Nonlinear Fiber Optics - 4 ed. Agrawal

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Index acoustic response function, 433 acoustic velocity, 330, 336 acoustic wave, 330, 347, 432 damping time of, 330 guided, 330, 415 adiabatic perturbation theory, 147 Airy function, 63 all-optical sampling, 414 amplifier Brillouin, 340–344 erbium-doped fiber, 150, 291, 292, 393 parabolic pulses in, 100 parametric, 381, 387–411 Raman, 150, 288–292, 305, 320, 390 semiconductor optical, 290 SPM effects in, 100 Yb-doped fiber, 101, 305, 337, 347 amplifier spacing, 149, 151 angular momentum conservation, 401, 403, 408 anisotropic stress, 177 annihilation operator, 415 anti-Stokes band, 282, 340, 358, 370, 378, 382, 386, 473 attenuation constant, 5 autocorrelation trace, 70, 124, 136, 309, 428 avalanche photodiode, 483 Babinet–Soleil compensator, 186 backward-pumping configuration, 291 Baker–Hausdorff formula, 42 bandwidth amplifier, 292, 390, 400 Brillouin-gain, 286, 416 parametric amplifier, 388–399 pulse, 67, 74 Raman-gain, 276, 288, 294, 374, 394 source, 66 spontaneous noise, 291 Stokes, 278 supercontinuum, 472 521 beat length, 11, 178, 190, 194, 207 Bessel function, 28 birefringence, 459, 465, 468, 489, 505 circular, 197 fluctuating, 265, 335, 408 linear, 178, 180, 185, 189, 194, 264, 388 modal, 11, 178, 180, 184, 189, 383 modulated, 196 nonlinear, 177–182, 189, 194, 254, 264 pump-induced, 184 random, 213 residual, 255, 266, 408 stress-induced, 386 temperature-induced, 386 XPM-induced, 256 Bloch equation, 266 Boltzmann constant, 515 boundary condition, 356, 361, 373 Bragg condition, 128 Bragg diffraction, 45, 128, 330 Bragg grating, see grating Brillouin amplifier, 340–344 Brillouin gain, 16, 330–333 Brillouin laser, 356–362 continuous-wave, 356 Fabry–Perot, 357 multiwavelength, 358 pulsed, 360 ring, 357, 360 self-seeded, 359 threshold of, 357 tunable, 358 Brillouin scattering, 15, 432 guided-acoustic-wave, 330 spontaneous, 330, 334, 335, 355, 415 stimulated, 329–362, 394, 415 Brillouin shift, 330, 331, 336, 342, 355, 360 Brillouin threshold, 333–339, 353, 354, 357 polarization effects on, 334
522 Index chalcogenide glass, see glass chaos, 354 feedback-induced, 356 period-doubling route to, 355 polarization, 196 quasi-periodic route to, 356 SBS-induced, 355 charge-delocalization model, 497 charge-transport model, 497 chemical vapor deposition, 4 Cherenkov radiation, 457, 480 chirp definition of, 56 dispersion-induced, 56, 58, 103, 106 linear, 56, 100 SPM-induced, 81, 86, 103, 106, 139 XPM-induced, 234, 240, 242, 246, 249, 257, 267, 297, 300, 301, 314 chirp parameter, 86, 139 circulator, 359, 361 coherence degradation of, 89, 493 degree of, 87, 493 temporal, 87, 493 coherence function, 88 coherence length, 333, 373, 378, 380, 501 coherent anti-Stokes Raman scattering, 473 collision length, 154 color center, 496, 498 continuum radiation, see radiation conversion efficiency, 339, 368, 393, 496, 497 core–cladding index difference, 3, 36, 377, 435, 436, 502 correlation length, 12, 214 coupled-mode equations, 180 couplers, 287, 428 Crank–Nicholson scheme, 45 cross-correlation, 70, 114, 302, 456 cross-phase modulation, 15, 177, 226–268, 378, 386, 405, 459 birefringence induced by, 178 coupling due to, 227 for measuring γ, 429 modulation instability by, 197, 229 nondispersive, 182 nonreciprocal nature of, 252 optical switching by, 251 phase shift induced by, 182 polarization effects on, 254 pulse compression due to, 248 SBS suppression with, 337 solitons formed by, 212, 233, 486 spectral changes due to, 239 supercontinuum and, 484 temporal changes due to, 244 wavelength shift by, 243 crosstalk Brillouin-induced, 344 FWM-induced, 380 Raman-induced, 292 cut-off wavelength, 29 demultiplexing, 414 depolarization, intrapulse, 266 dielectric constant, 27, 433 nonlinear, 33 diffusion length, 266, 409 directional coupler, 356, 361 dispersion anomalous, 10, 56, 112, 261, 306, 437 comb-like, 126, 143 fluctuations in, 398 fourth-order, 76, 114, 159, 464, 471 group-velocity, 10, 36, 89, 374, 381 GVD, 476 higher-order, 38, 391, 457, 478, 480, 481 material, 9, 376, 445 micro-management of, 495 normal, 10, 56, 101, 106, 112, 262, 457 origin of, 6–11 polarization-mode, 11, 214, 408, 461 second-order, see GVD third-order, 8, 40, 62–70, 74, 75, 98, 123, 158, 437, 457, 462, 476, 481 waveguide, 9, 376, 377, 380, 384, 445 dispersion compensation, 73, 74, 389, 393 dispersion length, 52, 149, 151, 182, 237, 261, 295, 307, 476, 480, 481, 483 dispersion management, 71–76, 128, 144, 388 dispersion map, 144, 219 dispersion parameter, 8, 9, 280, 442, 445, 465 dispersion relation, 121, 198–200, 230, 268, 330 dispersion slope, 9, 75, 393, 462 dispersion-compensating fiber, see fiber dispersion-decreasing fiber, see fiber dispersive waves, 139, 149, 218, 457, 463, 477, 480, 483, 484, 486 distributed amplification, 149, 291, 292 distributed feedback, 126, 313, 339, 388
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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 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 528 and 529: Index 523 distributed fiber sensors
Page 530 and 531: Index 525 four-photon, 412 gain-swi
Page 532 and 533: Index 527 Raman amplification with,
Page 534: Index 529 spectral hole burning, 36
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Nonlinear Fiber Optics - 4 ed. Agrawal

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