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Optical Solitons - Theoretical Challenges and Industrial Perspectives : Les Houches Workshop, September 28-October 2, 1998 : Centre de Physique Des Houches - Vladimir E. Zakharov

Optical Solitons - Theoretical Challenges and Industrial Perspectives : Les Houches Workshop, September 28-October 2, 1998

Centre de Physique Des Houches

By: Vladimir E. Zakharov (Editor), Stefan Wabnitz (Editor)

Paperback ISBN: 9783540663140
Number Of Pages: 384

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This text presents an overview of recent theoretical and experimental advances in the field of optical solitons, ranging from the mathematical foundations of integrability theory to the rapidly evolving technology of fiber soliton- based telecommunication systems. The subjects covered in the book can be broadly grouped into four main categories: optical soliton theory, fiber soliton telecommunications, optical soliton generation methods, and all-optical information processing via spatial solitons. This book should be a useful reference both for postgraduate students starting their research in the field, and researchers actively involved in nonlinear optics and optical communications.

Fundamentals of Optical Soliton Theory in Fibers
Introductionp. 1
Electromagnetic waves in dielectric materialsp. 1
Polarization effectsp. 1
Plane electromagnetic waves in dielectric materialsp. 3
Kerr effect and Kerr coefficientp. 5
Dielectric waveguidesp. 6
Envelope of electromagnetic wave in dielectric materialsp. 10
Lightwave envelope in fibers - derivation of nonlinear Schrödinger equationp. 10
Evolution of the wave packet due to the group velocity dispersionp. 12
Evolution of wave packet due to the nonlinearityp. 14
Lax theoremp. 15
The soliton solution of the nonlinear Schrödinger equationp. 15
Ultrafast communication based on optical solitonsp. 16
Conclusionp. 18
Hamiltonian Theory of Bäcklund Transformation
Introductionp. 19
Lattice equationsp. 22
Canonical Backhand transformationsp. 25
First integralsp. 27
Stability of Solitons
Introductionp. 31
Lyapunov stabilityp. 33
Nonlinear Schrödinger equationp. 33
The three-wave systemp. 36
Soliton solutions of the 3-wave systemp. 39
Nonlinear stabilityp. 41
Linear stabilityp. 43
Linear stability for 1D NLS solitonsp. 43
Solitons for the FF-SH interactionp. 46
Chaotic Dynamics of Optical Solitons
Introductionp. 51
Variational approach to solitons dynamics in random mediap. 52
Optical solitons in media with fluctuating quadratic potentialp. 53
Spatial soliton in array with fluctuating parametersp. 54
A random Kepler problemp. 55
Inverse scattering transform technique for solitons in random mediap. 56
Single soliton propagation in random mediap. 56
Interaction of optical solitons in random mediap. 59
Conclusionp. 61
Variationalism and Empirio-Criticism. (Exact and Variational Approaches to Fibre Optics Equations)
Introductionp. 63
Variational approachp. 64
What is wrong with the Variational approachp. 68
Propagation of Optical Pulses in Nonlinear Systems with Varying Dispersion
Introductionp. 73
Basic modelp. 74
Effective Hamiltonianp. 77
Monochromatic wave and its stabilityp. 81
Weak dispersion managementp. 82
Streng dispersion management (SDM)p. 85
Solitons and their stabilityp. 87
Dispersion-Managed Solitons
Introductionp. 91
Basic equationsp. 94
Linear solution and qualitative description of DM solitonsp. 96
DM pulse evolution over one periodp. 98
Root-mean-square momentum equationsp. 98
Power enhancementp. 105
How to find the DM soliton numericallyp. 106
A path-average theory of DM solitons in the time domainp. 106
Path-averaged equations in the spectral domainp. 110
Conclusionsp. 112
Dispersion-Managed Solitons: Applications to Terabit/s Transmission over Transoceanic Distances
Introductionp. 117
Modellingp. 119
Single pulse propagationp. 119
Perturbationp. 125
Experimentsp. 135
Set-upp. 135
Spectrum evolutionp. 136
Phase diagramp. 136
System marginp. 136
Comparison to a soliton transmission system with constant dispersionp. 139
Narrow band 1.02 Tbit/s (51 × 20 Gbit/s) soliton DWDM transmission over 1000 km of Standard fibrep. 140
Conclusionp. 141
Nonlinear Pulses in Ultra-Fast Optical Communications
Introductionp. 147
The DM solitonsp. 148
The Lagrangian methodp. 149
Hermite-Gaussianansatzp. 151
The DM solitons inWDMp. 153
Mechanism offrequencyshift for DM solitonp. 153
Optimal allocation of amplifierp. 156
Statistical analysis ofcollision induced timing jitterp. 158
NRZ pulse propagationp. 161
The NLS-Whitham equationsp. 163
Control of NRZ pulsep. 165
Soliton Wavelength-Division-Multiplexing System: From Numerical Design to Recirculating Loop Experiments
Introductionp. 171
Soliton transmission overdispersion-managedsystemsp. 173
Results from the analytical/basic numerical toolp. 175
Results from the numerical toolp. 177
Results from the experimental toolp. 178
Conclusionp. 181
Mode-Locked Fiber Ring Lasersand Fiber Ring Memories
Introductionp. 183
The passively mode-locked fiber ring laser and the master equationp. 184
Harmonic modelocking and the makings of an all-optical memoryp. 190
The first order solitonp. 199
Perturbation theory of solitonsp. 200
The stretched pulse fiber ring laserp. 208
Modulational Instabilities in Passive Cavities:Theory and Experiment
Introductionp. 215
Basic properties of the nonlinear fiber resonatorp. 217
The effects ofdispersion: Theoryp. 222
cw-MI and the MI-induced up-switching processp. 223
Period-doubling MIp. 225
Experimental resultsp. 226
Period-doubling MIp. 227
cw-MI and the MI-induced up-switching processp. 229
Conclusionp. 230
Recent Developments in the Theoryof Optical Gap Solitons
Introductionp. 233
Coupled-mode modelsp. 234
Stabilityp. 236
Quadratic gap solitonsp. 242
Conclusionsp. 246
Vector Modulational Instabilities and Soliton Experiments
Introductionp. 249
Observation of vector MI for normal dispersionp. 250
High-birefringence fiberp. 250
Low-birefringence fiberp. 251
Bimodal fiberp. 252
MI gain spectra from linear stability analysisp. 252
High-birefringence fiberp. 253
Low-birefringence fiberp. 253
Bimodal fiberp. 254
Induced vector MI and soliton generationp. 255
High-birefringence fiberp. 255
Low-birefringence fiberp. 258
Bimodal fiberp. 260
Conclusionsp. 262
Transient Raman Amplification
Introductionp. 265
Derivation of the SRS systemp. 269
Steady state regimep. 273
Transient SRS: A complete solutionp. 274
Raman soliton generationp. 276
Stokes phase flips and the Raman spikep. 277
The Raman spike in the time domainp. 278
Conclusionp. 280
Self-Structuration of Three-Wave Dissipative Solitonsin CW-Pumped Optical Cavities
Introductionp. 283
Three-wave modelp. 284
Two-wave adiabatic approximationp. 286
Self-pulsing in a cavityp. 289
The Description of the Ultrashort Pulse Propagationin Non-Linear Media Under Quasi-Resonance Condition
Introductionp. 293
Maxwell-Bloch, RMB, and SVEPA equationsp. 295
Solution of the Bloch equationp. 297
Scalar wave equationsp. 299
Non-linearwave equationp. 299
Unidirectional non-linearwave (mKdV equation)p. 302
Non-linear wave in SVEPAp. 303
Vector wavesp. 304
Generalised Maxwell-Bloch equationsp. 305
Solution of the generalised Bloch equationsp. 305
Vector non-linear wave equationp. 307
Unidirectional vector non-linearwavesp. 308
Polarised quasi-monochromatic non-linear wave (vector NLS equation)p. 309
Conclusionp. 310
Bright Spatial Soliton Interactions
Introductionp. 313
Coherent interactions: Basic theoretical propertiesp. 316
Kerrnonlinearitiesp. 317
Saturating nonlinearitiesp. 321
Coherent interactions: Experimentsp. 322
Incoherentsoliton interactionsp. 324
Full 3D soliton interactionsp. 326
Anisotropie soliton interactionsp. 329
Summaryp. 330
Spatial Solitons in Saturating Nonlinear Materials
Introductionp. 335
Dark and bright spatial solitonsp. 338
Saturating nonlinearitiesp. 340
Experimental demonstrationsp. 341
Conclusionsp. 346
Discrete Solitons in Nonlinear Waveguide Arrays
Introductionp. 349
Basic properties ofwaveguide arraysp. 352
Evolution equationsp. 352
Linear properties - "discrete diffraction"p. 353
Nonlinear properties - modulational instabilityp. 354
Discrete Solitonsp. 355
Moderately localized bright solitons - basic propertiesp. 355
Moderately localized bright solitons - self-trapping and switchingp. 358
Strongly localized discrete solitons - properties and stabilityp. 359
Further studiesp. 360
Experiments in nonlinear waveguide arraysp. 361
Conclusionsp. 364
Solitons in Cavities with Quadratic Nonlinearities
Introductionp. 367
The case ofquadratic nonlinearitiesp. 368
Why cavities?p. 369
Multidimensional spatial solitons in optical cavitiesp. 370
Optical bullets in nonlinear optical cavitiesp. 370
Temporal solitons in singly resonant optical parametric oscillatorsp. 371
Conclusionp. 379
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540663140
ISBN-10: 3540663142
Series: Centre de Physique Des Houches
Audience: General
Format: Paperback
Language: English
Number Of Pages: 384
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 2.11
Weight (kg): 0.56

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