FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK

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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.