Biswas / Konar Introduction to non-Kerr Law Optical Solitons

Erscheinungsjahr 2006
ISBN: 978-1-4200-1140-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 216 Seiten

Reihe: Chapman & Hall/CRC Applied Mathematics & Nonlinear Science

Despite remarkable developments in the field, a detailed treatment of non-Kerr law media has not been published. Introduction to non-Kerr Law Optical Solitons is the first book devoted exclusively to optical soliton propagation in media that possesses non-Kerr law nonlinearities.

After an introduction to the basic features of fiber-optic communications, the book outlines the nonlinear Schrödinger equation (NLSE), conserved quantities, and adiabatic dynamics of soliton parameters. It then derives the NLSE for Kerr law nonlinearity from basic principles, the inverse scattering transform, and the 1-soliton solution. The book also explains the variational principle and Lie transform. In each case of non-Kerr law solitons, the authors develop soliton dynamics, evaluated integrals of motion, and adiabatic dynamics of soliton parameters based on multiple-scale perturbation theory. The book explores intra-channel collision of optical solitons in both Hamiltonian and non-Hamiltonian type perturbations. In addition, it examines the stochastic perturbation of optical solitons, the corresponding Langevin equations, and optical couplers, followed by an introduction to optical bullets.

Establishing a basis in an important yet insufficiently documented subject, Introduction to non-Kerr Law Optical Solitons will help fuel advances in optical communication systems.

Zielgruppe

Researchers and senior undergraduate and graduate students in mathematics, physics, optics, and engineering.

Autoren/Hrsg.

Biswas, Anjan

Konar, Swapan

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

INTRODUCTION
History
Optical Waveguides

THE NONLINEAR SCHRÖDINGER EQUATION
Introduction
Traveling Waves
Integrals of Motion
Parameter Evolution
Quasi-Stationary Solution

KERR LAW NONLINEARITY
Introduction
Traveling Wave Solution
Inverse Scattering Transform
Integrals of Motion
Variational Principle
Quasi-Stationary Solution
Lie Transform

POWER LAW NONLINEARITY
Introduction
Traveling Wave Solution
Integrals of Motion
Quasi-Stationary Solution

PARABOLIC LAW NONLINEARITY
Introduction
Traveling Wave Solution
Integrals of Motion
Quasi-Stationary Solution

DUAL-POWER LAW NONLINEARITY
Introduction
Traveling Wave Solution
Integrals of Motion
Quasi-Stationary Solution

SATURABLE LAW NONLINEARITY
Introduction
The NLSE
Bistable Solitons
Arbitrary Pulse Propagation

SOLITON-SOLITON INTERACTION
Introduction
Mathematical Formulation
Quasi-Particle Theory

STOCHASTIC PERTURBATION
Introduction
Kerr Law
Power Law
Parabolic Law
Dual-Power Law

OPTICAL COUPLERS
Introduction
Twin-Core Couplers
Multiple-Core Couplers
Magneto-Optic Waveguides

OPTICAL BULLETS
Introduction
1 + 3 Dimensions

EPILOGUE
HINTS AND SOLUTIONS
BIBLIOGRAPHY
INDEX