Nonlinear Fiber Optics - 4 ed. Agrawal

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Index 527 Raman amplification with, 319 second-order, 215 solitons and, 216–220 PMD parameter, 12, 214, 218, 265, 409 Poincaré sphere, 191–195, 217, 255, 256, 266, 317, 335, 406, 408, 492 polarization degree of, 337 evolution of, 189–197, 255 induced, 31 intrapulse, 256 nonlinear, 31, 37, 247, 369, 402 static, 496 third-order, 254 polarization chaos, 196 polarization ellipse, 179, 190 nonlinear rotation of, see nonlinear polarization rotation rotation of, 191, 193 polarization instability, 194–197, 206, 468 effect on solitons, 207 observation of, 195 origin of, 194 polarization-dependent gain, 215, 319 polarization-diversity loop, 397, 401 polarization-division multiplexing, 218 polarization-mode dispersion, see PMD preform, 4, 181 rocking of, 196 spinning of, 202 principal axis, 178, 216, 488 principal states of polarization, 214 propagation constant, 7, 28 pseudorandom bit pattern, 346, 394 pseudospectral method, 41 pulse arbitrary-shape, 67 chirped, 85, 103 chirped Gaussian, 56 Gaussian, 54, 57, 84, 103, 107, 138, 246 hyperbolic secant, 58, 134, 138 parabolic, 100–102, 305 Q-switched, 337, 347, 417, 470 super-Gaussian, 58, 81, 85, 138 pulse broadening dispersion-induced, 53–76, 112 PMD-induced, 214, 219 pulse compression amplifier-induced, 100 soliton effect, 313 XPM-induced, 248, 314 pulse-to-pulse fluctuations, 493 pump depletion, 277, 279, 289, 299, 339, 341, 373, 399, 501 pump-phase modulation, 394, 397 pump-probe configuration, 241, 242, 245, 255, 260, 265, 429 quadrupole moment, 368, 496 quantum interference, 497 quantum limit, 394 quarter-wave plate, 185 quasi-CW regime, 283, 371, 374, 433, 502 quasi-monochromatic approximation, 32, 227 quasi-periodic route, 356 quasi-phase matching, 498 radiation Cherenkov, 457 continuum, 138, 139, 149, 218 nonsolitonic, 457–459, 462, 463, 480– 488 Raman amplification, 150, 288–292, 378 PMD effects on, 319 short-pulse, 305 vector theory of, 315 Raman amplifier, see amplifier Raman effect, 32, 247, 274 Raman gain, 16, 38, 275, 373, 378, 386, 398, 446, 462, 472 polarization dependence of, 315, 321 spectrum of, 275, 479 Raman laser, 285–288, 311 synchronously pumped, 304 Raman response, 37–40, 162, 280, 432, 462, 479 Raman scattering, 15, 432 interpulse, 248 intrapulse, 36, 38–40, 111–114, 123, 126, 143, 158, 162–168, 247, 308, 453– 464, 476, 477, 480 spontaneous, 274–277, 393, 417, 469, 495 stimulated, 89, 150, 274–285, 378, 440 Raman soliton, see solitons Raman threshold, 277, 278, 382, 440, 471 Raman-induced power transfer, 396, 398 Rayleigh scattering, 5, 6, 340 refractive index, 27, 425 effective, 360, 437 intensity-dependent, 239
528 Index nonlinear, 227, 424, 425 Raman-induced, 280 SBS-induced, 350 relaxation oscillations, 207, 338, 352, 353, 360 ring cavity, 357, 413, 466 rise time, 59 saddle point, 191 Sagnac effect, 252 Sagnac interferometer, 251, 358, 412, 428, 430 sampling oscilloscope, 302 SBS, 329–362 cascaded, 357, 358, 360 dynamics of, 344–356 experiments on, 338 gain spectrum of, 330–333 quasi-CW, 333–340 sensors based on, 344 suppression of, 335, 394, 398, 430 threshold of, 333–337, 339, 347, 394 transient regime of, 346 scanning electron microscope, 441, 445 Schrödinger equation, 67 nonlinear, see NLS equation second-harmonic generation, 69, 368, 496–502 selection rule, 330, 404 self-frequency shift, 40, 248 self-phase modulation, 15, 36, 79–114, 159, 378, 382, 386, 405, 426 self-pulsing, 361 self-similarity, 100, 305 self-steepening, 38, 107–111, 123, 160–162 Sellmeier equation, 6, 437 seperatrix, 191 signal-to-noise ratio, 152, 344, 394 sine–Gordon equation, 166 single-pump configuration, 391–394, 403 slow axis, 11, 178, 185, 193, 194, 207, 384, 386, 459, 465, 489, 505 slowly varying envelope approximation, 32, 45, 168, 345 solitary waves, see solitons soliton dragging, 211 soliton period, 135, 309 soliton trapping, 209, 211, 235, 459, 460, 484, 485 solitons amplification of, 149–152 birefringence effects on, 209 bistable, 144–145 black, 141, 142 bright, 140, 375 Brillouin, 350, 361 chirp effects on, 139 collision of, 154 dark, 140–143, 233 dispersion-managed, 144, 219 dissipative, 350, 375 experimental observation of, 136 fission of, 161, 165, 454, 464, 476, 480, 492, 494 four-wave mixing, 375 fundamental, 132–134, 136, 207, 314, 454, 476, 480, 481 gray, 141, 142 guiding-center, 151 higher-order, 134–137, 148, 161, 165, 207, 251, 307, 313, 454, 476, 480, 492 history of, 129 impact of fiber losses, 147 interaction of, 152–156 kink, 166 multicomponent, 237 parametric, 375 peak power for, 134 period of, 135 perturbation methods for, 146 PMD effects on, 216–220 polarization effects on, 207 Raman, 306, 309, 311, 454, 482, 484, 487, 503, 506 second-order, 135, 308 self-frequency shift of, 162–168, 313, 453, 480 stability of, 137 symbiotic, 233, 375 third-order, 135, 162 third-order dispersion and, 158 topological, 166 vector, 212, 217, 237, 492 XPM-coupled, 233, 375, 486 spectral asymmetry, 240, 475 spectral broadening, 79–87 asymmetric, 109, 240, 246 polarization-dependent, 257 SPM-induced, 109, 136, 158, 426, 446, 464, 473, 481, 501 XPM-induced, 240, 242, 485 spectral filtering, 143, 303 spectral fringes, 493
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Preface Since the publication of th
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Chapter 1 Introduction This introdu
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1.2. Fiber Characteristics 3 Figure
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1.2. Fiber Characteristics 7 1.49 1
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1.2. Fiber Characteristics 11 faste
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1.3. Fiber Nonlinearities 13 Figure
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1.3. Fiber Nonlinearities 15 Sectio
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1.3. Fiber Nonlinearities 17 1.3.3
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1.4. Overview 19 briefly. The last
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References 21 1.11 Equation (1.3.2)
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References 23 [63] M. Ibanescu, Y.
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Chapter 2 Pulse Propagation in Fibe
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2.2. Fiber Modes 27 where Ẽ(r,ω)
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2.2. Fiber Modes 29 across the core
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2.3. Pulse-Propagation Equation 31
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2.4. Numerical Methods 41 Equation
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2.4. Numerical Methods 43 Figure 2.
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2.4. Numerical Methods 45 the basic
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References 47 2.5 Derive an express
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References 49 [44] V. I. Karpman an
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Chapter 3 Group-Velocity Dispersion
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3.2. Dispersion-Induced Pulse Broad
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3.3. Third-Order Dispersion 63 This
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3.3. Third-Order Dispersion 65 Figu
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3.3. Third-Order Dispersion 67 6 5
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3.3. Third-Order Dispersion 69 Noti
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3.4. Dispersion Management 71 Figur
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3.4. Dispersion Management 73 10 3
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3.4. Dispersion Management 75 Figur
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References 77 3.10 An optical commu
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Chapter 4 Self-Phase Modulation An
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4.1. SPM-Induced Spectral Changes 8
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4.2. Effect of Group-Velocity Dispe
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4.3. Semianalytic Techniques 103 In
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4.3. Semianalytic Techniques 105 (1
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4.4. Higher-Order Nonlinear Effects
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Problems 115 4.2 Plot the spectrum
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References 117 [40] D. Marcuse, J.
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References 119 [109] J. Santhanam a
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5.1. Modulation Instability 121 of
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5.1. Modulation Instability 123 2 L
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5.1. Modulation Instability 125 Fig
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5.1. Modulation Instability 127 Fig
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5.2. Fiber Solitons 129 Figure 5.5:
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5.2. Fiber Solitons 131 and write i
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5.2. Fiber Solitons 133 Physically,
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5.3. Other Types of Solitons 141 1
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5.3. Other Types of Solitons 143 pr
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5.3. Other Types of Solitons 145 Th
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5.4. Perturbation of Solitons 147 w
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5.4. Perturbation of Solitons 149 w
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5.4. Perturbation of Solitons 151 t
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5.4. Perturbation of Solitons 153 b
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5.4. Perturbation of Solitons 155 F
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5.5. Higher-Order Effects 157 where
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5.5. Higher-Order Effects 159 Figur
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5.5. Higher-Order Effects 161 1 N =
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5.5. Higher-Order Effects 163 Integ
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5.5. Higher-Order Effects 165 Figur
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5.5. Higher-Order Effects 167 that
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Problems 169 Problems 5.1 Solve Eq.
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References 171 [27] E. Brainis, D.
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References 173 [93] L. F. Mollenaue
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References 175 [165] V. V. Afanasje
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Chapter 6 Polarization Effects As d
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6.1. Nonlinear Birefringence 179 wh
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6.1. Nonlinear Birefringence 181 re
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6.2. Nonlinear Phase Shift 183 dA y
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6.2. Nonlinear Phase Shift 185 wher
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6.2. Nonlinear Phase Shift 187 side
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6.3. Evolution of Polarization Stat
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6.4. Vector Modulation Instability
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6.5. Birefringence and Solitons 207
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6.6. Random Birefringence 213 where
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6.6. Random Birefringence 215 PMD,
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6.6. Random Birefringence 217 As in
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6.6. Random Birefringence 219 Figur
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References 221 6.9 Derive the dispe
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References 223 [63] P. Kockaert, M.
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References 225 [140] A. El Amari, N
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7.1. XPM-Induced Nonlinear Coupling
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7.2. XPM-Induced Modulation Instabi
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7.2. XPM-Induced Modulation Instabi
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7.3. XPM-Paired Solitons 233 This t
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7.3. XPM-Paired Solitons 235 The co
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7.3. XPM-Paired Solitons 237 It is
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7.4. Spectral and Temporal Effects
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7.5. Applications of XPM 249 Probe
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7.5. Applications of XPM 251 by hig
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7.5. Applications of XPM 253 Figure
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7.6. Polarization Effects 255 where
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7.6. Polarization Effects 257 Figur
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7.6. Polarization Effects 259 1 0.8
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7.6. Polarization Effects 261 4 Pum
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7.6. Polarization Effects 263 Figur
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7.7. XPM Effects in Birefringent Fi
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7.7. XPM Effects in Birefringent Fi
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Problems 269 7.2 Derive the dispers
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References 271 [33] M. Lisak, A. H
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References 273 [105] B. V. Vu, A. S
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8.1. Basic Concepts 275 Figure 8.1:
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8.1. Basic Concepts 277 set of two
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8.1. Basic Concepts 279 10 mW. Howe
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8.1. Basic Concepts 281 0.5 Raman R
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8.2. Quasi-Continuous SRS 283 four
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8.2. Quasi-Continuous SRS 285 Figur
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8.2. Quasi-Continuous SRS 291 wavel
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8.2. Quasi-Continuous SRS 293 1 0.8
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8.3. SRS with Short Pump Pulses 295
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8.4. Soliton Effects 307 Figure 8.1
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8.4. Soliton Effects 313 ton laser
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8.5. Polarization Effects 315 maxim
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8.5. Polarization Effects 317 where
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8.5. Polarization Effects 319 and s
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Problems 321 Figure 8.25: (a) Avera
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References 323 [4] W. Kaiser and M
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References 325 [75] M. Nakazawa, T.
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References 327 [144] V. I. Kruglov,
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Chapter 9 Stimulated Brillouin Scat
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9.1. Basic Concepts 331 Figure 9.1:
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9.2. Quasi-CW SBS 333 [20]. A part
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9.2. Quasi-CW SBS 335 (see Figure 8
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9.2. Quasi-CW SBS 337 pseudorandom
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9.2. Quasi-CW SBS 339 Figure 9.4: S
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9.3. Brillouin Fiber Amplifiers 341
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9.3. Brillouin Fiber Amplifiers 343
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9.4. SBS Dynamics 345 9.4.1 Coupled
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9.4. SBS Dynamics 347 Pump Power (k
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9.4. SBS Dynamics 349 Figure 9.11:
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9.4. SBS Dynamics 351 Δn SBS . If
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9.5. Brillouin Fiber Lasers 357 Fig
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9.5. Brillouin Fiber Lasers 359 Fig
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9.5. Brillouin Fiber Lasers 361 rin
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References 363 9.4 Estimate SBS thr
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References 365 [47] Y.-X. Fan, F.-Y
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References 367 [119] R. G. Harrison
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10.1. Origin of Four-Wave Mixing 36
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10.2. Theory of Four-Wave Mixing 37
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10.3. Phase-Matching Techniques 377
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10.4. Parametric Amplification 387
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10.5. Polarization Effects 401 Bril
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10.5. Polarization Effects 403 foll
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10.5. Polarization Effects 405 Jone
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10.5. Polarization Effects 407 to s
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10.5. Polarization Effects 409 Figu
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10.6. Applications of Four-Wave Mix
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Problems 417 Figure 10.24: Output s
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References 419 [5] R. W. Boyd, Nonl
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References 421 [79] A. Durécu-Legr
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References 423 [140] M. D. Levenson
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11.1. Nonlinear Parameter 425 11.1.
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11.1. Nonlinear Parameter 427 Figur
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11.1. Nonlinear Parameter 433 when
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11.2. Fibers with Silica Cladding 4
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11.3. Tapered Fibers with Air Cladd
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11.3. Tapered Fibers with Air Cladd
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11.4. Microstructured Fibers 441 he
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11.4. Microstructured Fibers 443 Ef
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11.5. Non-Silica Fibers 445 0.05 0.
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11.5. Non-Silica Fibers 447 Figure
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References 449 wavelength range of
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References 451 [57] H. Yokota, E. S
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Chapter 12 Novel Nonlinear Phenomen
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12.1. Intrapulse Raman Scattering 4
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12.2. Four-Wave Mixing 465 Figure 1
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12.2. Four-Wave Mixing 467 Figure 1
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12.3. Supercontinuum Generation 469
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Page 482 and 483: 12.4. Temporal and Spectral Evoluti
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Page 512 and 513: References 507 12.6 Derive an expre
Page 514 and 515: References 509 [45] J. E. Sharping,
Page 516 and 517: References 511 [111] J. Y. Y. Leong
Page 518 and 519: References 513 [180] A. L. Calvez,
Page 520 and 521: Appendix A 515 converted into decib
Page 522 and 523: Appendix B 517 % This code solves t
Page 524 and 525: Appendix C List of Acronyms Each sc
Page 526 and 527: Index acoustic response function, 4
Page 528 and 529: Index 523 distributed fiber sensors
Page 530 and 531: Index 525 four-photon, 412 gain-swi
Page 534: Index 529 spectral hole burning, 36
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