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 Authors/Editors

Dr. Anjan Biswas obtained his BSc (Honors) in mathematics fromSt. Xavier’s College, Calcutta, and subsequently earned his MSc and MPhil degrees in applied mathematics from the University of Calcutta, India. After that, he obtained his MA and PhD degrees in applied mathematics from the University of New Mexico, Albuquerque. His current research interests are in nonlinear optics, theory of solitons, plasma physics, and fluid dynamics. He is the author of 100 refereed journal papers and also serves as an editorial board member for three journals. Currently, he is an associate professor in the Department of Applied Mathematics and Theoretical Physics of Delaware State University in Dover.

Dr. S. Konar received his MSc degree in Nuclear Physics from University of Kalyani, India, in 1982. He earned an MTech in energy management. Dr. Konar has been awarded MPhil and PhD respectively in 1987 and 1990 by Jawaharlal Nehru University, New Delhi, India. At present, he is working as a professor of applied physics at Birla Institute of Technology, Mesra, Ranchi, India. His current research interest is in the field of photonics and optoelectronics, particularly classical solitons, soliton propagation in dispersionmanaged optical communication systems, nonlinear optical waveguide, induced focusing, self-focusing and all optical switching. He has published 64 research papers in international journals and presented 30 research papers in conferences.

About the Series

Chapman & Hall/CRC Applied Mathematics & Nonlinear Science

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
SCI040000
SCIENCE / Mathematical Physics
SCI053000
SCIENCE / Optics
SCI055000
SCIENCE / Physics
TEC019000
TECHNOLOGY & ENGINEERING / Lasers & Photonics