Preface xiii List of Abbreviations xv 1 Introduction 1 References 5 2 Waves Called Solitons 9 2.1 Linear and Nonlinear Effects of a Wave 9 2.2 Solitary Waves and Solitons 11 2.3 Solitons in Optical Fibers 13 2.4 Dissipative Optical Solitons 15 References 16 3 Fiber Dispersion and Nonlinearity 19 3.1 Fiber Chromatic Dispersion 19 3.1.1 Gaussian Input Pulses 21 3.

2 Fiber Nonlinearity 25 3.2.1 The Nonlinear Refractive Index 25 3.2.2 Relevance of Nonlinear Effects in Fibers 26 3.3 The Pulse Propagation Equation 28 3.3.1 The Normalized NLSE 29 3.

3.2 Propagation in the Absence of Dispersion and Nonlinearity 30 3.3.3 Effect of Dispersion Only 30 3.3.4 Effect of Nonlinearity Only 32 References 33 4 Nonlinear Effects in Optical Fibers 35 4.1 Self-Phase Modulation 35 4.1.

1 Modulation Instability 39 4.2 Cross-Phase Modulation 40 4.3 Four-Wave Mixing 42 4.4 Stimulated Raman Scattering 45 4.5 Stimulated Brillouin Scattering 49 References 52 5 Optical Amplification 57 5.1 General Concepts on Optical Amplifiers 57 5.2 Erbium-Doped Fiber Amplifiers 59 5.2.

1 Two-Level Model 60 5.3 Fiber Raman Amplifiers 63 5.4 Fiber Parametric Amplifiers 68 5.5 Lumped versus Distributed Amplification 72 5.6 Parabolic Pulses 74 References 76 6 Solitons in Optical Fibers 81 6.1 The Fundamental Soliton Solution 81 6.2 Higher-Order Solitons 83 6.3 Soliton Units 86 6.

4 Dark Solitons 87 6.5 Bistable Solitons 88 6.6 XPM-Paired Solitons 89 6.7 Optical Similaritons 90 6.8 Numerical Solution of the NLSE 92 6.9 The Variational Approach 94 6.10 The Method of Moments 97 References 98 7 Soliton Transmission Systems 101 7.1 Soliton Perturbation Theory 101 7.

2 Effect of Fiber Losses 102 7.3 Soliton Amplification 103 7.3.1 Lumped Amplification 104 7.3.2 Distributed Amplification 105 7.4 Soliton Interaction 107 7.5 Timing Jitter 110 7.

5.1 Gordon-Haus Jitter 110 7.5.2 Polarization-Mode Dispersion Jitter 113 7.5.3 Acoustic Jitter 113 7.5.4 Soliton Interaction Jitter 114 7.

6 WDM Soliton Systems 114 7.6.1 Lossless Soliton Collisions 114 7.6.2 Soliton Collisions in Perturbed Fiber Spans 116 7.6.3 Timing Jitter 117 References 117 8 Soliton Transmission Control 121 8.1 Fixed-Frequency Filters 121 8.

1.1 Control of Timing Jitter 122 8.1.2 Control of Soliton Interaction 123 8.1.3 Background Instability 125 8.2 Sliding-Frequency Filters 125 8.2.

1 Evolution of Soliton Parameters 126 8.2.2 Control of Timing Jitter 129 8.2.3 Control of Soliton Interaction 131 8.3 Synchronous Modulators 132 8.4 Amplifiers with Nonlinear Gain 133 8.4.

1 Stationary Solutions 134 8.4.2 Control of Soliton Interaction 137 References 139 9 Propagation of Ultrashort Solitons 141 9.1 Generalized NLSE 141 9.1.1 Third-Order Dispersion 142 9.1.2 Self-Steepening 143 9.

1.3 Intrapulse Raman Scattering 144 9.2 Timing Jitter of Ultrashort Solitons 145 9.3 Bandwidth-Limited Amplification of Ultrashort Solitons 147 9.4 Transmission Control Using Nonlinear Gain 151 9.4.1 Stationary Solutions 151 9.4.

2 Linear Stability Analysis 153 References 157 10 Dispersion-Managed Solitons 161 10.1 Dispersion Management 161 10.2 Characteristics of the Dispersion-Managed Soliton 163 10.3 The Variational Approach to DM Solitons 167 10.3.1 Generic Ansatz 167 10.3.2 Gaussian Pulses 168 10.

3.3 Stationary Solutions 169 10.4 Interaction Between DM Solitons 170 10.5 The Gordon-Haus Effect for DM Solitons 172 10.6 Effects of a Spectral Filter 173 10.6.1 Timing Jitter Control 174 10.7 Effects of an Amplitude Modulator 175 10.

8 WDM with DM Solitons 177 References 179 11 Polarization Effects 183 11.1 Fiber Birefringence and Polarization Mode Dispersion 183 11.1.1 PMD in Long Fiber Spans 185 11.1.2 PMD-Induced Pulse Broadening in Linear Systems 187 11.1.3 PMD Compensation 188 11.

2 Coupled Nonlinear Schrödinger Equations 190 11.3 Solitons in Fibers with Constant Birefringence 191 11.4 Vector Solitons 195 11.5 Solitons in Fibers with Randomly Varying Birefringence 196 11.6 PMD-Induced Soliton Pulse Broadening 197 11.7 Dispersion-Managed Solitons and PMD 200 References 202 12 Stationary Dissipative Solitons 207 12.1 Balance Equations for the CGL Equation 207 12.2 Exact Analytical Solutions 210 12.

2.1 Solutions of the Cubic CGLE 210 12.2.2 Solutions of the Quintic CGLE 212 12.3 Numerical Stationary Soliton Solutions 213 12.4 High-Energy Dissipative Solitons 216 12.5 Soliton Bound States 221 12.6 Impact of Higher-Order Effects 225 References 229 13 Pulsating Dissipative Solitons 233 13.

1 Dynamic Models for CGLE Solitons 233 13.1.1 The Variational Approach 234 13.1.1.1 Sech Ansatz 235 13.1.1.

2 Gaussian Ansatz 235 13.1.2 The Method of Moments 236 13.2 Plain Pulsating Solitons 238 13.2.1 Impact of Higher-Order Effects 239 13.3 Creeping Solitons 241 13.3.

1 Impact of Higher-Order Effects 242 13.4 Chaotic Solitons 244 13.5 Erupting Solitons 247 13.5.1 Impact of Higher-Order Effects 251 13.5.2 Experimental Observation of Soliton Explosions 253 References 256 14 Soliton Fiber Lasers 259 14.1 The First Soliton Laser 259 14.

2 Fundamentals of Fiber Soliton Lasers 260 14.3 Mode-Locking Techniques 262 14.3.1 Active Mode-Locking 262 14.3.2 Passive Mode-Locking 262 14.3.3 Nonlinear Optical Loop Mirrors 263 14.

3.4 Figure-Eight Laser 264 14.3.5 Nonlinear Polarization Rotation 265 14.3.6 Hybrid Mode-Locking 265 14.4 High-Energy Soliton Fiber Lasers 266 14.5 Modeling of Soliton Fiber Lasers 268 14.

6 Polarization Effects 272 14.7 Dissipative Soliton Molecules 273 14.8 Experimental Observation of Pulsating Solitons 274 References 279 15 Other Applications of Optical Solitons 285 15.1 All-Optical Switching 285 15.1.1 The Fiber Coupler 285 15.1.2 The Sagnac Interferometer 286 15.

2 2R Optical Regeneration 288 15.3 Pulse Compression 290 15.3.1 Grating-Fiber Compression 290 15.3.2 Higher-Order Soliton-Effect Compression 291 15.3.3 Compression of Fundamental Solitons 293 15.

3.4 Dissipative Soliton Compression 295 15.4 Solitons in Fiber Gratings 298 15.4.1 Pulse Compression Using Fiber Gratings 300 15.4.2 Fiber Bragg Solitons 302 References 305 16 Highly Nonlinear Optical Fibers 309 16.1 Highly Nonlinear Silica Fibers 309 16.

1.1 Tapered Fibers 310 16.2 Microstructured Optical Fibers 311 16.3 Non-Silica Fibers 318 16.4 Soliton Fission and Dispersive Waves 320 16.5 Four-Wave Mixing 324 16.6 Hollow-Core Microstructured Fibers 325 References 332 17 Supercontinuum Generation 337 17.1 Pumping with Femtosecond Pulses 337 17.

2 Modeling the Supercontinuum 341 17.3 Pumping with Picosecond Pulses 344 17.4 Continuous Wave Supercontinuum Generation 347 17.5 Mid-IR Supercontinuum Generation 350 17.6 Supercontinuum Coherence 352 17.6.1 Spectral Incoherent Solitons 354 17.7 Supercontinuum Generation in Hollow-Core Kagomé Fibers 356 References 365 Index 369.