Nonlinear Fiber Optics - 4 ed. Agrawal

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Index 525 four-photon, 412 gain-switched, 186, 314, 470 He–Ne, 357 Krypton-ion, 473 mode-locked, 168, 304, 312, 360, 412, 493 modulation-instability, 412 Nd-fiber, 292 Nd:YAG, 186, 288, 290, 300, 304, 310, 312, 313, 338, 340, 344, 348, 361, 381, 412, 474, 496 Q-switched, 288, 291, 337, 347, 412 Raman, 285–288, 304 Raman soliton, 311 self-pulsing, 127 semiconductor, 186, 290, 291, 314, 331, 339, 342, 344, 359, 388, 427, 495 soliton, 311 synchronously pumped, 312 Ti:sapphire, 437, 475, 489 xenon, 338 Yb-doped fiber, 102, 288, 337, 466 linear stability analysis, 121, 229, 352, 361 lithographic technique, 498 local oscillator, 343, 415 logic gates, 211 longitudinal modes, 342, 357, 360 Lorentzian spectrum, 331, 462 loss Brillouin, 344 cavity, 357 fiber, 5, 147, 277, 375 microbending, 29 polarization-dependent, 215 round-trip, 357 lumped-amplification scheme, 149, 151 Mach–Zehnder interferometer, 143, 186, 243, 428 Mach–Zehnder modulator, 143 magnetic dipole, 368, 496 Manakov equation, 410 Markovian process, 265 Maxwell’s equations, 25, 168, 441 FDTD method for, 46 Michelson interferometer, 250, 493 mode acoustic, 345 fundamental, 29, 502 guided, 27 HE 11 ,29 higher-order, 502 hybrid, 29 leaky, 503 linearly polarized, 30 LP 01 , 30, 206 LP 11 , 206 radiation, 27 TE, 29 TM, 29 mode-locking active, 360 self-induced, 360 modulation instability, 120–129, 197–206, 311, 383, 387, 412, 430, 468, 473 critical power for, 201 effects of SRS, 301 experiments on, 124, 203, 232 gain spectrum of, 122, 199, 201, 202, 231 induced, 123, 125, 126 SBS-induced, 354 SHG-induced, 500 sidebands of, 206, 430, 475 SPM-induced, 125 spontaneous, 123, 412, 466 vector, 197 XPM-induced, 229–233, 301 modulator amplitude, 360 electro-optic, 336, 351 LiNbO 3 , 143 liquid-crystal, 75 Mach–Zehnder, 143 phase, 76, 143, 336 moment method, 102–106, 156 momentum conservation, 369, 463 multiphoton ionization, 497 multiplexing polarization-division, 218 time-division, 75 wavelength-division, 9, 159, 292 multipole method, 441 Neumann function, 28 NLS equation, 36, 40, 121, 427 asymptotic solution of, 100 coupled, 228, 237, 265, 374 coupled vector, 264 cubic, 41 generalized, 40, 112, 454, 462, 477, 485
526 Index inverse scattering method for, 130 moment method for, 102 numerical methods for, 41 periodic solutions of, 235 quintic, 41 split-step method for, 41–45 variational method for, 103 vector form of, 215, 255 noise intensity, 495 quantum, 415, 493 Raman, 495 spontaneous-emission, 431 noise figure, 292, 394 nonlinear birefringence, 177, 178, 189 nonlinear length, 52, 80, 122, 188, 207, 261, 295, 454, 480, 493 nonlinear parameter, 35, 41, 103, 167, 187, 266, 280, 372, 409, 410, 424–448, 454, 505 nonlinear phase shift, see phase shift nonlinear polarization rotation, 179, 187, 193, 256, 318, 405, 488, 492 nonlinear response, 32, 37, 38, 40, 315, 393, 479, 490 nonlinear Schrödinger equation, see NLS equation nonlinear-index coefficient, 14, 17, 179, 371 measurements of, 424–434 NRZ format, 143 optical bistability, 252, 253 optical buffer, 352 optical shock, 108, 166 effect of dispersion on, 109 optical switching, 186, 251, 415, 459 optical wave breaking, see wave breaking outside vapor deposition, 4 overlap integral, 229, 371, 372, 500 packet switching, 415 Padé approximation, 45 parabolic pulse, see pulse parametric amplification, 387–411 dual-pump, 394–399 polarization effects on, 401–411 single-pump, 391–394 vector theory of, 401–411 parametric amplifier, see amplifier parametric gain, 373, 375, 389, 394, 400, 405 bandwidth of, 389 polarization dependence of, 403 parametric oscillator, 412, 464 tunable, 412 partially coherent light, 87–89 Pauli matrices, 215, 256, 265, 490 Pauli spin vector, 256, 265, 317, 406 period-doubling bifurcation, 355 phase conjugation, 389, 412 phase matching, 373, 387, 395 birefringence-induced, 383, 473 Cherenkov-type, 503 condition for, 370, 376, 390 for THG, 502 multimode fibers for, 377 near zero-dispersion wavelength, 381 quasi, 498 requirement for, 370 single-mode fibers for, 380 SPM-induced, 382 techniques for, 376–387 phase mismatch, 369, 390, 498 effective, 372 linear, 391, 395 nonlinear, 391, 392, 395, 504 phase modulation, 347 phase shift nonlinear, 80, 81, 182, 200, 239, 258, 405, 428, 458 rotation-induced, 252 SPM-induced, 428, 444 time-dependent, 239 XPM-induced, 239, 251, 258, 267, 337, 429, 488 phase-matching condition, 128, 180, 202, 227, 232, 282, 370, 376–399, 430, 457, 464, 466, 480, 481, 501, 502, 505 phase-retrieval algorithm, 483 phonon lifetime, 331, 333, 344, 347 photon-pair source, 416 photonic bandgap, 440 photosensitivity, 496 photovoltaic effect, 497 pitchfork bifurcation, 191 planar lightwave circuit, 75 Planck constant, 515 PMD, 11, 214, 265 effect on four-wave mixing, 408 first-order, 214 pulse broadening induced by, 214
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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 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 532 and 533: Index 527 Raman amplification with,
Page 534: Index 529 spectral hole burning, 36
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