Nonlinear Fiber Optics - 4 ed. Agrawal

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Index 529 spectral hole burning, 362 spectral narrowing, 86, 105 spectral recoil, 462, 463 spin decoherence, 266 split-step Fourier method, 41–45, 93, 98, 102, 261, 297, 478, 479 symmetrized, 43 spontaneous emission, 66, 152, 393, 415, 431 amplified, 358 spread-spectrum technique, 336 squeezing, 415 SRS, 274–321 cascaded, 279, 283, 292, 473 equations for, 279 fluctuations in, 285, 296 four-wave mixing effects on, 281 intrapulse, see Raman scattering quasi-CW, 283 single-pass, 283 soliton effects on, 306 threshold of, 276, 301 ultrafast, 294–303 steepest descent method, 278 stimulated Brillouin scattering, see SBS stimulated Raman scattering, see SRS Stokes band, 274, 279, 330, 340, 370, 374, 378, 382, 385, 471, 473, 477 Stokes parameters, 192, 216 Stokes vector, 192, 193, 217, 255, 266, 317, 406 streak camera, 69, 233 stress-induced anisotropy, 11 sum-frequency generation, 456 super-Gaussian pulse, see pulse supercontinuum, 38, 82, 114, 167, 379, 469 coherence properties of, 493 CW pumping of, 474–475 femtosecond pumping of, 475–495 noisy nature of, 493 numerical modeling of, 477 picosecond pumping of, 470–474 polarization effects on, 488 XPM effects on, 484 susceptibility linear, 14 nonlinear, 368 Raman, 433 second-order, 14, 368, 496 third-order, 14, 37, 178, 227, 275, 368, 402, 424, 502 synchronous pumping, 286, 304, 360 Taylor series, 391, 458, 478, 503 thermal poling, 498, 499 third-harmonic generation, 37, 70, 368, 370, 502–506 third-order dispersion, see dispersion third-order susceptibility, see susceptibility three-wave mixing, 370 time-dispersion technique, 286, 304, 312 time-division multiplexing, 75, 414, 470 time-resolved optical gating, 70 timing jitter, 143, 152, 218, 313 total internal reflection, 1, 440 two-photon absorption, 33, 70, 483 ultrafast signal processing, 413 undepleted-pump approximation, 372 V parameter, 3, 29, 435 vacuum fluctuations, 123 vacuum permeability, 26 vacuum permittivity, 26, 425 vapor-phase axial deposition, 4 variational method, 103–106, 146 walk-off length, 10, 182, 229, 242, 248, 255, 261, 281, 295, 297–299 wave breaking, 94–98, 101 supression of, 101 XPM-induced, 246, 262 wave equation, 26, 28 wave-vector mismatch, 373, 380, 384, 391, 497, 500 wavelength conversion, 389, 393, 397, 401, 412, 447 wavelength multicasting, 415 wavelength-selective feedback, 285 WDM, see multiplexing WDM systems, 73, 292, 380, 472 Wiener–Khintchine theorem, 88 zero-dispersion wavelength, 8–10, 62, 72, 129, 158, 159, 185, 235, 251, 309, 312, 375, 376, 380, 381, 387, 391, 393, 395, 398, 437, 455, 462, 463, 465, 467, 475, 478, 485
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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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12.4. Temporal and Spectral Evoluti
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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 532 and 533: Index 527 Raman amplification with,
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