Optical Solitons: Theoretical and Experimental Challenges

1 Importance of Optical Fiber Communications......Page 1
2 Birth of Optical Solitons......Page 3
3 Present Book......Page 6
1 Introduction......Page 8
2 Properties of Optical Solitons as a Result of IST......Page 9
3 Dielectric Properties of Optical Fibers......Page 11
4 Master Equation for Information Transfer in Optical Fibers......Page 14
5 Lagrangian Method and Soliton Perturbation Theory......Page 16
6 Dispersion Managed Solitons......Page 19
7 Some Recent Experimental Results of Optical Soliton Transmission......Page 24
References......Page 29
1 Introduction......Page 32
2 The Optical Fiber......Page 33
3 Modes in an Optical Fiber......Page 34
4 Typical Fiber Optic Communication System......Page 36
5 Attenuation......Page 37
6.1 Erbium Doped Fiber Amplifier (EDFA)......Page 39
6.2 Fiber Raman Ampli.er (FRA)......Page 46
6.3 Noise in Amplifiers......Page 49
7 Pulse Dispersion......Page 50
8 Dispersion Compensation......Page 54
9 Nonlinear Effects in Optical Fibers......Page 56
9.1 Self Phase Modulation (SPM)......Page 58
9.2 Cross Phase Modulation (XPM)......Page 62
9.3 Four Wave Mixing (FWM)......Page 64
10 Conclusions......Page 67
References......Page 68
1 Introduction......Page 70
2.1 Dielectric Slab as a Waveguide......Page 72
2.2 Novel Experiments in Dielectric Guides......Page 75
3.1 General Remarks and Standard DT Integration-Inclined Solitons as Illustration......Page 77
3.2 Binary DT Application......Page 78
4.1 About Derivation and Rescaling......Page 84
4.2 Integrability and Solutions of MB Equations......Page 86
4.3 Solutions over the Nonzero Backgrounds......Page 88
4.4 Periodic-Seed Solutions......Page 90
4.5 Nonreduced MB Equation Integrability......Page 91
4.6 The LvN Equation as Associated ZS Problem......Page 95
5.1 Lax Pair and Periodic-Seed Solutions......Page 96
5.2 Determinant Representation......Page 98
5.3 Perturbations of Solutions......Page 100
References......Page 101
1 Introduction......Page 104
2 Integrable Systems......Page 106
3 Hamiltonian Systems......Page 109
4 Dissipative Systems......Page 115
References......Page 122
1.1 Operator Representations......Page 126
1.2 Simple Numerical Integration......Page 127
2 Numerical Modelling......Page 128
2.1 Second Order Split Step Fourier Method......Page 129
3 Analytic Results......Page 130
3.1 Average Solitons......Page 131
3.2 Special Points in Constant Dispersion Systems......Page 132
3.3 Special Points in Dispersion Managed Systems......Page 135
3.4 Magic Points......Page 137
References......Page 138
1 Introduction......Page 140
2 CNLS Equations as Governing Equations for Intense Light Propagation in Multimode Fibers and Photorefractive Materials......Page 141
3 Soliton Solutions of the CNLS Equations......Page 144
3.1 N=2 Case......Page 145
3.2 N=3 Case......Page 150
3.3 N-CNLS Equations......Page 152
4.1 N=2 Case......Page 154
4.2 N=3 and Arbitrary Cases......Page 159
4.3 Shape Changing Collisions and Higher Order Solitons......Page 160
Acknowledgment......Page 162
References......Page 163
1 Introduction......Page 164
2 Mathematical Formulation for Pulses in Fiber Bragg Gratings......Page 165
2.1 Multi-soliton Solutions......Page 168
2.2 Quasi-periodic Solutions......Page 171
3 Gap Soliton Bullets......Page 172
3.1 Slowly Varying Envelope Approximation......Page 173
3.2 Weakly Nonlinear Theory......Page 174
3.3 Analysis of the 2D Perturbed NLSE......Page 177
4 Conclusions......Page 178
Appendix A......Page 180
Appendix B......Page 181
References......Page 182
1 Introduction......Page 184
2.1 Stopband of Linear Origin......Page 186
2.2 Stopbands due to Periodic Nonlinearities......Page 188
2.3 Nonlinearity-Induced Transparency in Short-Period Gratings......Page 190
3 Gap Solitons in Bragg Gratings with Kerr Nonlinearity......Page 192
4 Gap Solitons Supported by Frequency Conversion Processes......Page 197
5 Stability and Excitation......Page 198
6 Localization in Gap of Nonlinear Origin......Page 199
7 Summary and Further Developments......Page 201
References......Page 202
1 Introduction......Page 206
2.1 General Features of SRS......Page 207
2.2 Generalized Theory of the SSFS......Page 213
3 Suppression of the Soliton Self-frequency Shift......Page 218
4 Conclusion......Page 222
References......Page 224
1 Introduction......Page 225
3 Dispersion Managed Nonlinear Schrodinger Equation......Page 227
4.1 Lossless Case......Page 230
4.2 Lossy Case......Page 231
5 Intra-channel Quasi-linear Pulse Interactions......Page 235
5.1 Perturbed DMNLS Equation......Page 236
5.2 Energy Transfer......Page 237
5.3 Frequency and Timing Shifts......Page 239
Acknowledgments......Page 242
References......Page 243
1 Introduction......Page 244
2 Dispersion-Managed Transmission System......Page 245
3 Dispersion Map Parameters......Page 247
4 Interactions Between Neighboring DM Solitons......Page 251
5 Bi-Soliton Solution......Page 252
6 Error Preventable Line-Coding Scheme......Page 256
7 3 Out of 4 Encoding Scheme......Page 257
References......Page 260
1 Introduction......Page 262
2.1 Optical Fiber Laser Components and Construction......Page 263
2.2 Nonlinearity and Dispersion......Page 265
2.3 Typical Characteristics of Optical Fiber Soliton Lasers......Page 266
2.4 Soliton Generation Versus Soliton Transmission......Page 269
3.1 Active Mode-Locking......Page 271
3.2 Passively Mode-Locked Soliton Fiber Lasers......Page 272
3.3 Soliton Mode-Locking......Page 277
3.5 Other Soliton Lasers......Page 279
4 Theory of Soliton Lasers......Page 280
4.1 Exact Solutions......Page 284
4.2 Soliton Solutions for the Case of Slow Saturable Absorber......Page 286
4.3 Perturbation Approximation......Page 288
4.4 Stability......Page 290
References......Page 291
1 Introduction......Page 295
2 Theoretical Fundamentals......Page 296
3 Higher-Order Solitons and Supercontinuum Generation in Photonic Crystal Fibers......Page 301
4 Degenerate Four-Wave Mixing and Parametric Amplification......Page 307
5 Pulse Compression Without Chirp Control by High-Order Coherent Raman Scattering......Page 311
6 Formation of Optical Sub-cycle Pulses and Full Maxwell-Bloch Solitary Waves in Resonant Two-Level Medium......Page 315
References......Page 320
1 Introduction......Page 322
2 Experimental Setup......Page 323
3.1 Coupled Nonlinear Schrodinger Equations......Page 325
3.2 Linear Stability Analysis of Modulational Instability......Page 326
3.3 Influence of the Non-phase-matched Waves for a Single-Frequency Pump Field......Page 328
3.4 Suppression of MI for a Dual-Frequency Pump Field......Page 329
4 Generation of Terahertz Vector Dark-Soliton Trains from Induced Modulational Instability......Page 331
5 Modulational Instability in Highly Birefringent Air-Silica Microstructure Fiber......Page 335
6 Four Wave Mixing-Induced Modulational Instability in Highly Birefringent Fibers......Page 336
7 Bragg Modulational Instability Induced by a Dynamic Grating in an Optical Fiber......Page 341
References......Page 345
1 Introduction......Page 347
3 Solitary Wave Solution......Page 349
4 Two Wave Adiabatic Approximation......Page 351
5 Self Pulsing in a Cavity......Page 353
6 Three Wave Model......Page 356
7 Stability of the Degenerate Backward Optical Parametric Oscillator......Page 357
References......Page 364
1 Introduction......Page 366
2 Model and Numerical Analysis......Page 368
3 Experimental Technique......Page 370
4.1 Below Bandgap Hexagons and Dark Solitons......Page 371
4.2 Near Bandgap Bright and Dark Solitons......Page 374
4.3 Above Bandgap Bright Solitons......Page 377
4.4 Optical Pumping......Page 379
Acknowledgment......Page 382
References......Page 383
1 Introduction......Page 384
2 Theory......Page 385
3 Physical Parameters......Page 387
4 Experimental Setup......Page 389
5 Propagation and Diffraction of Picosecond Acoustic Wave Packets......Page 391
6 One-Dimensional Propagation Experiments......Page 395
7 Conclusion......Page 396
References......Page 398