Mathematical Theory of Dispersion-managed Optical Solitons

by Biswas, Anjan; Milovic, Daniela; Edwards, Matthew

• ISBN13: 9783642102196
• ISBN10: 3642102190
• Format: Hardcover
• Copyright: 2010-09-30
• Publisher: Springer Nature

Summary

"Mathematical Theory of Dispersion-Managed Optical Solitons" discusses recent advances covering optical solitons, soliton perturbation, optical cross-talk, Gabitov-Turitsyn Equations, quasi-linear pulses, and higher order Gabitov-Turitsyn Equations. Focusing on a mathematical perspective, the book bridges the gap between concepts in engineering and mathematics, and gives an outlook to many new topics for further research.The book is intended for researchers and graduate students in Applied Mathematics, Physics and Engineering and also it will be of interest to those who are conducting research in nonlinear fiber optics.Dr. Anjan Biswas is an Associate Professor at the Department of Applied Mathematics & Theoretical Physics, Delaware State University, Dover, DE, USA; Dr. Daniela Milovic is an Associate Professor at the Department of Telecommunications, Faculty of Electronic Engineering, University of Nis, Serbia; Dr. Matthew Edwards is the Dean of the School of Arts and Sciences at Alabama A & M University in Huntsville, AL, USA.

Author Biography

Dr. Anjan Biswas is an Associate Professor at the Department of Applied Mathematics Theoretical Physics, Delaware State University, Dover, DE, USA. Dr. Daniela Milovic is an Associate Professor at the Department of Telecommunications, Faculty of Electronic Engineering, University of Nis, Serbia. Dr. Matthew Edwards is the Dean of the School of Arts and Sciences at Alabama A M University in Huntsville, AL, USA.

Table of Contents

Introduction	p. 1
References	p. 3
Nonlinear Schrödinger's Equation	p. 5
Derivation of NLSE	p. 5
Limitations of conventional solitons	p. 9
Dispersion-management	p. 10
Mathematical formulation	p. 11
Integrals of motion	p. 15
Soliton perturbation theory	p. 18
Perturbation terms	p. 19
Variational principle	p. 20
Perturbation terms	p. 21
References	p. 22
Polarization Preserving Fibers	p. 27
Introduction	p. 27
Integrals of motion	p. 28
Gaussian pulses	p. 29
Super-Gaussian pulses	p. 30
Super-Sech pulses	p. 32
Variational principle	p. 35
Gaussian pulses	p. 35
Super-Gaussian pulses	p. 36
Perturbation terms	p. 36
Gaussian pulses	p. 37
Super-Gaussian pulses	p. 37
Stochastic perturbation	p. 38
References	p. 42
Birefringent Fibers	p. 45
Introduction	p. 45
Integrals of motion	p. 47
Gaussian pulses	p. 49
Super-Gaussian pulses	p. 49
Variational principle	p. 50
Gaussian pulses	p. 52
Super-Gaussian pulses	p. 53
Perturbation terms	p. 55
Gaussian pulses	p. 57
Super-Gaussian pulses	p. 58
References	p. 60
Multiple Channels	p. 63
Introduction	p. 63
Integrals of motion	p. 64
Gaussian pulses	p. 66
Super-Gaussian pulses	p. 67
Variational principle	p. 68
Gaussian pulses	p. 69
Super-Gaussian pulses	p. 70
Perturbation terms	p. 70
Gaussian pulses	p. 73
Super-Gaussian pulses	p. 74
References	p. 75
Optical Crosstalk	p. 77
In-band crosstalk	p. 78
Gaussian optical pulse	p. 80
Bit error rate	p. 84
Sech optical pulse	p. 85
Super-Sech optical pulse	p. 88
References	p. 93
Gabitov-Turitsyn Equation	p. 95
Introduction	p. 95
Polarization-preserving fibers	p. 96
Special solutions	p. 99
Birefringent fibers	p. 100
DWDM system	p. 104
Properties of the kernel	p. 107
Lossless Case	p. 108
Lossy Case	p. 108
References	p. 109
Quasi-linear Pulses	p. 111
Introduction	p. 111
Polarization-preserving fibers	p. 112
Lossless system	p. 112
Lossy system	p. 115
Birefringent fibers	p. 121
Lossless system	p. 122
lossy system	p. 124
Multiple channels	p. 129
Lossless system	p. 129
Lossy system	p. 131
References	p. 134
Higher Order Gabitov-Turitsyn Equations	p. 137
Introduction	p. 137
Polarization preserving fibers	p. 137
Birefringent fibers	p. 142
DWDM systems	p. 149
References	p. 154
Index	p. 157
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