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Spatial Solitons : Springer Series in Optical Sciences - Stefano Trillo

Spatial Solitons

Springer Series in Optical Sciences

By: Stefano Trillo (Editor), William Torruellas (Editor)

Hardcover

Published: January 2001
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Soliton-based concepts open the road for newly designed laser sources, new frequency converters and high-intensity laser-material interactions. Optical solitons as stable spatial patterns of complex nonlinear systems allow for the control of the diffraction of optical beams. Solitons also prevent unwanted chaotic behavior. Thus, solitary wave physics plays a significant role from modern optical physics to optical communication, optical switching, and optical storage. The book gives an updated overview of optical solitons and can serve as a reference and guide for advanced students and scientists working in the field and related areas of science where solitons are observed.

From the reviews of the first edition:





"This book is the volume 82 in Springer Series `Optical Sciences', which includes invited contributions from the majority of world leading experts and pioneers in the field. ... The content of the book covers a wide spectrum of issues concerning the propagation of spatial solitons, ranging from the most challenging theoretical problems to the most exciting experimental achievements to date." (Andrei Mourachkine, Physicalia, Vol. 38 (4), 2002)

List of Contributorsp. XVII
Introduction to Spatial Solitonsp. 1
Introductionp. 1
Solitons in one Transverse Dimensionp. 2
Experimentsp. 7
New Directionsp. 8
Acknowledgmentsp. 16
Referencesp. 16
Materials for Spatial Solitonsp. 19
Introductionp. 19
Third-Order Kerr and Kerr-Like Saturating Nonlinearitiesp. 20
Higher-Order Kerr-Like Nonlinearitiesp. 25
Photorefractive Materialsp. 27
Second-Order Nonlinearities for Quadratic Solitonsp. 29
Conclusionsp. 32
p. 33
One-Dimensional Spatial Solitons in Kerr Mediap. 37
Introductionp. 37
Early and Miscellaneous Experimentsp. 38
Spatial Solitons in Homogeneous Semiconductor Waveguidesp. 40
Homogeneous AlGa As Passive Waveguidesp. 41
Weak-Beam-Spatial-Soliton Interactionsp. 43
Dragging and Trapping of Orthogonally Polarized Spatial Solitonsp. 44
Generation of Manakov Solitonsp. 47
Stability of Orthogonally Polarized Solitonsp. 48
Soliton Reconfigurable Interconnectp. 48
Spatial Solitons in Semiconductor Optical Amplifiersp. 50
Discrete Solitonsp. 52
Summaryp. 57
Referencesp. 58
Photorefractive Spatial Solitonsp. 61
Introductionp. 61
Photorefractive Beam Nonlinearityp. 61
Space-Charge Fieldp. 62
Beam Propagationp. 63
Self-Trapping Mechanismsp. 64
Quasi-Steady-State Solitonsp. 64
Screening Solitonsp. 67
Screening Slab-Solitonsp. 71
Screening Needle Solitonsp. 73
Self-bendingp. 75
Photovoltaic Solitonsp. 75
Self-Trapping in Semiconductorsp. 76
Self-Trapping in Paraelectricsp. 76
Material Nonlinearities and Solitonsp. 78
Nonlinear Beam Interactionsp. 78
Applicationsp. 79
Acknowledgmentsp. 80
Referencesp. 80
Incoherent Solitons: Self-Trapping of Weakly Correlated Wavepacketsp. 87
Introduction, First Experiments, and Intuitionp. 87
The Modal Theory of Incoherent Solitonsp. 92
The Coherent-Density Theory and the Propagation of Mutual Coherencep. 97
Dark Incoherent Solitonsp. 101
Coherence Properties of Incoherent Solitonsp. 107
Modulational Instability and Pattern Formation with Incoherent Wavepacketsp. 112
Effects of Anisotropic Coherence and Propagation Dynamicsp. 120
Prospectsp. 122
Dedication and Acknowledgmentsp. 123
Referencesp. 123
Quadratic Solitonsp. 127
Introduction and Historical Remarksp. 127
Summary of Theoretical Resultsp. 128
Basic Models for Quadratic Solitonsp. 128
(1 + 1)-Dimensional Quadratic Solitonsp. 131
Solitons in the Cascading Limitp. 131
Two-Wave Bright Solitonsp. 132
Two-Wave Dark Solitonsp. 134
(2 + 1)-Dimensional Quadratic Solitonsp. 136
General Remarksp. 136
Fundamental Cylindrical Solitonsp. 137
Soliton Scattering and Fusionp. 139
Important Generalizations and Related Problemsp. 141
Walking Solitonsp. 141
Three-Wave Quadratic Solitonsp. 142
Competing Nonlinearitiesp. 143
Doughnut Modes and Vortex Solitonsp. 144
Quadratic Light Bulletsp. 145
Discrete x$((2)$) Systems and Nonlinear Photonic Modesp. 146
Summary of Experimental Resultsp. 148
Freely Propagating Spatial Solitonsp. 149
(1 + 1)-Dimensional Spatial Solitonsp. 149
(2 + 1)-Dimensional Spatial Solitonsp. 150
Temporal Solitons and Light Bulletsp. 158
Quadratic Solitons in Cavitiesp. 159
Soliton Interactionp. 160
Transverse Effectsp. 160
Concluding Remarksp. 162
Acknowledgmentsp. 164
Referencesp. 164
Bragg Solitons: Theory and Experimentsp. 169
Introductionp. 169
Theory of Periodic Structuresp. 175
Coupled-Mode Theoryp. 175
Dispersion Relation and Eigenfunctionsp. 178
CW Solutions to the Coupled-Mode Equationsp. 180
Nonlinear-Schrödinger-Equation Limitp. 181
Bragg Grating Solitons and Gap Solitonsp. 182
Experimental Considerations: Grating Fabricationp. 183
Optical-Fiber Bragg Gratingsp. 183
Semiconductorsp. 186
Chalcogenide Glassesp. 187
Experimental Apparatusp. 187
Summary of Experimental Resultsp. 189
Continuous-Wave Experimentsp. 189
Pulse Experimentsp. 191
Further Developmentsp. 195
Optical Push Broomp. 195
Frequency Conversion and Generationp. 197
Nonuniform Gratingsp. 198
Novel Nonlinear Grating-Based Compressorsp. 198
Polarization Effectsp. 199
Optical AND Gatep. 199
Polarization Rotation and Polarization Instabilityp. 200
Copropagating Geometriesp. 202
Gratings with Quadratic Nonlinearitiesp. 202
Outlookp. 203
Acknowledgmentsp. 204
Referencesp. 205
Stability of Spatial Optical Solitonsp. 211
Introductionp. 211
Linear Eigenvalue Problemp. 213
Soliton Internal Modes and Stabilityp. 214
Stability Criterion for Fundamental Solitonsp. 218
Marginal Stability Point: Asymptotic Analysisp. 222
Nonlinear Guided Waves and Impurity Modesp. 223
Model and General Remarksp. 223
Stability of Symmetric and Asymmetric Modesp. 225
Symmetric Modesp. 225
Asymmetric Modesp. 226
Example: Competing Power-Law Nonlinearitiesp. 226
Multicomponent Solitary Wavesp. 228
General Theory: N Coupled NLS Equationsp. 228
Example: Two Coupled NLS Equationsp. 231
Multihump Solitary Wavesp. 234
Oscillatory Instabilitiesp. 237
Symmetry-Breaking Instabilitiesp. 239
Concluding Remarksp. 242
Acknowledgmentsp. 243
Referencesp. 243
Nonlinear Wave Collapsep. 247
Introductionp. 247
General Results on the Collapse of a Single Componentp. 250
Interaction Regimes of Several Collapsing Componentsp. 253
Collapse with Four-Wave Mixing and Walk-Offp. 258
Interplay between Quadratic and Cubic Nonlinearitiesp. 261
Conclusionp. 265
Acknowledgmentsp. 265
Referencesp. 265
Discrete Solitonsp. 269
Introductionp. 269
Basic Mathematical Modelsp. 271
Discrete Diffraction and Modulational Instabilityp. 273
Linear Plane Waves and Discrete Diffractionp. 273
Nonlinear Plane Waves and Their Modulational Instabilityp. 275
Cubic Nonlinearityp. 275
Quadratic Nonlinearityp. 276
Solitons in Cubic Nonlinear Mediap. 278
Types of Soliton Solutionsp. 278
Even (Intersite) Bright Solitonsp. 278
Odd (On-Site) Bright Solitonsp. 279
Topological and Flat-Top Solitonsp. 280
Stability Analysisp. 281
Bright Solitonsp. 282
Topological and Flat-Top Solitonsp. 283
Solitons in Quadratic Nonlinear Mediap. 285
Types of Soliton Solutionsp. 285
Even Bright Solitonsp. 285
Odd Bright Solitonsp. 286
Topological and Flat-Top Solitonsp. 286
Stability Analysisp. 287
Bright Solitonsp. 287
Topological and Flat-Top Solitonsp. 288
Conclusionsp. 290
Acknowledgmentsp. 290
Referencesp. 290
Optical Vortex Solitonsp. 293
Introductionp. 293
Vortex Wavefunctionsp. 294
Vortex Wavevectorsp. 295
r-Vortex Solutionsp. 297
Hankel Transform into Vortex Modesp. 298
Point Vortexp. 299
Multiple Vorticesp. 300
Nonlinear Refractionp. 303
Optical Vortex Solitonsp. 304
Pinched Optical Vortexp. 306
Conservation of Momentump. 307
Closing Thoughtsp. 308
Referencesp. 309
Solitons of the Complex Ginzburg-Landau Equationp. 311
Introductionp. 311
Balance Equations and Perturbation Theoryp. 315
Exact Solutionsp. 317
Solutions of the Cubic CGLEp. 318
The Solution with Arbitrary Amplitudep. 320
Chirp-Free Solitonp. 320
Dark-Soliton Solution of the Cubic Equationp. 321
Solitons of the Quintic CGLEp. 322
Relation Between Coefficientsp. 322
Solutions with Fixed Amplitudep. 322
The Solution with Arbitrary Amplitudep. 323
Flat-Top Solitonsp. 323
Rational Solutionp. 324
Chirp-Free Solitonp. 324
Reduction to a Set of Ordinary Differential Equationsp. 324
Stability Issuesp. 326
Stable Solitonsp. 327
Multiplicity of Solutionsp. 330
Composite Solitonsp. 330
Moving Solitonsp. 331
Coexistence of Solitonsp. 332
Collisionsp. 333
Soliton Bound Statesp. 334
Conclusionsp. 337
Referencesp. 337
Existence, Stability, and Properties of Cavity Solitonsp. 343
Introductionp. 343
Historyp. 344
Mean-Field Models and Cavity Solitonsp. 346
Cavity Solitons in Semiconductor Microresonatorsp. 351
Stationary Solutions and Stabilityp. 352
Applicationsp. 355
Conclusionp. 355
Acknowledgmentsp. 356
Referencesp. 356
Parametric Solitons in Passive Structures with Feedbackp. 359
Introductionp. 359
General Models for Quadratic Passive Cavitiesp. 360
Mean-Field Modelsp. 361
Order-Parameter Equationsp. 363
Competing Instabilities in Intracavity Parametric Mixingp. 366
Optical Parametric Oscillatorsp. 370
Localized Phase Defects or Domain Walls in DOPOsp. 370
Below-Threshold Bright Signal Solitons in DOPOsp. 374
Solitons in NDOPOsp. 376
Role of Walk-Offp. 376
Intracavity Second-Harmonic Generationp. 378
Pattern Formation and Localized Structuresp. 378
Vectorial (Type II) Effectsp. 381
Parametric Gap Solitons in Distributed-Feedback Structuresp. 383
Summary and Further Developmentsp. 387
Acknowledgmentsp. 389
Referencesp. 389
Spatial Solitons in Resonatorsp. 395
Introductionp. 395
Solitons in a Laser with a Nonlinear Absorberp. 397
Parametric-Mixing Solitonsp. 404
Nonlinear Semiconductor Resonatorsp. 408
Acknowledgmentsp. 415
Referencesp. 415
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540416531
ISBN-10: 3540416536
Series: Springer Series in Optical Sciences
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 460
Published: January 2001
Publisher: SPRINGER VERLAG GMBH
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 2.69
Weight (kg): 0.85