic waves each of a different frequency
and each modulated separately.
optical mixing rod. An optical mixing box that has the
general shape of a right circular cylinder, usually
with pigtails to serve as entrance and exit ports.
optical power budget. In an optical transmission system,
the distribution of the available power that is
required for transmission within specified distortion
limits or error rates. The distribution is
usually in terms of decibels for each component of
the system from source to sink. Components include
the light source pigtail, connectors, cable, splices,
and detector pigtail.
optical power density. The optical energy per unit time
transmitted by a light beam through a unit area normal
to the direction of propagation or the direction
of maximum power gradient, expressed in watts per
square meter or joules per second-(square meter).
A watt is a J/S.
optical power efficiency. The ratio of the emitted
electromagnetic power of an optical source to the
electrical input power to the aource.
optical repeater. An optical/optical, optical/electrical,
or electricalloptical signal amplification and
processing device. The repeater usually accepts an
optical signal, converts it into an electrical signal
(photodetection) amplifies it, and converts it
back to an optical signal for further transmission.
optical sensor.
See slab dielectric optical wave-
optical waveguide.
guide.
optics.
optoacoustics.
See fiberoptic sensor.
See integrated optics.
Synonym for acoustooptics.
optoelectronic. 1. Pertaining to the conversion of
optical power or energy into electrical power or
energy, such as the conversion of an optical signal
into an electrical signal. Also see electrooptic.
2. Synonym for electrooptic.
optoelectronic device.
optomagnetic. See magnetooptic.
See electrooptic device,
optostrain. Pertaining to the change in lightwave propagation
characteristics caused by changes in waveguide
parameters due to strain resulting from applied
stress (tensile, compression, shear, bending,
torsional or combinational stress). Synonymous with
optostress.
optostress. A synonym for optostrain.
ordinary bend. A bend in the core of an optical fiber
in which the central axis of the core may be said to
have a bend with finite nonzero radius. If the
radius of the bend is smaller than the critical
radius, light will leak from the core as total internal
reflection no longer takes place. Bending a
fiber from more than to less than the critical
radius can be used to modulate the light intensity
or the leakage. Contrast with microbend.
See combined metal oxide semicon-
oxide semiconductor.
ductor.
parameter.
— PD.
P
See refractive index profile parameter.
See photodetector.
phase detection. Obtaining an output electrical signal
proportional to an input lightwave phase angle that
varies with respect to a fixed reference in accordance
with a baseband input signal. Often phase detection
can be accomplished by conversion to amplitude
detection.
?hase-lock loop. An electronic circuit that controls
an oscillator so that it maintains a constant phase
angle relative to a reference signal source. The
system can be used in situations in which signals
that are shifted in phase with respect to one another
maintain a fixed or specified phase relationship.
In spread-spectrum systems a phase-lock loop
is used to cause an oscillator internal to the feedback
loop to oscillate at an incoming carrier frequency.
The feedback, or servoloop, circuit utilizes
the output of a phase-sensitive detector, via a
low pass filter, to control the frequency of its own
reference signal. The feedback loop is damped to
permit tracking of the carrier phase changes at the
input, but not tracking of the modulation changes.
The arrangement also provides a low noise threshold.
In fiberoptic systems, a similar arrangement can
be used to control the phase of a continuous or modulated
lightwave carrier.
phase modulation (PM). Angle modulation in which the
instantaneous phase angle of an unmodulated sine
wave carrier is varied proportionally in accordance
with the instantaneous value of the amplitude of a
modulating signal.
phase velocity. The velocity with which a specific
point on a sine wave (e.g., the peak value of the
electric vector of an electromagnetic wave) is propagated
in a material medium or in free space. This
concept can only strictly be applied to a single
frequency wave, such as an unmodulated carrier wave.
The phase velocity is the propagation velocity of a
uniform plane sinusoidal wave, given as the wavelength
times the frequency of the wave. The phase
A-15

velocity is also the velocity at which an observer
would have to move to make the wave characteristics
appear to remain constant in phase in a given medium.
The phase velocity in a given medium is equal
to the velocity of propagation of the wave divided
by the refractive index of the medium when the wave
is an electromagnetic wave. It is not the velocity
of electromagnetic energy propagation, although it
may be higher than the velocity of light in free
space. For a given frequency, the wavelength is less
in material media than in free space when electromagnetic
waves are involved. In nondispersive media,
the phase velocity and the group velocity are equal.
Also see group velocity.
photodetector (PD). A device that is capable of extracting
information from a lightwave by producing
an electrical output signal from an optical input
signal.
yhoton. A quantum of electromagnetic energy. The
energy of a photon is hf, where h is Planck’s constant,
and f is the frequency of the radiation.
ylane of polarization.
See polarization plane.
p-n junction. In a semiconductor (solid-state) device,
the interface between semiconducting ~terial that
has been doped positively, i.e., with an impurity
material that produces holes (acceptor sites) on one
side of the interface, and material that produces
relatively free electrons (donor sites) on the other
side. The junction is usually assumed to be abrupt,
or linearly graded in its transition region across
the interface.
Pockel cell. A material, usually a crystal, whose refractive
index change is linearly proportional to a
change in an applied electric field, the material
being configured so as to be part of another system,
such as an optical path. The cell thus provides a
means of modulating the light in the optical path.
polarimetric sensor. In fiberoptic, a sensor in which
a baseband input signal alters the polarization of a
lightwave in an optical fiber or the output intensity
is varied by a process of polarization selection.
polarization. The direction of the electric field vector
of an electromagnetic wave, such as a lightwave.
It is the property of a radiated electromagnetic
wave that describes the time-varying direction and
amplitude of the electric field vector, that, together
with the magnetic field vector, makes up the
wave. It is specifically illustrated by the figure
that is traced in space as a function of time by
the extremity (tip) of the vector that represents
the electric field with its base at a fixed point in
space, as observed along the direction of propagation.
In general, for a plane polarized wave, the
figure is elliptical and it is traced in a clockwise
or counterclockwise sense. Circular polarization
and linear polarization are obtained when the ellipse
becomes a circle or a straight line, respectively.
Clockwise sense rotation of the electric field vector
is designated right-hand polarization, and counterclockwise
sense rotation is designated left-hand
polarization. Sense of rotation is obtained by viewing
the rotating electric field vector while facing
in the direction of propagation. The direction of
propagation is the forward direction of a right-hand
screw obtained when the electric vector is rotated
through the smaller angle into the magnetic vector,
A-16
the direction of propagation being perpendicular
to both fields, namely, the direction of the Poynting
vector.
polarization diversity. 1. Pertaining to the ability
to change the direction of polarization of an electromagnetic
wave, usually at the source of radiation,
by changing the direction of the polarization
plane, the horizontal or vertical polarization, i.e.,
the polarization angle with respect to a fixed reference
or the linear, circular, elliptical, or helical
polarization. 2. Pertaining to two or more types
of polarization. 3. Any method of diversity transmission
and reception in which the same information
signal is transmitted and received simultaneously
on orthogonally polarized waves with fade-independent
propagation characteristics. Also see diversity
reception.
polarization modulation. The modulation of an electromagnetic
wave in such a manner that the polarization
of the carier wave, such as the direction of polarization
of the electric and magnetic fields, or their
relative phasing, to produce changes in polarization
angle in linear, circular, or elliptical polarization,
is varied according to a characteristic of an
information-bearing input signal, such as a pulseor-no-pulse
digital signal. In optical fibers or
other waveguides, polarization shifts that are made
in accordance with an input signal variation are a
practical means of modulation.
polarization multiplexing. Multiplexing accomplished by
using two mor more lightwave polarization modes in
the same transmission medium at the same time with
the same frequency. Each polarization mode would
constitute a separate channel.
polarization plane. In a transverse, or ordinary, electromagnetic
(TEM) wave, the plane defined by the
electric and magnetic field vectors of the wave;
i.e., both field vectors at a point lie in, and
therefore define, the polarization plane. The direction
of propagation, or power flow, of the wave
is perpendicular to both the electric and magnetic
field vectors at the point, i.e., perpendicular to
the polarization plane at that point. The wavefront
lies in the polarization plane. The Poynting vector,
ExH, is perpendicular to the polarization plane.
polarized light. A light beam whose electric vector
vibrates in a direction that doea not change, unless
the propagation direction changes; i.e., it is in a
plane perpendicular to the direction of propagation.
If the time-varying electric vector can be broken
into two perpendicular components that have equal
amplitude and that differ in phase by 1/4 wavelength,
the light is said to be circularly polarized.
Circular polarization is obtained whenever
the phaae difference between the two perpendicular
components is any odd, integral number of quarter
wavelengths. If the electric vector is resolvable
into two perpendicular components of unlike amplitudes
and differing in phase by values other than
O, 1/4, 1/2, 3/4, 1, etc., wavelengths, the light
beam is said to be elliptically polarized.
population inversion. A redistribution of energy levels
in a population of elements such that, instead of
having more atoms with lower-energy-level electrona,
there are fewer atoms with higher-energy-level electrona.
That ia, an increaae in the total number of
electrons in the higher excited states occurs at
the expense of the energy in the electrons in the

ground or lower state and at the expense of the
resonant energy source (i.e. , the pump). This is
not an equilibrium condition. It is forced and must
be maintained, i.e, stimulated. The generation of
population inversion is caused by pumping. When
electrons revert to their lower levels, photons are
emitted obtaining laser action. In a stimulated
material, such as a semiconductor, the upper energy
level of two possible electronic energy levels in a
given atom, distribution of atoms, molecule, or distribution
of molecules, has a higher probability
(usually only slightly higher) of being occupied by
an electron. When population inversion occurs, the
probability of downward energy transition giving
rise to radiation, is greater than the probability
of upward energy transitions, giving rise to photon
absorption, resulting in a net radiation level, thus
obtaining stimulated emission, i.e., laser action.
=“
See transmitted power.
power budget. The allocation of available power in a
system to the various functions that need to be performed.
For example, in a fiberoptic data link, the
distribution of available optical power among all
the elements of the link, such as couplers, splices,
fibers, and pigtails; or in a satellite communication
system, the distribution of the available power
in a satellite for maintaining orientation, maintaining
orbit control, and for the reception and retransmission
of signals. See optical power budget.
power density.
See optical power density.
power margin. An extra amount of power that may be
specified by a designer because of uncertainties in
the empirical design method, loss, characteristics,
material variability, and variation in equipment performance
parameters and characteristics. For example,
in an optical power budget, the optical power,
PM, that remains after subtracting the sum of all
the optical losses, PL, and the power input required
by a photodetector, PR, from the available optical
power output by a source, P5, i.e.,
profile.
pM = ps
- [pL+pR].
See radial refractive index profile.
profile mlsmstch loss.
mismatch loss.
profile parameter.
parameter.
*“
See refractive-index-profile
See refractive index profile
See electromagnetic pulse (EMP).
punch-through voltage. In a semiconductor junction, a
voltage equal to that required to just overcome the
potential barrier of the junction to permit the flow
of electrons that are in the conduction band.
R
radial refractive-index profile. In an optical fiber
with a circular cross section, the refractive index
described as a function of the radial distance from
the center. For example, the function:
n=n~ f(r)
where n is the refractive index at a radial distance
r from the center, nl is the refractive index at the
center, and f(r) is the function of r that expresses
the index at the distance r from the center , usually
independent of radial direction. Also see refractive
index profile parameter.
radiation. See light amplification by stimulated emission
of radiation (laser).
~. See light ray; meridional ray; reflected ray;
skew ray.
Rayleigh scattering. The scattering of lightwaves propagating
in material media due to the atomic or molecular
structure of the material and variations in
the structure as a function of distance. The scattering
losses vary as the reciprocal of the fourth
power of the wavelength. The distances between
scattering centers must be small compared to the
wavelength. Rayleigh scattering sets a theoretical
lower limit to the attenuation of a propagating
lightwave as a function of wavelength, ranging from
10 dB/km at 0.50 micron to 1 dB/km at 0.95 micron.
Material scattering is caused primarily by Rayleigh
scattering. Rayleigh scattering is also due to the
variation in molecular density of intrinsic material;
for example, the familiar light green color of
pop bottles is due to Rayleigh scattering from distributed
iron atoms. This represents the limiting
absorption. Also since it decreases with A, this
has resulted in using higher wavelengths to achieve
low-loss fiber. Minimum attenuation is due to decreases
in absorption due to Rayleigh scattering
and increases due to OH- vibration. Also see scattering.
ray trapping. Preventing a lightwave from leaking from
a waveguide. For example, total internal reflection
causes ray trapping.
recombination.
See electron-hole recombination.
reflected ray. A ray of electromagnetic radiation,
usually light leaving a reflecting surface. The ray
Indicates the path after reflection.
reflection. When electromagnetic waves, such as light
rays, strike a smooth, polished surface, their return
or bending back into the medium from whence
they came. Specular or regular reflection from a
polished surface, such as a mirror, will return a
major portion of the light in a definite direction
lying in the plane of the incident ray and the normal.
After specular reflection, light can be made
to form a sharp image of the original source. Diffuse
reflection occurs when the surface is rough and
the reflected light is scattered from each point in
the surface. These diffuse rays cannot be made to
form an image of the original source, but only of
the diffusely reflecting surface itself. Also see
Snell’s law; internal reflection; total internal
reflection.
reflection coefficient. 1. The ratio of the reflected
field strength to the incident field strength when
an electromagnetic wave is incident upon an interface
surface between dielectric media of different
refractive indices. If, at oblique incidence, the
magnetic field component of the incident wave is
parallel to the interface, the reflection coefficient
is given by:
A-17
R = (nlcosA -
n2cosB)/(nlcosA + n2cosB)

where nl and n2 are the reciprocals of the refractive
indices of the incident and transmitted mediums,
respectively, and A and B are the angles of
incidence and refraction (with respect to normal),
respectively. If, at oblique incidence, the electric
field component of the incident wave is parallel
to the interface, the reflection coefficient is
given by:
R = (n2cosA -
nlcosB)/(n2cosA + n~cosB)
These equations are known as the Fresnel equations
for such cases. For large smooth surfaces, the reflection
coefficient may be near unity, such as for
highly polished mirrors. At near grazing incidence
angles, that is nearly 90° from the normal to the
surface, even rough surfaces may reflect relatively
well, i.e., total reflection occurs. 2. At any
specified point in a transmission line between a
power source and a power sink (absorber), the vector
ratio of the electric field associated with the reflected
wave to that associated with the incident
wave. The reflection coefficient, RC, is given by
RC = (Z2-Zl)/(Z2+Zl) = (SWR-1)/(SWR+l),
where Z1 iS the impedance looking toward the source,
Z2 is the impedance looking toward the load, and SWR
ia the standing wave ratio. Also see transmission
coefficient.
reflection sensor.
sensor.
See near total internal reflection
reflective star-coupler. An optical-fiber coupling device
that enables signals in one or more fibers to
be transmitted to one or more other fibers by entering
the signals into one side of an optical cylinder,
fiber, or other piece of material, with a reflecting
back-surface in order to reflect the diffused
signals back to the output ports on the same
aide of the material, for conduction away in one or
more fibers.
refraction. The bending of oblique (non-normal) incident
electromagnetic waves or raya as they cross the
interface between a transmission medium of one refractive
index into a medium of a different refractive
index. The velocityof propagationof theelectromagnetic
waves change when passing from a medium
to one with a different refractive index. Also see
Snell’s law
refraction angle. When an electromagnetic wave strikes
an interface surface between media with different
refractive indices and is wholly or partially transmitted
into the new medium, the acute angle between
the normal to the surface at the point of incidence
and the refracted ray.
refractive index. 1. The ratio of the velocity of
light in a vacuum to the velocity of a given frequency
of light in the transmission medium whose refractive
index is desired; e.g., n = 2.6 for certain
kinds of glass. 2. The ratio of the sines of the
incidence angle and the refraction angle when light
passes from one medium to another. The index between
two media ia the relative index, while the
index when the first medium is a vacuum is the absolute
index of the second medium. The refractive
index expressed in tables is the abaolute index,
i.e., vacuum-to-substance at a certain temperature,
with light of a certain frequency. Examples: vacuum,
1.000; air, 1.000292; water, 1.33; ordinary crown
glass, 1.516. Since the index of air is very cloae
to that of vacuum, the two are often used interchangeably.
The refractive index of a substance
is given as:
where p is the magnetic permeability of the substance,
E ia the electric permittivity, P. is the
magnetic permeability of a vacuum, and E. is the
electric permittivity of a vacuum, although nearly
the same relative to air.
refractive index profile.
profile.
See radial refractive index
refractive-index-profile mismatch loss. A 10SS Of Sig -
nal power that occurs when two optical fibers are
butt-coupled and their refractive index profiles are
not the same.
refractive index profile parameters. The exponent i in
the relation that expresaes the refractive index as
a function of the radial diatance from the central
axis of an circular optical fiber, i.e., in the
expression:
nfnl =
[1-(r/a)i]l/2
where n is the refractive index at the radial distance
r and a is the radiua of the fiber core. For
a step-index fiber i= co for ra; for
a parabolic graded-index fiber, i=2. A value of i=
2.25 will minimize or eliminate intermodal dispersion
and maximum the length-bandwidth product.
rejection ratio. See common-mode rejection ratio
(CMRR).
~. A bounded region in a material medium,
such as a free rectangular space in a laser
crystal, a length of metal hollow tubing closed on
both ends, a short length of optical fiber with mirrors
on both ends, or the reflection could be due to
a 3-dB coupler or a splice associated with the insertion
loss, or a region of such geometrical dimension,
such as two parallel walls that are a multiple
or submultiple of wavelengths apart, that a standing
wave (electromagnetic, acoustic, or elastic) can
be austained and raised to high intensity by application
of stimulation (applied energy of appropriate
frequency) from outside or inside the cavity. Resonant
cavities are used in some lasers in which they
form part of the laser head.
ribbon.
See optical fiber ribbon.
risetime. In pulse circuits, the time required for a
pulse to reach a specific magnitude from a given
level. For example, the time required for a voltage
or a light pulse to change from 0.1 to 0.9 of its
maximum value.
risetime budget. In fiberoptic transmission systems,
an accounting of all the riaetimea (time required
for a lightpulse to reach a apecified level) in a
aequence of optical and electrical components. Because
the distribution of photon energies in lightwaves
are Gausaian, the risetimes of a aequence of
components are combined as the aquare root of the
sum of the squarea of the individual ristimes.
A-18

s
Sagnac interferometer. An interferometer in which a
lightwave is split and passed in opposite directions
around the same rigid rotating loop by means of mirrors
to a single photodetector. The phase cancellation
and enhancement, and hence light intensity at
the photodetector, will vary as the angular velocity
is varied, thus obtaining a measure of angular acceleration.
scatter. The process in which the direction, frequency,
phase, or polarization of sound or electromagnetic
waves is changed when the waves encounter one
or more discontinuities in the transmission medium
that have lengths of the order of a wavelength.
Scattering usually implies a random or disordered
change or distribution in the incident energy.
scattering. The deflection of electromagnetic waves
caused by movement of free and bound charges (e.g.,
electrons, protons, and ions) in a transmission
medium, the scattered fields being created as a result
of the movement. The scattered field and the
incident field define the total field. See Rayleigh
scattering.
sm. See space-division multiplexing.
—
self-focusing optical fiber. ATI optical fiber that is
capable of focusing lightwaves by precision-control
of geometry, refractive indices, light wavelength,
and other parameters. The fiber is frequency-selective.
SELFOC fiber. Self-focusing optical fiber produced by
Nippon Electric Company and Nihon Sheet Glass Company.
semiconductor. A material, such as diamond, silicon,
galium-arsenide, germanium, gray tin, tellurium, and
selenium, that has a filled valence-electron energy
band separated by a finite band-gap energy from a
higher-energy conduction band. Thus, semiconductors
are neither insulators, with large band gaps and
small electronic nobilities, nor metallic conductors
with extremely high conductivities. Semiconductors
possess covalent bonding wherein electron pairs are
held tightly in the region between adjacent atoms or
ions. The band-gap energy is the energy required to
break an electron out of one of theae bonds. Semiconductors
are often grown in single crystals and
sliced or cut, to form diodes, transistors, lasers,
and LEDS, thus preserving an ordered crystal lattice
structure suitable for accepting positive or negative
dopants. See combined metal oxide semiconductor;
metal oxide semiconductor.
sensor. A device or means to extend the natural senses.
For example, equipment that detects or indicates
terrain configuration or that detects the presence
of objects or their motion by means of energy
that is emitted or reflected by the objects; equipment
that detects physical variables, such as temperature,
pressure, humidity, weight, vibration, or
acceleration; equipment that detects the presence or
intensity of illumination, radio waves, ionization
density, electric fields, or magnetic fields; or
equipment that detects the presence of chemicals,
such as pollutants and irritants; or the presence of
radioactivity. Most detectors are in fact transducers,
since they convert energy to another form
and amplify it. They are usually designed to meas–
ure variations in the quantities that they are sensing.
A fiberoptic sensor makes use of changes in
its light propagation properties to detect and measure
the environmental changes it is subjected to.
See brightfield sensor; fiberoptic sensor; darkfield
sensor; interferometric sensor; intensity sensor;
microbend sensor; near total internal reflection
sensor; polarimetric sensor.
sensor array. A spatial distribution of sensors. The
spatial distribution may be used to obtain baseband
directional information and to achieve various forms
of multiplexing.
sheath.
See fiberoptic sheath.
signal. 1. A time-dependent value attached to a transient
physical phenomenon used to convey data, e.g.,
the variation of light intensity at a point in an
optical waveguide to represent a binary digit, the
light-level change propagating as a pulse along the
guide. 2. An impulse, either electrical, as in a
wire; acoustic, as used in aonar; or a short burst
of light energy, as generated by a laser and coupled
to an optical fiber for guidance and transmission
and for conversion back to an electrical pulse at
the far end of the fiber.
signal processing. The transformation of an input signal,
i.e., a specific wave shape, into some other
desirable form or other wave shape, usually by means
of particular electronic circuits, lens systems,
waveguides, antennae, or other circuit elements,
such as detectors, rectifiers, pulse compressors,
pulse expanders, pulse generators, nonlinear circuits,
or gates. It includes the detection, shaping,
converting, coding, or time positioning of an
electrical, electromagnetic, or acoustic signal.
single heterojunction. In a laser diode, a single junction
involving two energy level shifts and two refractive
index shifts, used to provide increased confinement
of radiation direction, improved control of
radiative recombination, and reduced nonradiative
(thermal) recombination. Synonymous with close-confinement
junction.
single-mode fiber. An optical fiber that supports the
propagation of only one mode. Usually a low-loss
optical waveguide with a very small core (2 to 12
microns diameter). It requires a laser source for
the input signals because of the very small entrance
aperture (acceptance cone) and the narrow spectral
width. The small core radius approaches the wavelength
of the source, consequently only a single
mode is generated and propagated.
skew ray. In an optical fiber, a light ray that is not
confined to a plane, does not pass through the optical
axis, is not parallel to the optical axis, and
yet is totally internally reflected, thus taking a
curling (corkscrew) path. In certain graded index
fibers, the skew ray travels in a helical path along
the fiber never intersecting the optical axis, particularly
as long as the fiber is straight. It is
not confined to the meridian plane or any other
plane, nor is it a meridional ray. Also see meridional
ray.
A-19

slab dielectric optical waveguide. An optical waveguide
consisting of rectangular layers or ribbons
of materials of differing refractive indices that
support one or more lightwave transmission modes,
with the energy of the transmitted waves confined
primarily to the layer of highest refractive index,
the lower indexed medium serving aa cladding, jacketing,
or surrounding medium. Slab dielectric optical
waveguides are used in integrated optical circuits
for geometrical convenience, in contrast to
the optical fibers in cables for long-distance
transmission.
slab dielectric waveguide. An electromagnetic waveguide
consisting of a dielectric transmission medium
of rectangular cross section. The width and thickness
of the guide may be controlled to support
specific propagation modes; it may be cladded, protected,
distributed, and electronically controllable;
and it may be mounted on integrated electrooptical
circuit substrate.
Snell’s law. When electromagnetic wavea, such as light,
pass from a given transmission medium to a medium
of higher refractive index (denser) medium, its path
is deviated toward the normal. When paasing into
a less dense medium, its path is deviated away from
the normal. Often called the law of refraction,
Snell’s law defines this phenomenon
the relation between the incidence
by describing
angle and the
refraction angle as follows:
sin@l/sine2 = n2/nl
where 81 is the incidence angle, ’32 is the refraction
angle, n2 is the refractive index of the medium
containing the refracted ray, and nl is the refractive
index of the medium containing the incident
ray. Stated in another way, both laws, that of reflection
and of refraction, are attributed to Snell,
namely, when the incident ray, the normal to the
surface at the point of incidence of the ray on the
surface, the reflected ray, and the refracted ray
all lie in a single plane, the angle between the incident
ray and the normal is equal in magnitude to
the angle between the reflected ray and the normal.
The ratio of the sine of the angle between the normal
and the incident ray, to the sine of the angle
between the normal and the refracted ray, is a constant
for a given wavelength of incident light.
Also see refraction.
source. In fiberoptic sensors, as in communications,
that part of a syatem from which signals or messages
are considered to originate. A fiberoptic sensor is
the source of baseband signals in a fiberoptic system.
The source may be an optical source (unmodulated)
or a signal source used to modulate the optical
source. See light source.
source-free medium. In fiberoptic, a transmission
medium that does not contain a source of electromagnetic
radiation, such as electric charges or magnetic
poles, other than a propagating or standing
electromagnetic wave.
space-division multiplexing. The use of spatial separation
between light beams, conductors, optical
fibers or other transmission media in order to obtain
channel isolation. For example, the combining
of several independent and isolated fibers or wires
in a single bundle or cable in order to use each
fiber (or bundle) as a separate communication path,
channel, or set of channels. A typical arrangement
for multiplexing might be to use time-division multiplexing
on each space-division multiplexed fiber pair
in an optical cable.
splitter.
See beam splitter.
~. In a laser, emission that does
not bear an amplitude, phase, or time relationship
with an applied signal and is therefore a random
noiselike form of light radiation. Alao see stimulated
emission.
spreading.
star-coupler.
See geometric spreading.
See reflective star-coupler.
step-index fiber. A fiber in which there is an abrupt
change in refractive index between the core and
cladding along a fiber diameter, with the core refractive
index being higher than the cladding refractive
index. There may be more then one layer,
each layer with a different refractive index that
is uniform throughout the layer, but usually with
decreasing indices in the outside layers.
stimulated emission. In a laser, the emission of light
caused by a signal applied to the laser such that
the response is directly proportional to, and in
phase coherence with, the electromagnetic field of
the stimulating signal. This coherency between applied
signal and response contributes to the usefulness
of the laaer. Also see spontaneous emission.
stimulated emission of radiation. See light amplification
by stimulated emission of radiation (laser).
strength member. In fiberoptic cables, a component of
the cable that provides tensile strength and bending
resistance, therefore limiting stress (and strain)
on the optical fibers in the cable.
stripper.
See cladding mode stripper.
substrate. A material used to support or serve as a
foundation, vehicle, or carrier for other material
that has the required characteristics for specific
application but does not have the proper phyaical
strength to support itself, e.g., a block of material
upon which active materials may be deposited by
evaporative techniques or on which active materials
may be bonded by cementing or etching techniques.
The substrate is usually inert or passive relative
to the active material mounted upon it.
switch.
See waveguide switch.
solid state. Pertaining to the conduction of electric
currents or magnetic flux, or the propagation of
electromagnetic waves, within materials other than
gases or other than a vacuum.
A-20

— TDM.
T
See time-division multiplexing.
telecommunication. Communication over relatively large
distances by any transmission, emission, or recep -
tion of signals, signa, writing, images, and sounds,
or intelligence of any nature by wire, radio, visual,
or other electrical, electromagnetic, optical,
acoustic, or mechanical means. The process enables
one or more users to pass to one or more other users
information of any nature delivered in desirable
forms, such as written or printed matter, fixed or
moving pictures, words, music, visible or audible
signals, or signals that can control the functioning
of equipment or mechanisms. Also see telemetry.
telemetry. The branch of science and technology devoted
to the process of measuring the values of variables,
such as pressure, temperature, humidity, blood flow,
radiation levels, or sound levels; transmitting the
results of the measurements by some means to a distant
station; and interpreting, indicating, displaying,
recording, or using the information that is
obtained. Also see telecommunication.
time.
See coherence time.
time-division multiplexing (TDM). Multiplexing in which
separate channels are established by connecting one
circuit automatically to many signal sources sequentially
in time. The signals from the several
sources, such as an array of fiberoptic sensors,
share the time of the circuit by using the circuit
in successive time slots. Each discrete time interval
is assigned to a particular signal source. Synchronizing
pulses are used to asaist in demultiplexing
at the distant end of the circuit. Thus, the
time of an optical fiber can be divided among many
signal sources, by allowing two or more signal
sources to use the channel at different times. The
channel may be shared by automatically switching to
the several sources and connecting each one to the
channel during the specific time period allocated
to that source. For example, if each aource is assigned
to a given channel for 1 Vsec out of each
millisecond, 1,000 sources can be accommodated
(multiplexed) by the channel. During a given time
interval the entire available frequency spectrum
can be used by the channel to which it is assigned.
In general, time-division multiplexed systema use
pulae transmission or analog sampling. The multiplexed
pulse string may be considered to be the
interleaved pulse strings of the individual channels.
The individual channel pulses may be modulated in
either an analog or digital manner.
total internal reflection. Reflection that occurs within
a substance when the incidence angle of a light
ray striking a boundary surface is greater than the
critical angle and therefore the entire energy of
the ray is reflected back into the substance and
none is transmitted across the surface.
total internal reflection senaor. See near total internal
reflection sensor.
transducer. A device capable of transforming energy
from one form to another, usually with such fidelity
that if the original energy time and spatial distribution
represents information, the transformed energy
can represent the same information or a function
A-21
of that information. For example, a fiberoptic sensor
that converts a pulse pressure wave into a modulated
lightwave, a microphone that converts a sound
wave to a corresponding electrical current, a modulated
laser that converta electrical currents to
modulated lightwaves, a photodetector that converts
modulated lightwaves to electrical current, or a
piezoelectric crystal that produces a voltage proportional
to the time derivative of the pressure
wave that impinges upon it. See optoacoustic transducer.
transmission coefficient. The ratio of the transmitted
field strength to the incident field strength when
an electromagnetic wave is incident upon an interface
surface between dielectric media of different
refractive indices. If, at oblique incidence, the
electric field component of the incident wave is
parallel to the interface, the transmission coefficient
is given by:
T = 2n2cosA/(n2cosA + nlcosB)
where nl and n2 are the reciprocals of the refractive
indices of the incident and transmitted media,
respectively, and A and B are the incidence angle
and refraction angle (with respect to the normal to
the interface surface), respectively. If, at oblique
incidence, the magnetic field component of the
incident wave is parallel to the interface surface,
the transmission coefficient is given by:
T = 2n2cosA/(nlcosA + n2cosB)
These equations are known as the Fresnel equations
for these cases.
transmission medium. Any subatance that can be or Is
used for the propagation of signals, usually in the
form of modulated radio, light, acoustic waves, or
electric currents, from one point to another, such
as an optical fiber, cable, or bundle; a wire; a
dielectric slab; water; or air. Free space can also
be considered as a transmission medium for electromagnetic
waves.
transmitted power. The energy per unit time usually
expressed in watta, propagated through a specified
croas sectional area, such as a fiber cable or other
waveguide, or a specified cross-sectional area perpendicular
to the direction of propagation, such as
in a specified solid angle, or through a fictitious
sphere completely surrounding the transmitter. Since
instantaneous transmitted power can vary with time
and the specified croas-sectional area can change,
the power can assume various forms of measurement,
such as the peak envelope power, the power in a given
direction, the power averaged over time, the power
averaged over an area or solid angle, the total carrier
power delivered to an antenna, the total power
radiated and integrated over all directions, or it
may be the power limited to a specified portion of
a frequency spectrum or bandwidth.
trapping.
See ray trapping.

v
vacancy defect. In the somewhat ordered array of atoms
and molecules in optical-fiber material, a site at
which an atom or molecule is missing in the array.
The defect can serve as a scattering center, causing
diffusion, heating, absorption and resultant attenuation.
Also see interstitial defect.
valence band. In a semiconductor, the range of electron
energy, lower than that of the conduction
band, possessed by electrons that are held bound to
an atom of the material, thus reducing conductivity
for electric currents even under the influence of
an applied electric field. When electron engergies
are raised, e.g., by thermal excitation or by phonons,
electrons with the highest energy levels of
the valence band are raised to the lower energy
levels of the conduction band, thus leaving holes
in the atoms whose electrons remain in the valence
band.
velocity.
See phase velocity.
V-parameter. A parameter that can be used to calculate
or express the number of propagating modes that a
step-indexed optical fiber is capable of supporting,
expressed mathematically as:
fn =
(2na/k)(n12 - n22)1/2
where fn is the V-parameter (V-value or normalized
frequency), a is the optical fiber core radius, Ais
the source wavelength, and nl and n2 are the refractive
indices of the core and cladding of the optical
fiber. For a large number of modes, the mode volume
is given by:
N = fn2/2
where N is the number of modes, or mode volume, and
fn Is the V-parameter (V-value or normalized frequency)
above. Synonymous with normalized frequency;
V-value.
V-value. Synonym for V-parameter.
wave.
w
See electromagnetic wave; evanescent wave.
wave equation. The equation, based on Maxwell’s equations,
the constitutive relations, and the vector
algebra, that relates the electromagnetic field of
an electromagnetic wave time and space derivatives
with the transmission medium electrical permittivity
and magnetic permeability in a region without electrical
charges or currents. The solution of the wave
equation yields the electric and magnetic field
strength everywhere as a function of time and space
coordinates, field strengths, and transmission media
parameters. The wave equation is given as either:
72H- ~ca2H/at2 = o ‘r
v2E - vEa2E/at2 = o
in a current- and charge-free nonconducting medium,
where E is the electric field intensity, H is the
magnetic field intensity, c is the electric permittivity,
and p is the magnetic permeability. V is the
vector spatial derivative operator. The wave equation
applies in optical waveguides.
wavefront. A surface normal to an electromagnetic ray
as it propagates from a source, the surface of the
wavefront passing through those parts of the waves
that are in the same phase. For parallel rays, the
wavefront is a plane. For rays diverging from or
converging toward a point, the wavefront is spherical.
The wavefront is perpendicular to the direction
of propagation of the wave, and the electric
and magnetic field vectors of the wave define a
plane that is tangent to the wavefront surface at
the point that the field vectors are determined.
The front is a three-dimensional surface all the
points on which are the same optical path length
from the wave source.
waveguide. Any structure capable of confining and supporting
the energy of an electromagnetic wave to a
specific relatively narrow controllable path that is
capable of being altered, such as a rectangular
cross-section metal pipe, an optical fiber of circular
cross section, or a coaxial cable. See slab
dielectric waveguide.
waveguide delay distortion. In an optical waveguide,
the distortion in received signal caused by the differences
in propagation time for each wavelength,
(i.e., the delay versus wavelength effect for each
propagating mode), causing a spreading of a received
signal pulse at the detector. Waveguide delay distortion
contributes to group-delay distortion as
does material dispersion and multimode group-delay
spread.
waveguide dispersion. The part of the total dispersion
attributable to the dimensions of the waveguide. The
cross-section dimensions are critical. They determine
the modes that are allowed and not allowed to
propagate. Waveguide dispersion increases as the
spectral width of the source increases due to the
actual dimensions and their variation along the
length of the guide.
wavelength. The length of a wave measured from any
point on a wave to the corresponding point on the
next cycle of the wave, such as from crest to crest.
Wavelength determines the nature of the various
forms of radiant energy that comprise the electromagnetic
spectrum, e.g., it determines the color of
light. For a sinusoidal wave, the wavelength is the
distance between points of corresponding phase of
two consecutive cycles of the wave. The wavelength
k, iS related to the phase velocity v, and the frequency
f, by the relation i= vlf.
wavelength-division multiplexingg (WDM). In optical communication
systems, the multiplexing of lightwaves in
a single transmission medium or channel, such that
each of the waves are of a different wavelength and
are modulated separately before insertion into the
medium. Usually, several sources are used, such as
a laser, or several lasera, or a dispersed white
light source or aources, each having a distinctly
different center wavelength. WDM is the same as
frequency-division multiplexing (FDM) applied to
visible light frequencies of the electromagnetic
spectrum.
wave number. The value of 2n times the reciprocal of
the wavelength of a single-frequency sinusoidal wave
such as a singlefrequency uniform plane-polarized
A-22

electromagnetic wave, e.g. , a monochromatic lightwave.
The wave number is usually used for waves in
or near the visible spectrum, since wavelength is
more readily measured than frequency, but it is frequency,
or wave number, that iS directly related to
to energy. For example, photon energy is given by:
P.E.
= hkc/2n = hf = hcl~
where h is Planck’s constant, k is the wave number,
c is the velocity of the light, f 1S the frequency,
and k is the wavelength. The wave number is the
number of wavelengths per unit distance in the direction
of propagation. Also see wave parameter.
waveguide switch. A mechanically or electrically controlled
device that is capable of stopping, attenuating,
or diverting the propagation of electromagnetic
energy at a specific point in a waveguide.
wave parameter. 1. Any feature of a wave, such as its
amplitude, phase or shape. 2. A unit that is used
in regard to periodic waves, such as electromagnetic
waves. The wave parameter, p, is given by the relation
p = 2n/A, where A is the wavelength. Also see
wave number.
— WDM.
See wavelength-division multiplexing.
3-dB coupler. In fiberoptic, a coupler that splits
the optical energy in an optical waveguide into two
equal parts and couples each part into a separate
waveguide. The 3-dB coupler ideally distributea 50%
of the input optical power to each of the output
channels. However, in actual practice, the ratio
may vary, for example, 45% into one and 55% into the
other output channel. Some optical energy may be
lost or absorbed by the coupler.
A-23