Applications of Nonlinear Fiber Optics

1 Fiber Gratings
1.1 Basic Concepts
1.1.1 Bragg Diffraction
1.1.2 Photosensitivity
1.2 Fabrication Techniques
1.2.1 Single-Beam Internal Technique
1.2.2 Dual-Beam Holographic Technique
1.2.3 Phase-Mask Technique
1.2.4 Point-by-Point Fabrication Technique
1.2.5 Technique Based on Ultrashort Optical Pulses
1.3 Grating Characteristics
1.3.1 Coupled-Mode Equations
1.3.2 CW Solution in the Linear Case
1.3.3 Photonic Bandgap
1.3.4 Grating as an Optical Filter
1.3.5 Experimental Verification
1.4 CW Nonlinear Effects
1.4.1 Nonlinear Dispersion Curves
1.4.2 Optical Bistability
1.5 Modulation Instability
1.5.1 Linear Stability Analysis
1.5.2 Effective NLS Equation
1.5.3 Experimental Results
1.6 Nonlinear Pulse Propagation
1.6.1 Bragg Solitons
1.6.2 Relation to NLS Solitons
1.6.3 Experiments on Bragg Solitons
1.6.4 Nonlinear Switching
1.6.5 Effects of Birefringence
1.7 Related Periodic Structures
1.7.1 Long-Period Gratings
1.7.2 Nonuniform Bragg Gratings
1.7.3 Transient and Dynmaic Gratings
Problems
References

2 Directional Couplers
2.1 Coupler Characteristics
2.1.1 Coupled-Mode Equations
2.1.2 Low-Power CW Beams
2.1.3 Linear Pulse Switching
2.2 Nonlinear Effects
2.2.1 Quasi-CW Switching
2.2.2 Experimental Results
2.2.3 Nonlinear Supermodes
2.2.4 Modulation Instability
2.3 Ultrashort Pulse Propagation
2.3.1 Nonlinear Switching of Optical Pulses
2.3.2 Variational Approach
2.3.3 Coupler-Paired Solitons
2.3.4 Higher-Order Effects
2.4 Other Types of Couplers
2.4.1 Asymmetric Couplers
2.4.2 Active Couplers
2.4.3 Grating-Assisted Couplers
2.4.4 Birefringent Couplers
2.5 Multicore Fiber Couplers
2.5.1 Dual-Core Photonic Crystal Fibers
2.5.2 Multicore Fibers
Problems
References

3 Fiber Interferometers
3.1 Fabry–Perot and Ring Resonators
3.1.1 Transmission Resonances
3.1.2 Optical Bistability
3.1.3 Nonlinear Dynamics and Chaos
3.1.4 Modulation Instability
3.1.5 Cavity Solitons and their applications
3.2 Sagnac Interferometers
3.2.1 Nonlinear Transmission
3.2.2 Nonlinear Switching
3.2.3 Applications
3.3 Mach–Zehnder Interferometers
3.3.1 Nonlinear Characteristics
3.3.2 Applications
3.4 Michelson Interferometers
Problems
References

4 Fiber Amplifiers
4.1 Basic Concepts
4.1.1 Pumping and Gain Coefficient
4.1.2 Amplifier Gain and Bandwidth
4.1.3 Amplifier Noise
4.2 Erbium-Doped Fiber Amplifiers
4.2.1 Gain Spectrum
4.2.2 Amplifier Gain
4.2.3 Amplifier Noise
4.3 Dispersive and Nonlinear Effects
4.3.1 Maxwell–Bloch Equations
4.3.2 Ginzburg–Landau Equation
4.4 Modulation Instability
4.4.1 Distributed Amplification
4.4.2 Periodic Lumped Amplification
4.4.3 Noise Amplification
4.5 Amplifier Solitons
4.5.1 Properties of Autosolitons
4.5.2 Maxwell–Bloch Solitons
4.6 Pulse Amplification
4.6.1 Anomalous-Dispersion Regime
4.6.2 Normal-Dispersion Regime
4.6.3 Higher-Order Effects
4.7 Fiber-Optic Raman Amplifiers
4.7.1 Pulse Amplification through Raman Gain
4.7.2 Self-Similar Evolution and Similariton Formation
Problems
Reference

5 Fiber Lasers
5.1 Basic Concepts
5.1.1 Pumping and Optical Gain
5.1.2 Cavity Design
5.1.3 Laser Threshold and Output Power
5.2 CW Fiber Lasers
5.2.1 Nd-Doped Fiber Lasers
5.2.2 Yb-Doped Fiber Lasers
5.2.3 Erbium-Doped Fiber Lasers
5.2.4 DFB Fiber Lasers
5.2.5 Self-Pulsing and Chaos
5.3 Short-Pulse Fiber Lasers
5.3.1 Q-Switched Fiber Lasers
5.3.2 Physics of Mode Locking
5.3.3 Active Mode Locking
5.3.4 Harmonic Mode Locking
5.4 Passive Mode Locking
5.4.1 Saturable Absorbers
5.4.2 Nonlinear Fiber-Loop Mirrors
5.4.3 Nonlinear Polarization Rotation
5.4.4 Hybrid Mode Locking
5.4.5 Other Mode-Locking Techniques
5.5 Role of Fiber Nonlinearity and Dispersion
5.5.1 Saturable-Absorber Mode Locking
5.5.2 Additive-Pulse Mode Locking
5.5.3 Spectral Sidebands and Pulse Width
5.5.4 Phase Locking and Soliton Collision
5.5.5 Polarization Effects
Problems
References

6 Pulse Compression
6.1 Physical Mechanism
6.2 Grating-Fiber Compressors
6.2.1 Grating Pair
6.2.2 Optimum Compressor Design
6.2.3 Practical Limitations
6.2.4 Experimental Results
6.3 Soliton-Effect Compressors
6.3.1 Compressor Optimization
6.3.2 Experimental Results
6.3.3 Higher-Order Nonlinear Effects
6.4 Fiber Bragg Gratings
6.4.1 Gratings as a Compact Dispersive Element
6.4.2 Grating-Induced Nonlinear Chirp
6.4.3 Bragg-Soliton Compression
6.5 Chirped-Pulse Amplification
6.5.1 Chirped Fiber Gratings
6.5.2 Photonic Crystal Fibers
6.6 Dispersion-Managed Fibers
6.6.1 Dispersion-Decreasing Fibers
6.6.2 Comb-like Dispersion Profiles
6.7 Other Compression Techniques
6.7.1 Cross-Phase Modulation
6.7.2 Gain Switching in Semiconductor Lasers
6.7.3 Optical Amplifiers
6.7.4 Fiber-Loop Mirrors and Other Devices
Problems
References

7 Fiber-Optic Communications
7.1 System Basics
7.1.1 Loss Management
7.1.2 Dispersion Management
7.2 Impact of Fiber Nonlinearities
7.2.1 Stimulated Brillouin Scattering
7.2.2 Stimulated Raman Scattering
7.2.3 Self-Phase Modulation
7.2.4 Cross-Phase Modulation
7.2.5 Four-Wave Mixing
7.3 Solitons in Optical Fibers
7.3.1 Properties of Optical Solitons
7.3.2 Loss-Managed Solitons
7.3.3 Dispersion-Managed Solitons
7.3.4 Timing Jitter
7.4 Pseudo-Linear Lightwave Systems
7.4.1 Intrachannel Nonlinear Effects
7.4.2 Intrachannel XPM
7.4.3 Intrachannel FWM
7.5 Coherent Detection
7.5.1 Symbols, Baud, and Modulation Formats
7.5.2 Heterodyne Detection
7.5.3 Impact of Nonlinear Effects
7.6 Space-Division Multiplexing
7.6.1 Multicore Fibers
7.6.2 Multimode Fibers
Problems
References

8 Optical Signal Processing
8.1 Wavelength Conversion
8.1.1 XPM-Based Wavelength Converters
8.1.2 FWM-Based Wavelength Converters
8.2 Ultrafast Optical Switching
8.2.1 XPM-Based Sagnac-Loop Switches
8.2.2 Polarization-Discriminating Switches
8.2.3 FWM-Based Ultrafast Switches
8.3 Applications of Time-Domain Switching
8.3.1 Channel Demultiplexing
8.3.2 Data-Format Conversion
8.3.3 All-Optical Sampling
8.4 Optical Regenerators
8.4.1 SPM- and XPM-Based Regenerators
8.4.2 FWM-Based Regenerators
8.4.3 Phase-Preserving Regenerators
8.4.4 Multichannel Optical Regenerators
8.4.5 Optical 3R Regenerators
Problems
References

9 Highly Nonlinear Fibers
9.1 Microstructured Fibers
9.1.1 Design and Fabrication
9.1.2 Nonlinear and Dispersive Properties
9.2 Wavelength Shifting and Tuning
9.2.1 Raman-Induced Frequency Shifts
9.2.2 Four-Wave Mixing
9.3 Supercontinuum Generation
9.3.1 Multichannel Telecommunication Sources
9.3.2 Nonlinear Microscopy and Spectroscopy
9.3.3 Optical Coherence Tomography
9.3.4 Optical Frequency Metrology
9.4 Kerr Frequency Combs
9.4.1 Fiber-based Ring Cavities
9.4.2 Properties of Cavity Solitons
9.5 Photonic Bandgap Fibers
9.5.1 Properties of Hollow-Core PCFs
9.5.2 Applications of Air-Core PCFs
9.5.3 Fluid-Filled Hollow-core PCFs
Problems
References

10 Quantum Applications
10.1 Quantum Theory of Pulse Propagation
10.1.1 Quantum Nonlinear Schr¨odinger Equation
10.1.2 Quantum Theory of Self-Phase Modulation
10.1.3 Generalized NLS Equation
10.1.4 Quantum Solitons
10.2 Squeezing of Quantum Noise
10.2.1 Physics behind Quadrature Squeezing
10.2.2 FWM-Induced Quadrature Squeezing
10.2.3 SPM-Induced Quadrature Squeezing
10.2.4 SPM-Induced Amplitude Squeezing
10.2.5 Polarization Squeezing
10.3 Quantum Nondemolition Schemes
10.3.1 QND Measurements through Soliton Collisions
10.3.2 QND Measurements through Spectral Filtering
10.4 Quantum Sources
10.4.1 Single-Photon Sources
10.4.2 Photon-Pair Sources
10.4.3 Impact of spontaneous Raman scattering
10.4.4 Heralded Single-Photon Sources
10.5 Quantum Entanglement
10.5.1 Polarization Entanglement
10.5.2 Time-Bin Entanglement
10.5.3 Continuous-Variable Entanglement
10.6 Applications of Quantum States
10.6.1 Quantum Cryptography
10.6.2 Quantum Networks
Problems
References