Nonlinear fiber optics Machine generated contents note: ch. 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 ch. 2 Pulse Propagation in Fibers 2.1.Maxwells 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 2.3.3.Raman Response Function and its Impact 2.3.4.Extension to Multimode Fibers 2.4.Numerical Methods 2.4.1.Split Step Fourier Method 2.4.2.Finite Difference Methods Problems References ch. 3 Group Velocity Dispersion Note continued: 9.5.Brillouin Fiber Lasers 9.5.1.CW Operation 9.5.2.Pulsed Operation Problems References ch. 10 Four Wave Mixing 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 Four Wave Mixing 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.Review of Early Work 10.4.2.Gain Spectrum and Its Bandwidth 10.4.3.Single Pump Configuration 10.4.4.Dual Pump Configuration 10.4.5.Effects of Pump Depletion 10.5.Polarization Effects 10.5.1.Vector Theory of Four Wave Mixing 10.5.2.Polarization Dependence of Parametric Gain 10.5.3.Linearly and Circularly Polarized Pumps Note continued: 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.Evolution of Chirped Gaussian Pulses 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 ch. 4 Self Phase Modulation 4.1.SPM Induced Spectral Changes 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.Optical Wave Breaking 4.2.4.Experimental Results Note continued: 4.2.5.Effect of Third Order Dispersion 4.2.6.SPM Effects in Fiber Amplifiers 4.3.Semianalytic Techniques 4.3.1.Moment Method 4.3.2.Variational Method 4.3.3.Specific Analytic Solutions 4.4.Higher Order Nonlinear Effects 4.4.1.Self Steepening 4.4.2.Effect of GVD on Optical Shocks 4.4.3.Intrapulse Raman Scattering Problems References ch. 5 Optical Solitons 5.1.Modulation Instability 5.1.1.Linear Stability Analysis 5.1.2.Gain Spectrum 5.1.3.Experimental Results 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.Second and 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.Bistable Solitons 5.3.3.Dispersion Managed Solitons 5.3.4.Optical Similaritons 5.4.Perturbation of Solitons Note continued: 8.3.5.Experimental Results 8.3.6.Synchronously Pumped Raman Lasers 8.3.7.Short Pulse Raman Amplification 8.4.Soliton Effects 8.4.1.Raman Solitons 8.4.2.Raman Soliton Lasers 8.4.3.Soliton Effect Pulse Compression 8.5.Polarization Effects 8.5.1.Vector Theory of Raman Amplification 8.5.2.PMD Effects on Raman Amplification Problems References ch. 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.Brillouin Threshold 9.2.2.Polarization Effects 9.2.3.Techniques for Controlling the SBS Threshold 9.2.4.Experimental Results 9.3.Brillouin Fiber Amplifiers 9.3.1.Gain Saturation 9.3.2.Amplifier Design and Applications 9.4.SBS Dynamics 9.4.1.Coupled Amplitude Equations 9.4.2.SBS with Q Switched Pulses 9.4.3.SBS Induced Index Changes 9.4.4.Relaxation Oscillations 9.4.5.Modulation Instability and Chaos Since the 4th edition appeared a fast evolution of the field has occurred. The fifth edition of this classic work provides an up to date account of the nonlinear phenomena occurring inside optical fibers the basis of all our telecommunications infastructure as well as being used in the medical field. Reflecting the big developments in research this new edition includes major new content: slow light effects Which offers a reduction in noise and power consumption and more ordered network traffic stimulated Brillouin scattering vectorial treatment of highly nonlinear fibers and a brand new chapter on supercontinuum generation in optical fibers. Continues to be industry bestseller providing unique source of comprehensive coverage on the subject of nonlinear fiber optics Updated coverage of intrapulse Raman scattering four wave mixing and Harmonic GenerationIncludes a new chapter excusively devoted to supercontinuum generation in optical fibers Note continued: 10.5.4.Effect of Residual Fiber Birefringence 10.6.Applications of Four Wave Mixing 10.6.1.Parametric Oscillators 10.6.2.Ultrafast Signal Processing 10.6.3.Quantum Correlation and Noise Squeezing 10.6.4.Phase Sensitive Amplification Problems References ch. 11 Highly Nonlinear Fibers 11.1.Nonlinear Parameter 11.1.1.Units and Values of n2 11.1.2.SPM Based Techniques 11.1.3.XPM Based Technique 11.1.4.FWM Based Technique 11.1.5.Variations in n2 Values 11.2.Fibers with Silica Cladding 11.3.Tapered Fibers with Air Cladding 11.4.Microstructured Fibers 11.4.1.Design and Fabrication 11.4.2.Modal and Dispersive Properties 11.4.3.Hollow Core Photonic Crystal Fibers 11.4.4.Bragg Fibers 11.5.Non Silica Fibers 11.5.1.Lead Silicate Fibers 11.5.2.Chalcogenide Fibers 11.5.3.Bismuth Oxide Fibers 11.6.Pulse Propagation in Narrow Core Fibers 11.6.1.Vectorial Theory Note continued: 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.Vector Form of the NLS Equation 6.6.3.Effects of PMD on Solitons Problems References ch. 7 Cross Phase Modulation 7.1.XPM Induced Nonlinear Coupling 7.1.1.Nonlinear Refractive Index 7.1.2.Coupled NLS Equations 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.Periodic Solutions 7.3.4.Multiple Coupled NLS Equations 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 Note continued: 11.6.2.Frequency Dependent Mode Profiles Problems References ch. 12 Novel Nonlinear Phenomena 12.1.Soliton Fission and Dispersive Waves 12.1.1.Fission of Second and Higher Order Solitons 12.1.2.Generation of Dispersive Waves 12.2.Intrapulse Raman Scattering 12.2.1.Enhanced RIFS Through Soliton Fission 12.2.2.Cross correlation Technique 12.2.3.Wavelength Tuning through RIFS 12.2.4.Effects of Birefringence 12.2.5.Suppression of Raman Induced Frequency Shifts 12.2.6.Soliton Dynamics Near a Zero Dispersion Wavelength 12.2.7.Multipeak Raman Solitons 12.3.Four Wave Mixing 12.3.1.Role of Fourth Order Dispersion 12.3.2.Role of Fiber Birefringence 12.3.3.Parametric Amplifiers and Wavelength Converters 12.3.4.Tunable Fiber Optic Parametric Oscillators 12.4.Second Harmonic Generation 12.4.1.Physical Mechanisms 12.4.2.Thermal Poling and Quasi Phase Matching 12.4.3.SHG Theory Note continued: 7.5.2.XPM Induced Optical Switching 7.5.3.XPM Induced Nonreciprocity 7.6.Polarization Effects 7.6.1.Vector Theory of XPM 7.6.2.Polarization Evolution 7.6.3.Polarization Dependent Spectral Broadening 7.6.4.Pulse Trapping and Compression 7.6.5.XPM Induced Wave Breaking 7.7.XPM Effects in Birefringent Fibers 7.7.1.Fibers with Low Birefringence 7.7.2.Fibers with High Birefringence Problems References ch. 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 8.1.4.Effect of Four Wave Mixing 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.Raman Induced Index Changes Note continued: 13.6.1.Spectral Domain Degree of Coherence 13.6.2.Techniques for Improving Coherence 13.6.3.Spectral Incoherent Solitons 13.7.Optical Rogue Waves 13.7.1.L Shaped Statistics of Pulse to Pulse Fluctuations 13.7.2.Techniques for Controlling Rogue Wave Statistics 13.7.3.Modulation Instability Revisited Problems References Note continued: 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.Moment Equations for Pulse Parameters 5.5.2.Third Order Dispersion 5.5.3.Self Steepening 5.5.4.Intrapulse Raman Scattering 5.5.5.Propagation of Femtosecond Pulses Problems References ch. 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.Poincare 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 Note continued: 12.5.Third Harmonic Generation 12.5.1.THG in Highly Nonlinear Fibers 12.5.2.Effects of Group Velocity Mismatch 12.5.3.Effects of Fiber Birefringence Problems References ch. 13 Supercontinuum Generation 13.1.Pumping with Picosecond Pulses 13.1.1.Nonlinear Mechanisms 13.1.2.Experimental Progress After 2000 13.2.Pumping with Femtosecond Pulses 13.2.1.Microstructured Silica Fibers 13.2.2.Microstructured Nonsilica Fibers 13.3.Temporal and Spectral Evolutions 13.3.1.Numerical Modeling of Supercontinuum 13.3.2.Role of Cross Phase Modulation 13.3.3.XPM Induced Trapping 13.3.4.Role of Four Wave Mixing 13.4.CW or Quasi CW Pumping 13.4.1.Nonlinear Mechanisms 13.4.2.Experimental Progress 13.5.Polarization Effects 13.5.1.Birefringent Microstructured Fibers 13.5.2.Nearly Isotropic Fibers 13.5.3.Nonlinear Polarization Rotation in Isotropic Fibers 13.6.Coherence Properties