Nonlinear Fiber Optics

✍ Scribed by Govind P. Agrawal

• Publisher: Academic Press is an Imprint of Elsevier
• Year: 2013
• Tongue: English
• Leaves: 631
• Edition: 5
• Category: Library

✦ Table of Contents

front_matter
copyright
dedications
author_biography
preface
1. Introduction
1.1 HISTORICAL PERSPECTIVE
1.2 FIBER CHARACTERISICS
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 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
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 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
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
4.4 HIGHER-ORDER NONLINEAR EFFECTS
4.3.3 Specific Analytic Solutions
4.4.1 Self-Steepening
4.4.2 Effect of GVD on Optical Shocks
4.4.3 Intrapulse Raman Scattering
REFERENCES
PROBLEMS
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
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
REFERENCES
PROBLEMS
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 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
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 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
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 Phase Matching in Multimode Fibers
10.3.3 Phase Matching in Single-Mode Fibers
10.3.3.1 Nearly Phase-Matched Four-Wave Mixing
10.3.3.2 Phase Matching Near the Zero-Dispersion Wavelength
10.3.3.3 Phase Matching Due to Self-Phase Modulation
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
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
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
11.6.2 Frequency-Dependent Mode Profiles
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 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
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
13.2.1 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
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
A. System of Units
B. Numerical Code for theNLS Equation
C. List of Acronyms
Index
A
B
C
D
E
F
G
H
I
J
K
L
M
N
P
Q
R
S
T
U
V
W
X
Z