Introduction to non-Kerr Law Optical Solitons

by Biswas; Anjan

• ISBN13: 9781584886389
• ISBN10: 1584886382
• Edition: 1st
• Format: Hardcover
• Copyright: 2006-11-10
• Publisher: Chapman & Hall/

Summary

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.

Table of Contents

1 Introduction	1	(6)
1.1 History	1	(2)
1.2 Optical Waveguides	3	(4)
1.2.1 Types of Optical Fibers	5	(1)
1.2.2 Advantages of Fiber-Optic Communications	5	(2)
2 The Nonlinear Schrödinger's Equation	7	(20)
2.1 Introduction	7	(4)
2.1.1 Nonlinearity Classification	8	(3)
2.2 Traveling Waves	11	(1)
2.3 Integrals of Motion	12	(5)
2.4 Parameter Evolution	17	(3)
2.4.1 Perturbation Terms	17	(3)
2.5 Quasi-Stationary Solution	20	(7)
2.5.1 Mathematical Theory	21	(1)
2.5.2 Application	22	(5)
3 Kerr Law Nonlinearity	27	(30)
3.1 Introduction,	27	(5)
3.1.1 The Nonlinear Schrödinger's Equation	29	(3)
3.2 Traveling Wave Solution	32	(1)
3.3 Inverse Scattering Transform	33	(6)
3.3.1 1-Soliton Solution	37	(2)
3.4 Integrals of Motion	39	(4)
3.4.1 Hamiltonian Structure	41	(2)
3.5 Variational Principle	43	(3)
3.6 Quasi-Stationary Solution	46	(3)
3.7 Lie Transform	49	(8)
3.7.1 Introduction	50	(4)
3.7.2 Application	54	(3)
4 Power Law Nonlinearity	57	(10)
4.1 Introduction	57	(1)
4.2 Traveling Wave Solution	58	(1)
4.3 Integrals of Motion	59	(3)
4.4 Quasi-Stationary Solution	62	(5)
5 Parabolic Law Nonlinearity	67	(10)
5.1 Introduction	67	(2)
5.2 Traveling Wave Solution	69	(1)
5.3 Integrals of Motion	70	(2)
5.4 Quasi-Stationary Solution	72	(5)
6 Dual-Power Law Nonlinearity	77	(10)
6.1 Introduction	77	(1)
6.2 Traveling Wave Solution	78	(1)
6.3 Integrals of Motion	79	(3)
6.4 Quasi-Stationary Solution	82	(5)
7 Saturable Law Nonlinearity	87	(14)
7.1 Introduction	87	(1)
7.2 The NLSE	88	(2)
7.2.1 Conserved Quantities	90	(1)
7.3 Bistable Solitons	90	(1)
7.4 Arbitrary Pulse Propagation	91	(10)
7.4.1 Lossless Uniform Media (Γ = 0)	94	(2)
7.4.2 Stationary Pulse Propagation	96	(1)
7.4.3 Lossy Media (&Gamma not = to 0)	97	(4)
8 Soliton—Soliton Interaction	101	(34)
8.1 Introduction	101	(1)
8.2 Mathematical Formulation	102	(7)
8.2.1 Kerr Law	104	(1)
8.2.2 Power Law	105	(1)
8.2.3 Parabolic Law	106	(2)
8.2.4 Dual-Power Law	108	(1)
8.3 Quasi-Particle Theory	109	(26)
8.3.1 Kerr Law	113	(4)
8.3.1.1 Non-Hamiltonian Perturbations	114	(1)
8.3.1.2 Hamiltonian Perturbations	115	(2)
8.3.2 Power Law	117	(7)
8.3.2.1 Non-Hamiltonian Perturbations	119	(2)
8.3.2.2 Hamiltonian Perturbations	121	(3)
8.3.3 Parabolic Law	124	(4)
8.3.3.1 Non-Hamiltonian Perturbations	126	(1)
8.3.3.2 Hamiltonian Perturbations	127	(1)
8.3.4 Dual-Power Law	128	(17)
8.3.4.1 Non-Hamiltonian Perturbations	131	(1)
8.3.4.2 Hamiltonian Perturbations	131	(4)
9 Stochastic Perturbation	135	(10)
9.1 Introduction	135	(2)
9.2 Kerr Law	137	(2)
9.3 Power Law	139	(2)
9.4 Parabolic Law	141	(1)
9.5 Dual-Power Law	142	(3)
10 Optical Couplers	145	(16)
10.1 Introduction	145	(3)
10.1.1 Types of Couplers and Their Functions	146	(1)
10.1.1.1 Three- and Four-Port Couplers	146	(1)
10.1.1.2 Star Coupler or Multiport Couplers	146	(1)
10.1.2 Optical Switching	147	(1)
10.2 Twin-Core Couplers	148	(4)
10.3 Multiple-Core Couplers	152	(5)
10.3.1 Coupling with Nearest Neighbors	153	(2)
10.3.2 Coupling with All Neighbors	155	(2)
10.4 Magneto-Optic Waveguides	157	(4)
10.4.1 Mathematical Analysis	158	(3)
11 Optical Bullets	161	(6)
11.1 Introduction	161	(1)
11.2 1 + 3 Dimensions	162	(5)
11.2.1 Integrals of Motion	162	(2)
11.2.2 Parameter Evolution	164	(3)
12 Epilogue	167	(6)
Hints and Solutions	173	(2)
Bibliography	175	(20)
Index	195