FIBEROPTIC SENSOR TECHNOLOGY HANDBOOK

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-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
Page 1 and 2: FIBEROPTIC SENSOR TECHNOLOGY HANDBO
Page 3 and 4: FOREWORD THE FIBEROPTIC SENSOR TECH
Page 5 and 6: 4.2 Phase 4.2.1 4.2.2 4.2.3 4.2.4 4
Page 7 and 8: CHAPTER 1 INTRODUCTION 1.1 BACKGROU
Page 9 and 10: CHAPTER 2 FIBEROPTIC SENSOR COMPONE
Page 11 and 12: fleeted each time it is incident on
Page 13 and 14: 6=0 REFERENCE PLANE that propagate
Page 15 and 16: in the right center of Fig. 2.13. T
Page 17: The vertical height of the various
Page 21 and 22: : 1.5 z o GeOz 0 ~ =1.49 u w > ~1.4
Page 23 and 24: tension it collapses to eliminate t
Page 25 and 26: MAXIMUM TENSILE STRENGTH (GN/m2 = l
Page 27 and 28: mately a 0.5 electron-volt increase
Page 29 and 30: I in one portion of the recombinati
Page 31 and 32: crated electron-hole paira that are
Page 33 and 34: sink fiber. Likewise angular misali
Page 35 and 36: fused together. The ends are bent a
Page 37 and 38: A laboratory beam splitter set-up u
Page 39 and 40: aged multichannel unit. High-streng
Page 41 and 42: CHAPTER 4 LIGHTWAVES IN FIBEROPTIC
Page 43 and 44: tor addition indefinitely, as indic
Page 45 and 46: modes. Since at point (a) the two e
Page 47 and 48: as a number of wavelengths. An expr
Page 49 and 50: 100 meters of fiber, length changes
Page 51 and 52: the aingle-sideband phaae noiae int
Page 53 and 54: sets up periodic spatial fluctuatio
Page 55 and 56: ient configuration in the lower rig
Page 57 and 58: sors or a pressure gradient sensor.
Page 59 and 60: nickel H. = 3.6 oersteds and for a
Page 61 and 62: optical source of constant intensit
Page 63 and 64: in a straight section of the fiber
Page 65 and 66: A simplified design of the cladding
Page 67 and 68: Referring once more to Fig. 5.35, i
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The path length AL traveled by ligh
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5.4.9 Fiberoptic Rotation-Rate Sens
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a modulation scheme, the output of
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Fig. 5.60 lists several sources of
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CHAPTER 6 FIBEROPTIC SENSOR ARRAYS
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method of sensor energization will
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1 The preceding discussion applied
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SIMPLEX FIBEROPTIC TRANSMITTER FIBE
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MAXIMUM ALLOWABLE RISETIME = 0.7/RN
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PROCESSING STATION TRANSMISSION wAV
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fiberoptic cable (optical cable), a
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angstrom. A unit of length equal to
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core. The central primary light-con
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diffraction. 1. The procesa by whic
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fiberoptic. Pertaining to optical f
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methods of coupling power outside t
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M Mach-Zehnder interferometer. An i
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N nanometer. One thousandth of a mi
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velocity is also the velocity at wh
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where nl and n2 are the reciprocals
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slab dielectric optical waveguide.
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v vacancy defect. In the somewhat o
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