
Nonlinear Fiber Optics
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Content
- Cover
- Contents
- Preface
- Chapter 1 Introduction
- 1.1 Historical Perspective
- 1.2 Fiber Characteristics
- 1.2.1 Material and Fabrication
- 1.2.2 Fiber Losses
- 1.2.3 Chromatic Dispersion
- 1.2.4 Polarization-Mode Dispersion
- 1.3 Fiber Nonlinearities
- 1.3.1 Nonlinear Refraction
- 1.3.2 Stimulated Inelastic Scattering
- 1.3.3 Importance of Nonlinear Effects
- 1.4 Overview
- Problems
- References
- Chapter 2 Pulse Propagation in Fibers
- 2.1 Maxwell's Equations
- 2.2 Fiber Modes
- 2.2.1 Eigenvalue Equation
- 2.2.2 Single-Mode Condition
- 2.2.3 Characteristics of the Fundamental Mode
- 2.3 Pulse-Propagation Equation
- 2.3.1 Nonlinear Pulse Propagation
- 2.3.2 Higher-Order Nonlinear Effects
- 2.4 Numerical Methods
- 2.4.1 Split-Step Fourier Method
- 2.4.2 Finite-Difference Methods
- Problems
- References
- Chapter 3 Group-Velocity Dispersion
- 3.1 Different Propagation Regimes
- 3.2 Dispersion-Induced Pulse Broadening
- 3.2.1 Gaussian Pulses
- 3.2.2 Chirped Gaussian Pulses
- 3.2.3 Hyperbolic-Secant Pulses
- 3.2.4 Super-Gaussian Pulses
- 3.2.5 Experimental Results
- 3.3 Third-Order Dispersion
- 3.3.1 Changes in Pulse Shape
- 3.3.2 Broadening Factor
- 3.3.3 Arbitrary-Shape Pulses
- 3.3.4 Ultrashort-Pulse Measurements
- 3.4 Dispersion Management
- 3.4.1 GVD-Induced Limitations
- 3.4.2 Dispersion Compensation
- 3.4.3 Compensation of Third-Order Dispersion
- Problems
- References
- Chapter 4 Self-Phase Modulation
- 4.1 SPM-Induced Spectral Broadening
- 4.1.1 Nonlinear Phase Shift
- 4.1.2 Changes in Pulse Spectra
- 4.1.3 Effect of Pulse Shape and Initial Chirp
- 4.1.4 Effect of Partial Coherence
- 4.2 Effect of Group-Velocity Dispersion
- 4.2.1 Pulse Evolution
- 4.2.2 Broadening Factor
- 4.2.3 OpticalWave Breaking
- 4.2.4 Experimental Results
- 4.2.5 Effect of Third-Order Dispersion
- 4.3 Higher-Order Nonlinear Effects
- 4.3.1 Self-Steepening
- 4.3.2 Effect of GVD on Optical Shocks
- 4.3.3 Intrapulse Raman Scattering
- Problems
- References
- Chapter 5 Optical Solitons
- 5.1 Modulation Instability
- 5.1.1 Linear Stability Analysis
- 5.1.2 Gain Spectrum
- 5.1.3 Experimental Observation
- 5.1.4 Ultrashort Pulse Generation
- 5.1.5 Impact on Lightwave Systems
- 5.2 Fiber Solitons
- 5.2.1 Inverse Scattering Method
- 5.2.2 Fundamental Soliton
- 5.2.3 Higher-Order Solitons
- 5.2.4 Experimental Confirmation
- 5.2.5 Soliton Stability
- 5.3 Other Types of Solitons
- 5.3.1 Dark Solitons
- 5.3.2 Dispersion-Managed Solitons
- 5.3.3 Bistable Solitons
- 5.4 Perturbation of Solitons
- 5.4.1 Perturbation Methods
- 5.4.2 Fiber Losses
- 5.4.3 Soliton Amplification
- 5.4.4 Soliton Interaction
- 5.5 Higher-Order Effects
- 5.5.1 Third-Order Dispersion
- 5.5.2 Self-Steepening
- 5.5.3 Intrapulse Raman Scattering
- 5.5.4 Propagation of Femtosecond Pulses
- Problems
- References
- Chapter 6 Polarization Effects
- 6.1 Nonlinear Birefringence
- 6.1.1 Origin of Nonlinear Birefringence
- 6.1.2 Coupled-Mode Equations
- 6.1.3 Elliptically Birefringent Fibers
- 6.2 Nonlinear Phase Shift
- 6.2.1 Nondispersive XPM
- 6.2.2 Optical Kerr Effect
- 6.2.3 Pulse Shaping
- 6.3 Evolution of Polarization State
- 6.3.1 Analytic Solution
- 6.3.2 Poincar ´ e-Sphere Representation
- 6.3.3 Polarization Instability
- 6.3.4 Polarization Chaos
- 6.4 Vector Modulation Instability
- 6.4.1 Low-Birefringence Fibers
- 6.4.2 High-Birefringence Fibers
- 6.4.3 Isotropic Fibers
- 6.4.4 Experimental Results
- 6.5 Birefringence and Solitons
- 6.5.1 Low-Birefringence Fibers
- 6.5.2 High-Birefringence Fibers
- 6.5.3 Soliton-Dragging Logic Gates
- 6.5.4 Vector Solitons
- 6.6 Random Birefringence
- 6.6.1 Polarization-Mode Dispersion
- 6.6.2 Polarization State of Solitons
- Problems
- References
- Chapter 7 Cross-Phase Modulation
- 7.1 XPM-Induced Nonlinear Coupling
- 7.1.1 Nonlinear Refractive Index
- 7.1.2 Coupled NLS Equations
- 7.1.3 Propagation in Birefringent Fibers
- 7.2 XPM-Induced Modulation Instability
- 7.2.1 Linear Stability Analysis
- 7.2.2 Experimental Results
- 7.3 XPM-Paired Solitons
- 7.3.1 Bright-Dark Soliton Pair
- 7.3.2 Bright-Gray Soliton Pair
- 7.3.3 Other Soliton Pairs
- 7.4 Spectral and Temporal Effects
- 7.4.1 Asymmetric Spectral Broadening
- 7.4.2 Asymmetric Temporal Changes
- 7.4.3 Higher-Order Nonlinear Effects
- 7.5 Applications of XPM
- 7.5.1 XPM-Induced Pulse Compression
- 7.5.2 XPM-Induced Optical Switching
- 7.5.3 XPM-Induced Nonreciprocity
- Problems
- References
- Chapter 8 Stimulated Raman Scattering
- 8.1 Basic Concepts
- 8.1.1 Raman-Gain Spectrum
- 8.1.2 Raman Threshold
- 8.1.3 Coupled Amplitude Equations
- 8.2 Quasi-Continuous SRS
- 8.2.1 Single-Pass Raman Generation
- 8.2.2 Raman Fiber Lasers
- 8.2.3 Raman Fiber Amplifiers
- 8.2.4 Raman-Induced Crosstalk
- 8.3 SRS with Short Pump Pulses
- 8.3.1 Pulse-Propagation Equations
- 8.3.2 Nondispersive Case
- 8.3.3 Effects of GVD
- 8.3.4 Experimental Results
- 8.3.5 Synchronously Pumped Raman Lasers
- 8.4 Soliton Effects
- 8.4.1 Raman Solitons
- 8.4.2 Raman Soliton Lasers
- 8.4.3 Soliton-Effect Pulse Compression
- 8.5 Effect of Four-Wave Mixing
- Problems
- References
- Chapter 9 Stimulated Brillouin Scattering
- 9.1 Basic Concepts
- 9.1.1 Physical Process
- 9.1.2 Brillouin-Gain Spectrum
- 9.2 Quasi-CW SBS
- 9.2.1 Coupled Intensity Equations
- 9.2.2 Brillouin Threshold
- 9.2.3 Gain Saturation
- 9.2.4 Experimental Results
- 9.3 Dynamic Aspects
- 9.3.1 Coupled Amplitude Equations
- 9.3.2 Relaxation Oscillations
- 9.3.3 Modulation Instability and Chaos
- 9.3.4 Transient Regime
- 9.4 Brillouin Fiber Lasers
- 9.4.1 CW Operation
- 9.4.2 Pulsed Operation
- 9.5 SBS Applications
- 9.5.1 Brillouin Fiber Amplifiers
- 9.5.2 Fiber Sensors
- Problems
- References
- Chapter 10 Parametric Processes
- 10.1 Origin of Four-Wave Mixing
- 10.2 Theory of Four-Wave Mixing
- 10.2.1 Coupled Amplitude Equations
- 10.2.2 Approximate Solution
- 10.2.3 Effect of Phase Matching
- 10.2.4 Ultrafast FWM
- 10.3 Phase-Matching Techniques
- 10.3.1 Physical Mechanisms
- 10.3.2 Phase Matching in Multimode Fibers
- 10.3.3 Phase Matching in Single-Mode Fibers
- 10.3.4 Phase Matching in Birefringent Fibers
- 10.4 Parametric Amplification
- 10.4.1 Gain and Bandwidth
- 10.4.2 Pump Depletion
- 10.4.3 Parametric Amplifiers
- 10.4.4 Parametric Oscillators
- 10.5 FWM Applications
- 10.5.1 Wavelength Conversion
- 10.5.2 Phase Conjugation
- 10.5.3 Squeezing
- 10.5.4 Supercontinuum Generation
- 10.6 Second-Harmonic Generation
- 10.6.1 Experimental Results
- 10.6.2 Physical Mechanism
- 10.6.3 Simple Theory
- 10.6.4 Quasi-Phase-Matching Technique
- Problems
- References
- Appendix A Decibel Units
- Appendix B Nonlinear Refractive Index
- References
- Appendix C Acronyms
- Index
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