Nonlinear Fiber Optics

Govind Agrawal9780120451432, 0120451433

Since the publication of the first edition of this book in 1989, the field of nonlinear fiber optics has virtually exploded. The third edition is intended to bring the book up to date so that it remains a unique source of comprehensive coverage on the subject of nonlinear fiber optics. An attempt was made to include recent research results on all topics relevant to the field of nonlinear fiber optics.Nonlinear Fiber Optics, 3rd Edition, provides a comprehensive and up-to-date account of the nonlinear phenomena occurring inside optical fibers. It retains most of the material that appeared in the first edition, with the exception of Chapter 6, which is now devoted to the polarization effects relevant for light propagation in optical fibers. The contents include such important topics as self- and cross-phase modulation, stimulated Raman and Brillouin scattering, four-wave mixing, modulation instability, and optical solutons. A proper understanding of these topics is essential for scientists and engineers interested in various aspects of lightwave technology.Such an ambitious objective increased the size of the book to the extent that it was necessary to create a separate but complimentary book, Applications of Nonlinear Fiber Optics, which is devoted to applications in the domain of lightwave technology.This revised edition of Nonlinear Fiber Optics should serve well the needs of the scientific community including graduate students in Optics, Physics, and Electrical Engineering, engineers in the optical communication industry, and scientists working in fiber optics and nonlinear optics.

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Table of contents :
Nonlinear Fiber Optics……Page 1
Contents……Page 6
Preface……Page 13
1.1 Historical Perspective……Page 15
1.2 Fiber Characteristics……Page 17
1.2.1 Material and Fabrication……Page 18
1.2.2 Fiber Losses……Page 19
1.2.3 Chromatic Dispersion……Page 21
1.2.4 Polarization-Mode Dispersion……Page 27
1.3.1 Nonlinear Refraction……Page 31
1.3.2 Stimulated Inelastic Scattering……Page 33
1.3.3 Importance of Nonlinear Effects……Page 34
1.4 Overview……Page 36
2 Pulse Propagation in Fibers……Page 45
7.3.2 Bright–Gray Soliton Pair……Page 0
2.2.1 Eigenvalue Equation……Page 48
2.2.2 Single-Mode Condition……Page 50
2.2.3 Characteristics of the Fundamental Mode……Page 51
2.3.1 Nonlinear Pulse Propagation……Page 53
2.3.2 Higher-Order Nonlinear Effects……Page 59
2.4.1 Split-Step Fourier Method……Page 65
2.4.2 Finite-Difference Methods……Page 69
3.1 Different Propagation Regimes……Page 77
3.2 Dispersion-Induced Pulse Broadening……Page 80
3.2.1 Gaussian Pulses……Page 81
3.2.2 Chirped Gaussian Pulses……Page 83
3.2.3 Hyperbolic-Secant Pulses……Page 85
3.2.4 Super-Gaussian Pulses……Page 86
3.2.5 Experimental Results……Page 89
3.3 Third-Order Dispersion……Page 90
3.3.1 Changes in Pulse Shape……Page 91
3.3.2 Broadening Factor……Page 93
3.3.3 Arbitrary-Shape Pulses……Page 96
3.3.4 Ultrashort-Pulse Measurements……Page 99
3.4.1 GVD-Induced Limitations……Page 100
3.4.2 Dispersion Compensation……Page 102
3.4.3 Compensation of Third-Order Dispersion……Page 104
4.1 SPM-Induced Spectral Broadening……Page 111
4.1.1 Nonlinear Phase Shift……Page 112
4.1.2 Changes in Pulse Spectra……Page 114
4.1.3 Effect of Pulse Shape and Initial Chirp……Page 118
4.1.4 Effect of Partial Coherence……Page 120
4.2.1 Pulse Evolution……Page 123
4.2.2 Broadening Factor……Page 127
4.2.3 OpticalWave Breaking……Page 129
4.2.4 Experimental Results……Page 132
4.2.5 Effect of Third-Order Dispersion……Page 134
4.3 Higher-Order Nonlinear Effects……Page 136
4.3.1 Self-Steepening……Page 137
4.3.2 Effect of GVD on Optical Shocks……Page 140
4.3.3 Intrapulse Raman Scattering……Page 142
5 Optical Solitons……Page 149
5.1.1 Linear Stability Analysis……Page 150
5.1.2 Gain Spectrum……Page 152
5.1.3 Experimental Observation……Page 154
5.1.4 Ultrashort Pulse Generation……Page 156
5.1.5 Impact on Lightwave Systems……Page 158
5.2 Fiber Solitons……Page 160
5.2.1 Inverse Scattering Method……Page 161
5.2.2 Fundamental Soliton……Page 163
5.2.3 Higher-Order Solitons……Page 166
5.2.4 Experimental Confirmation……Page 168
5.2.5 Soliton Stability……Page 170
5.3.1 Dark Solitons……Page 173
5.3.2 Dispersion-Managed Solitons……Page 178
5.3.3 Bistable Solitons……Page 179
5.4 Perturbation of Solitons……Page 180
5.4.1 Perturbation Methods……Page 181
5.4.2 Fiber Losses……Page 183
5.4.3 Soliton Amplification……Page 185
5.4.4 Soliton Interaction……Page 190
5.5 Higher-Order Effects……Page 194
5.5.1 Third-Order Dispersion……Page 195
5.5.2 Self-Steepening……Page 197
5.5.3 Intrapulse Raman Scattering……Page 200
5.5.4 Propagation of Femtosecond Pulses……Page 204
6 Polarization Effects……Page 217
6.1.1 Origin of Nonlinear Birefringence……Page 218
6.1.2 Coupled-Mode Equations……Page 220
6.1.3 Elliptically Birefringent Fibers……Page 222
6.2.1 Nondispersive XPM……Page 224
6.2.2 Optical Kerr Effect……Page 225
6.2.3 Pulse Shaping……Page 230
6.3 Evolution of Polarization State……Page 232
6.3.1 Analytic Solution……Page 233
6.3.3 Polarization Instability……Page 238
6.3.4 Polarization Chaos……Page 241
6.4 Vector Modulation Instability……Page 242
6.4.1 Low-Birefringence Fibers……Page 243
6.4.2 High-Birefringence Fibers……Page 245
6.4.3 Isotropic Fibers……Page 248
6.4.4 Experimental Results……Page 249
6.5 Birefringence and Solitons……Page 252
6.5.1 Low-Birefringence Fibers……Page 253
6.5.2 High-Birefringence Fibers……Page 254
6.5.3 Soliton-Dragging Logic Gates……Page 257
6.5.4 Vector Solitons……Page 258
6.6.1 Polarization-Mode Dispersion……Page 260
6.6.2 Polarization State of Solitons……Page 262
7 Cross-Phase Modulation……Page 274
7.1.1 Nonlinear Refractive Index……Page 275
7.1.2 Coupled NLS Equations……Page 277
7.1.3 Propagation in Birefringent Fibers……Page 278
7.2.1 Linear Stability Analysis……Page 279
7.2.2 Experimental Results……Page 282
7.3 XPM-Paired Solitons……Page 284
7.3.3 Other Soliton Pairs……Page 286
7.4 Spectral and Temporal Effects……Page 288
7.4.1 Asymmetric Spectral Broadening……Page 289
7.4.2 Asymmetric Temporal Changes……Page 295
7.4.3 Higher-Order Nonlinear Effects……Page 298
7.5.1 XPM-Induced Pulse Compression……Page 300
7.5.2 XPM-Induced Optical Switching……Page 303
7.5.3 XPM-Induced Nonreciprocity……Page 304
8.1 Basic Concepts……Page 312
8.1.1 Raman-Gain Spectrum……Page 313
8.1.2 Raman Threshold……Page 314
8.1.3 Coupled Amplitude Equations……Page 318
8.2.1 Single-Pass Raman Generation……Page 320
8.2.2 Raman Fiber Lasers……Page 323
8.2.3 Raman Fiber Amplifiers……Page 326
8.2.4 Raman-Induced Crosstalk……Page 332
8.3.1 Pulse-Propagation Equations……Page 334
8.3.2 Nondispersive Case……Page 335
8.3.3 Effects of GVD……Page 338
8.3.4 Experimental Results……Page 341
8.3.5 Synchronously Pumped Raman Lasers……Page 346
8.4 Soliton Effects……Page 347
8.4.1 Raman Solitons……Page 348
8.4.2 Raman Soliton Lasers……Page 353
8.4.3 Soliton-Effect Pulse Compression……Page 355
8.5 Effect of Four-Wave Mixing……Page 357
9.1 Basic Concepts……Page 369
9.1.1 Physical Process……Page 370
9.1.2 Brillouin-Gain Spectrum……Page 371
9.2 Quasi-CW SBS……Page 373
9.2.2 Brillouin Threshold……Page 374
9.2.3 Gain Saturation……Page 376
9.2.4 Experimental Results……Page 378
9.3.1 Coupled Amplitude Equations……Page 381
9.3.2 Relaxation Oscillations……Page 382
9.3.3 Modulation Instability and Chaos……Page 385
9.3.4 Transient Regime……Page 387
9.4.1 CW Operation……Page 389
9.4.2 Pulsed Operation……Page 391
9.5.1 Brillouin Fiber Amplifiers……Page 394
9.5.2 Fiber Sensors……Page 397
10.1 Origin of Four-Wave Mixing……Page 403
10.2.1 Coupled Amplitude Equations……Page 406
10.2.2 Approximate Solution……Page 408
10.2.3 Effect of Phase Matching……Page 410
10.2.4 Ultrafast FWM……Page 411
10.3.1 Physical Mechanisms……Page 413
10.3.2 Phase Matching in Multimode Fibers……Page 414
10.3.3 Phase Matching in Single-Mode Fibers……Page 418
10.3.4 Phase Matching in Birefringent Fibers……Page 422
10.4.1 Gain and Bandwidth……Page 426
10.4.2 Pump Depletion……Page 428
10.4.3 Parametric Amplifiers……Page 430
10.4.4 Parametric Oscillators……Page 431
10.5 FWM Applications……Page 432
10.5.1 Wavelength Conversion……Page 433
10.5.2 Phase Conjugation……Page 434
10.5.3 Squeezing……Page 436
10.5.4 Supercontinuum Generation……Page 438
10.6.1 Experimental Results……Page 441
10.6.2 Physical Mechanism……Page 443
10.6.3 Simple Theory……Page 445
10.6.4 Quasi-Phase-Matching Technique……Page 448
Decibel Units……Page 459
Nonlinear Refractive Index……Page 461
References……Page 466
Acronyms……Page 468
Index……Page 471