Optical Solitons: Theoretical and Experimental Challenges (Lecture Notes in Physics, 613)

✍ Scribed by Kuppuswamy Porsezian (editor), Valakkattil Chako Kuriakose (editor)

• Publisher: Springer
• Year: 2003
• Tongue: English
• Leaves: 399
• Edition: 2003
• Category: Library

✦ Synopsis

Optical Solitons represent one of the most exciting and fascinating concepts in modern communications, arousing special interest due to their potential applications in optical fibre communication. This volume focuses on the explicit integration of analytical and experimental methods in nonlinear fibre optics and integrated optics. It covers all important recent technical issues in optical-soliton communication. For example, individual chapters are devoted to topics such as dispersion management and fibre Bragg grating. All authors are leading authorities in their fields.

✦ Table of Contents

Chapter 1
1 Importance of Optical Fiber Communications
2 Birth of Optical Solitons
3 Present Book
Chapter 2
1 Introduction
2 Properties of Optical Solitons as a Result of IST
3 Dielectric Properties of Optical Fibers
4 Master Equation for Information Transfer in Optical Fibers
5 Lagrangian Method and Soliton Perturbation Theory
6 Dispersion Managed Solitons
7 Some Recent Experimental Results of Optical Soliton Transmission
8 Concluding Remarks
References
Chapter 3
1 Introduction
2 The Optical Fiber
3 Modes in an Optical Fiber
4 Typical Fiber Optic Communication System
5 Attenuation
6 Optical Ampli.ers
6.1 Erbium Doped Fiber Amplifier (EDFA)
6.2 Fiber Raman Ampli.er (FRA)
6.3 Noise in Amplifiers
7 Pulse Dispersion
8 Dispersion Compensation
9 Nonlinear Effects in Optical Fibers
9.1 Self Phase Modulation (SPM)
9.2 Cross Phase Modulation (XPM)
9.3 Four Wave Mixing (FWM)
10 Conclusions
References
Chapter 4
1 Introduction
2 Planar Dielectric Waveguides
2.1 Dielectric Slab as a Waveguide
2.2 Novel Experiments in Dielectric Guides
3 Nonlinear Resonance: N-wave Interactions
3.1 General Remarks and Standard DT Integration-Inclined Solitons as Illustration
3.2 Binary DT Application
4 Linear Resonance: MB Equations
4.1 About Derivation and Rescaling
4.2 Integrability and Solutions of MB Equations
4.3 Solutions over the Nonzero Backgrounds
4.4 Periodic-Seed Solutions
4.5 Nonreduced MB Equation Integrability
4.6 The LvN Equation as Associated ZS Problem
5 Nonresonant Propagation (Kerr Effect): Manakov Solitons
5.1 Lax Pair and Periodic-Seed Solutions
5.2 Determinant Representation
5.3 Perturbations of Solutions
Acknowledgment
References
Chapter 5
1 Introduction
2 Integrable Systems
3 Hamiltonian Systems
4 Dissipative Systems
References
Chapter 6
1 Introduction
1.1 Operator Representations
1.2 Simple Numerical Integration
2 Numerical Modelling
2.1 Second Order Split Step Fourier Method
2.2 Fourth Order Split Step Fourier Method
3 Analytic Results
3.1 Average Solitons
3.2 Special Points in Constant Dispersion Systems
3.3 Special Points in Dispersion Managed Systems
3.4 Magic Points
4 Conclusions
References
Chapter 7
1 Introduction
2 CNLS Equations as Governing Equations for Intense Light Propagation in Multimode Fibers and Photorefractive Materials
3 Soliton Solutions of the CNLS Equations
3.1 N=2 Case
3.2 N=3 Case
3.3 N-CNLS Equations
4 Shape Changing Collisions in Coupled Nonlinear Schr¨odinger Equations
4.1 N=2 Case
4.2 N=3 and Arbitrary Cases
4.3 Shape Changing Collisions and Higher Order Solitons
5 Conclusion
Acknowledgment
References
Chapter 8
1 Introduction
2 Mathematical Formulation for Pulses in Fiber Bragg Gratings
2.1 Multi-soliton Solutions
2.2 Quasi-periodic Solutions
2.3 Study of Pulse Dynamics in Nonuniform Gratings
3 Gap Soliton Bullets
3.1 Slowly Varying Envelope Approximation
3.2 Weakly Nonlinear Theory
3.3 Analysis of the 2D Perturbed NLSE
4 Conclusions
Acknowledgements
Appendix A
Appendix B
References
Chapter 9
1 Introduction
2 Reflection Versus Transparency in Short Period Gratings
2.1 Stopband of Linear Origin
2.2 Stopbands due to Periodic Nonlinearities
2.3 Nonlinearity-Induced Transparency in Short-Period Gratings
3 Gap Solitons in Bragg Gratings with Kerr Nonlinearity
4 Gap Solitons Supported by Frequency Conversion Processes
5 Stability and Excitation
6 Localization in Gap of Nonlinear Origin
7 Summary and Further Developments
Acknowledgment
References
Chapter 10
1 Introduction
2 General Features and Theoretical Model
2.1 General Features of SRS
2.2 Generalized Theory of the SSFS
3 Suppression of the Soliton Self-frequency Shift
4 Conclusion
Acknowledgments
References
Chapter 11
1 Introduction
2 Perturbed Nonlinear Schrodinger Equation
3 Dispersion Managed Nonlinear Schrodinger Equation
4 Quasi-linear Pulse Propagation
4.1 Lossless Case
4.2 Lossy Case
5 Intra-channel Quasi-linear Pulse Interactions
5.1 Perturbed DMNLS Equation
5.2 Energy Transfer
5.3 Frequency and Timing Shifts
6 Conclusion
Acknowledgments
References
Chapter 12
1 Introduction
2 Dispersion-Managed Transmission System
3 Dispersion Map Parameters
4 Interactions Between Neighboring DM Solitons
5 Bi-Soliton Solution
6 Error Preventable Line-Coding Scheme
7 3 Out of 4 Encoding Scheme
8 Conclusion
References
Chapter 13
1 Introduction
2 Fundamentals of Optical Fiber Soliton Lasers
2.1 Optical Fiber Laser Components and Construction
2.2 Nonlinearity and Dispersion
2.3 Typical Characteristics of Optical Fiber Soliton Lasers
2.4 Soliton Generation Versus Soliton Transmission
3 Experimental Developments in Optical Fiber Soliton Lasers
3.1 Active Mode-Locking
3.2 Passively Mode-Locked Soliton Fiber Lasers
3.3 Soliton Mode-Locking
3.4 Hybrid Mode-Locking
3.5 Other Soliton Lasers
4 Theory of Soliton Lasers
4.1 Exact Solutions
4.2 Soliton Solutions for the Case of Slow Saturable Absorber
4.3 Perturbation Approximation
4.4 Stability
References
Chapter 14
1 Introduction
2 Theoretical Fundamentals
3 Higher-Order Solitons and Supercontinuum Generation in Photonic Crystal Fibers
4 Degenerate Four-Wave Mixing and Parametric Amplification
5 Pulse Compression Without Chirp Control by High-Order Coherent Raman Scattering
6 Formation of Optical Sub-cycle Pulses and Full Maxwell-Bloch Solitary Waves in Resonant Two-Level Medium
Acknowledgement
References
Chapter 15
1 Introduction
2 Experimental Setup
3 Vector Modulational Instability in Highly Birefringent Fibers
3.1 Coupled Nonlinear Schrodinger Equations
3.2 Linear Stability Analysis of Modulational Instability
3.3 Influence of the Non-phase-matched Waves for a Single-Frequency Pump Field
3.4 Suppression of MI for a Dual-Frequency Pump Field
4 Generation of Terahertz Vector Dark-Soliton Trains from Induced Modulational Instability
5 Modulational Instability in Highly Birefringent Air-Silica Microstructure Fiber
6 Four Wave Mixing-Induced Modulational Instability in Highly Birefringent Fibers
7 Bragg Modulational Instability Induced by a Dynamic Grating in an Optical Fiber
8 Conclusions
Acknowledgments
References
Chapter 16
1 Introduction
2 Three Wave Model
3 Solitary Wave Solution
4 Two Wave Adiabatic Approximation
5 Self Pulsing in a Cavity
6 Three Wave Model
7 Stability of the Degenerate Backward Optical Parametric Oscillator
8 Conclusion
Acknowledgements
References
Chapter 17
1 Introduction
2 Model and Numerical Analysis
3 Experimental Technique
4 Experimental Results and Discussions
4.1 Below Bandgap Hexagons and Dark Solitons
4.2 Near Bandgap Bright and Dark Solitons
4.3 Above Bandgap Bright Solitons
4.4 Optical Pumping
5 Conclusion
Acknowledgment
References
Chapter 18
1 Introduction
2 Theory
3 Physical Parameters
4 Experimental Setup
5 Propagation and Diffraction of Picosecond Acoustic Wave Packets
6 One-Dimensional Propagation Experiments
7 Conclusion
References