Nonlinear Fiber Optics

Contents
Author biography
Preface
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
2 Pulse propagation in fibers
	2.1 Maxwell's equations
	2.2 Fiber modes
		2.2.1 Eigenvalue equation
		2.2.2 Characteristics of the fundamental mode
	2.3 Pulse-propagation equation
		2.3.1 Nonlinear wave equation
		2.3.2 Higher-order nonlinear effects
		2.3.3 Raman response function and its impact
	2.4 Numerical methods
		2.4.1 Split-step Fourier method
		2.4.2 Finite-difference methods
	Problems
	References
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 Chirped Gaussian pulses
		3.3.2 Broadening factor
		3.3.3 Ultrashort-pulse measurements
	3.4 Dispersion management
		3.4.1 Dispersion compensation
		3.4.2 Compensation of third-order dispersion
		3.4.3 Dispersion-varying fibers
	Problems
	References
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
		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
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 of loss and third-order dispersion
		5.1.6 Spatial modulation of fiber parameters
	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
		5.4.1 Perturbation methods
		5.4.2 Fiber loss
		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
	5.6 Propagation of femtosecond pulses
	Problems
	References
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 Poincaré-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 Higher-order effects
		6.6.1 Extended coupled-mode equations
		6.6.2 Impact of TOD and Raman nonlinearity
		6.6.3 Interaction of two vector solitons
	6.7 Random birefringence
		6.7.1 Polarization-mode dispersion
		6.7.2 Vector form of the NLS equation
		6.7.3 Effects of PMD on solitons
	Problems
	References
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
		7.5.2 XPM-induced optical switching
		7.5.3 XPM-induced wavelength conversion
	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
	7.8 Two counterpropagating waves
	Problems
	References
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
		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
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
	9.5 Brillouin fiber lasers
		9.5.1 CW operation
		9.5.2 Pulsed operation
	Problems
	References
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 Nearly phase-matched four-wave mixing
		10.3.3 Phase matching near the zero-dispersion wavelength
		10.3.4 Phase matching through self-phase modulation
		10.3.5 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
		10.5.4 Effect of residual fiber birefringence
	10.6 Applications of four-wave mixing
		10.6.1 Parametric amplifiers and wavelength converters
		10.6.2 Tunable fiber-optic parametric oscillators
		10.6.3 Ultrafast signal processing
		10.6.4 Quantum correlation and noise squeezing
		10.6.5 Phase-sensitive amplification
	Problems
	References
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 Theory of narrow-core fibers
	Problems
	References
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 Frequency combs and cavity solitons
		12.3.1 CW-pumped ring cavities
		12.3.2 Nonlinear dynamics of ring cavities
		12.3.3 Frequency combs without a cavity
	12.4 Second-harmonic generation
		12.4.1 Physical mechanisms
		12.4.2 Thermal poling and quasi-phase matching
		12.4.3 SHG theory
	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
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
	13.3 Temporal and spectral evolution of pulses
		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 results
	13.5 Polarization effects
	13.6 Coherence properties
		13.6.1 Effect of pump coherence
		13.6.2 Spectral incoherent solitons
		13.6.3 Techniques for improving spectral coherence
	13.7 Ultraviolet and mid-infrared supercontinua
		13.7.1 Extension into ultraviolet region
		13.7.2 Extension into mid-infrared region
	13.8 Optical rogue waves
		13.8.1 L-shaped statistics of pulse-to-pulse fluctuations
		13.8.2 Techniques for controlling rogue-wave statistics
		13.8.3 Modulation instability revisited
	Problems
	References
14 Multimode fibers
	14.1 Modes of optical fibers
		14.1.1 Step-index fibers
		14.1.2 Graded-index fibers
		14.1.3 Multicore fibers
		14.1.4 Excitation of fiber modes
	14.2 Nonlinear pulse propagation
		14.2.1 Multimode propagation equations
		14.2.2 Few-mode fibers
		14.2.3 Random linear mode coupling
		14.2.4 Graded-index fibers
	14.3 Modulation instability and solitons
		14.3.1 Modulation instability
		14.3.2 Multimode solitons
		14.3.3 Solitons in specific fiber modes
	14.4 Intermodal nonlinear phenomena
		14.4.1 Intermodal FWM
		14.4.2 Intermodal SRS
		14.4.3 Intermodal SBS
	14.5 Spatio-temporal dynamics
		14.5.1 Spatial beam cleanup
		14.5.2 Supercontinuum generation
	14.6 Multicore fibers
	Problems
	References
A System of units
B Nonlinear response of fibers
	References
C Derivation of the generalized NLS equation
D Numerical code for the NLS equation
E List of acronyms
Index