Introduction to non-Kerr Law Optical Solitons: 1st Edition (Hardback) book cover

Introduction to non-Kerr Law Optical Solitons

1st Edition

By Anjan Biswas, Swapan Konar

Chapman and Hall/CRC

216 pages | 22 B/W Illus.

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pub: 2006-11-10
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Description

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.

Reviews

". . . well-written . . . well-documented."

– Georg Hebermehl, in Zentralblatt Math, 2009

Table of Contents

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

About the Series

Chapman & Hall/CRC Applied Mathematics & Nonlinear Science

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Subject Categories

BISAC Subject Codes/Headings:
SCI040000
SCIENCE / Mathematical Physics
SCI053000
SCIENCE / Optics
SCI055000
SCIENCE / Physics
TEC019000
TECHNOLOGY & ENGINEERING / Lasers & Photonics