Fundamentals of Nonlinear Optics, 2nd Edition

Fundamentals of Nonlinear Optics, 2nd Edition

by Peter E. Powers, Joseph W. Haus
Released April 2017
Publisher(s): CRC Press
ISBN: 9781498736862

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Book description

This fully revised edition of the groundbreaking text by the late Peter Powers offers enhanced coverage while remaining the most ‘essentials only,’ practical introductory treatment available. It includes a brand new chapter on quantum nonlinear optics, other added sections and improvements, as well as many new problems and examples. This up-to-date treatment reflects the latest device applications and importance of nonlinear optics in development of materials, optical switching and processing, and nonlinear guided wave optics.

Table of contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright Page
  5. Dedication
  6. Contents
  7. Preface to the First Edition
  8. Preface to the Second Edition
  9. Authors
  10. 1. Introduction
    1. 1.1 Historical Background
    2. 1.2 Unifying Themes
    3. 1.3 Overview of Nonlinear Effects Covered in This Book
    4. 1.4 Labeling Conventions and Terminology
    5. 1.5 Units
    6. Problems
    7. References
    8. Further Reading
  11. 2. Linear Optics
    1. 2.1 Introduction
      1. 2.1.1 Linearity
      2. 2.1.2 Maxwell’s Equations
      3. 2.1.3 Poynting’s Theorem
      4. 2.1.4 Intensity
      5. 2.1.5 Linear Polarization
      6. 2.1.6 Complex Representation of Polarization
      7. 2.1.7 Energy Exchange between a Field and Polarization
    2. 2.2 Tensor Properties of Materials
      1. 2.2.1 Tensors
    3. 2.3 Wave Equation
      1. 2.3.1 Constitutive Relationships for Complex Amplitudes
      2. 2.3.2 Wave Equation in Homogeneous Isotropic Materials
      3. 2.3.3 Dispersion
      4. 2.3.4 Wave Equation in Crystals
      5. 2.3.5 Fresnel’s Equation
      6. 2.3.6 o-Waves and e-Waves
      7. 2.3.7 Poynting Vector Walk-Off
    4. 2.4 Determining e-Waves and o-Waves in Crystals
      1. 2.4.1 Homogeneous Isotropic
      2. 2.4.2 Uniaxial Crystal
      3. 2.4.3 Biaxial Crystals
    5. 2.5 Index Ellipsoid
    6. 2.6 Applications
      1. 2.6.1 Slowly Varying Envelope Approximation and Gaussian Beams
      2. 2.6.2 Gaussian Beam Propagation Using the q-Parameter
      3. 2.6.3 M2 Propagation Factor
      4. 2.6.4 Example of Formatting a Beam for SHG
    7. Problems
    8. References
    9. Further Reading
  12. 3. Introduction to the Nonlinear Susceptibility
    1. 3.1 Introduction
      1. 3.1.1 Nonlinear Polarization
      2. 3.1.2 Parametric Processes
    2. 3.2 Classical Origin of the Nonlinearity
      1. 3.2.1 One-Dimensional Linear Harmonic Oscillator
      2. 3.2.2 One-Dimensional Anharmonic Oscillator
      3. 3.2.3 Third-Order Effects in Centrosymmetric Media
    3. 3.3 Details of the Nonlinear Susceptibility, χ(2)
      1. 3.3.1 Degeneracy and Subtleties of Squaring the Field
      2. 3.3.2 Tensor Properties of Susceptibility
      3. 3.3.3 Permuting the Electric Fields in the Nonlinear Polarization
      4. 3.3.4 Full Permutation Symmetry in Lossless Media
      5. 3.3.5 Kleinman’s Symmetry
      6. 3.3.6 Contracting the Indices in χ(2)ijk
      7. 3.3.7 Effective Nonlinearity and deff
      8. 3.3.8 Example Calculation of deff
    4. 3.4 Connection between Crystal Symmetry and the d-Matrix
      1. 3.4.1 Centrosymmetric Crystals
      2. 3.4.2 Example Calculation of d-Matrix for 3m Crystals
    5. 3.5 Electro-Optic Effect
      1. 3.5.1 EO Effects and the r-Matrix
      2. 3.5.2 Example Calculation of EO Effect in KH2DPO4
      3. 3.5.3 EO Wave Plates
      4. 3.5.4 EO Sampling: Terahertz Detection
      5. 3.5.5 Connection between d and r
    6. Problems
    7. References
    8. Further Reading
  13. 4. Three-Wave Processes in the Small-Signal Regime
    1. 4.1 Introduction to the Wave Equation for Three Fields
      1. 4.1.1 Wave Equation for a Three-Wave Process
      2. 4.1.2 Slowly Varying Envelope Approximation Extended
      3. 4.1.3 Introduction to Phase Matching
      4. 4.1.4 First Solution to the Coupled Amplitude Equations
      5. 4.1.5 k-Vector Picture
    2. 4.2 Birefringent Phase Matching
      1. 4.2.1 Birefringent Phase-Matching Types
      2. 4.2.2 Example: Phase-Matching Problem
      3. 4.2.3 Phase-Matching SHG
    3. 4.3 Tuning Curves and Phase-Matching Tolerances
      1. 4.3.1 Phase-Matching Bandwidth and Angular Acceptance
    4. 4.4 Taylor Series Expansion Techniques for Determining Bandwidth
      1. 4.4.1 Temperature Bandwidth
      2. 4.4.2 Phase-Matching Bandwidth and Acceptance Bandwidth
      3. 4.4.3 Angular Acceptance and Noncritical Phase Matching
    5. 4.5 Noncollinear Phase Matching
      1. 4.5.1 Off-Axis Propagation SVEA Equations
      2. 4.5.2 Noncollinear Application
    6. Problems
    7. Reference
    8. Further Reading
  14. 5. Quasi-Phase Matching
    1. 5.1 Introduction to Quasi-Phase Matching
    2. 5.2 Linear and Nonlinear Material Considerations
    3. 5.3 QPM with Periodic Structures
    4. 5.4 QPM Calculation: An Example
    5. 5.5 Fourier Transform Treatment of QPM
    6. 5.6 Tolerances
    7. 5.7 Fabricating Quasi-Phase-Matched Structures
    8. Problems
    9. Reference
    10. Further Reading
  15. 6. Three-Wave Mixing beyond the Small-Signal Limit
    1. 6.1 Introduction
    2. 6.2 DFG with a Single Strong Pump
      1. 6.2.1 Defining Equations for the Undepleted Pump Approximation
      2. 6.2.2 Solution for Difference-Frequency Output
      3. 6.2.3 Solution with Specific Boundary Conditions
    3. 6.3 DFG with Strong Pump and Loss
    4. 6.4 Solutions for All Three Coupled Amplitude Equations
      1. 6.4.1 Manley–Rowe Relations
      2. 6.4.2 Analytic Solution for Three Plane Waves
    5. 6.5 Spontaneous Parametric Scattering (Optical Parametric Generation)
    6. Problems
    7. References
    8. Further Reading
  16. 7. χ(2) Devices
    1. 7.1 Introduction
    2. 7.2 Optimizing Device Performance: Focusing
      1. 7.2.1 Overlap of Gaussian Beams with Nonlinear Polarization
      2. 7.2.2 Parametric Interactions with Focused Gaussian Beams
      3. 7.2.3 Optimizing Gaussian Beam Interactions
    3. 7.3 Resonator Devices
      1. 7.3.1 Resonant SHG
      2. 7.3.2 Optical Parametric Oscillator
      3. 7.3.3 OPO with Gaussian Beams
      4. 7.3.4 Doubly Resonant OPOs
      5. 7.3.5 Singly Resonant OPOs
      6. 7.3.6 Cavity Design
      7. 7.3.7 Pulsed OPOs
      8. 7.3.8 Backward OPOs
    4. Problems
    5. References
    6. Further Reading
  17. 8. χ(3) Processes
    1. 8.1 Introduction
    2. 8.2 Nonlinear Polarization for χ(3) Processes
      1. 8.2.1 Defining Relationships
      2. 8.2.2 Permutation Symmetries for χ(3)
      3. 8.2.3 Symmetry Considerations for Centrosymmetric Media
    3. 8.3 Wave Equation for χ(3) Interactions
      1. 8.3.1 Four Distinct Frequencies
      2. 8.3.2 Manley–Rowe Relations
    4. 8.4 Self-Induced Effects
      1. 8.4.1 Nonlinear Index of Refraction
      2. 8.4.2 Nonlinear Absorption
      3. 8.4.3 Cross-Phase Shifts
      4. 8.4.4 Self-Focusing
      5. 8.4.5 Optical Bistability
    5. 8.5 Parametric Amplifiers
      1. 8.5.1 Introduction
      2. 8.5.2 Two Undepleted Inputs
      3. 8.5.3 One Undepleted Input
      4. 8.5.4 Pump Depletion
    6. 8.6 Noncollinear Processes
    7. 8.7 Degenerate Four-Wave Mixing
      1. 8.7.1 Introduction
      2. 8.7.2 Pump Phase Shifts
      3. 8.7.3 Probe and Signal Fields
      4. 8.7.4 Optical-Phase Conjugation
    8. 8.8 z-SCAN
      1. 8.8.1 Introduction
      2. 8.8.2 Measuring the Nonlinear Index of Refraction
      3. 8.8.3 Nonlinear Absorption
    9. Problems
    10. Reference
    11. Further Reading
  18. 9. Raman and Brillouin Scattering
    1. 9.1 Introduction
    2. 9.2 Spontaneous Raman Scattering
      1. 9.2.1 Classical Model of Spontaneous Raman Scattering
      2. 9.2.2 Raman Scattering Cross Section
      3. 9.2.3 Raman Microscope
    3. 9.3 Stimulated Raman Scattering
      1. 9.3.1 Introduction
      2. 9.3.2 Classical Calculation for Inducing a Molecular Vibration
      3. 9.3.3 Nonlinear Polarization for a Stimulated Raman Process
      4. 9.3.4 Wave Equation for the Stokes Field
      5. 9.3.5 Amplification of the Stokes Field Off Resonance
      6. 9.3.6 Stokes Amplification with a Depleted Pump
    4. 9.4 Anti-Stokes Generation
      1. 9.4.1 Classical Derivation of the Anti-Stokes Nonlinear Polarization
      2. 9.4.2 Wave Equation for Stokes and Anti-Stokes in the Undepleted Pump Approximation
      3. 9.4.3 Stokes and Anti-Stokes Generation with Pump Depletion
    5. 9.5 Raman Amplifiers
    6. 9.6 Photoacoustic Effects: Raman-Nath Diffraction
    7. 9.7 Brillouin Scattering
      1. 9.7.1 Spontaneous Brillouin Scattering
      2. 9.7.2 Classical Model for the Stimulated Brillouin Scattering
      3. 9.7.3 Nonlinear Polarization for the Stimulated Brillouin Scattering
      4. 9.7.4 Coupled Intensity Equations and Solutions for the Stimulated Brillouin Scattering
      5. 9.7.5 Brillouin with Linear Absorption
      6. 9.7.6 Mitigating Brillouin Effects
    8. Problems
    9. References
  19. 10. Nonlinear Optics Including Diffraction and Dispersion
    1. 10.1 Introduction
    2. 10.2 Spatial Effects
      1. 10.2.1 Diffraction and the Poynting Vector Walk-Off
      2. 10.2.2 Split-Step Technique
      3. 10.2.3 Linear Propagation: Beam Propagation Method
      4. 10.2.4 Nonlinear Propagation for Three-Wave Mixing
    3. 10.3 Temporal Effects
      1. 10.3.1 Time-Dependent Field Definitions
      2. 10.3.2 Time-Dependent Linear Polarization
      3. 10.3.3 Time-Dependent Nonlinear Polarization
      4. 10.3.4 Wave Equation for Fields with a Time-Dependent Envelope
    4. 10.4 Dynamical Solutions to the Nonlinear Envelope Equation
      1. 10.4.1 Self-Phase Modulation
      2. 10.4.2 Numerical Solutions with Pulses
        1. 10.4.2.1 Dispersion Step
        2. 10.4.2.2 Nonlinear Step
      3. 10.4.3 Nonlinear Schrodinger Equation
      4. 10.4.4 Modulation Instability
      5. 10.4.5 Fundamental Soliton Solution
      6. 10.4.6 Spatial Solitons
      7. 10.4.7 Dark and Gray Solitons
    5. 10.5 Dynamical Stimulated Raman Scattering
      1. 10.5.1 Dynamical SRS Equations Solution
    6. Problems
    7. References
    8. Further Reading
  20. 11. Quantum Nonlinear Optics
    1. 11.1 Introduction
    2. 11.2 Quantizing Equations of Motion
      1. 11.2.1 Classical to Quantum Equations of Motion
      2. 11.2.2 Heisenberg Uncertainty Relations
    3. 11.3 Electromagnetic Field
      1. 11.3.1 Coherent State Representation
      2. 11.3.2 Electromagnetic Wave Function
      3. 11.3.3 Electromagnetic Signals
    4. 11.4 Quantum Amplifiers and Attenuators
      1. 11.4.1 Quantum Attenuator Model
      2. 11.4.2 Quantum Amplifier Model
      3. 11.4.3 Quantum Initiation: Optical Parametric Generator
      4. 11.4.4 Schrödinger’s Cat States
    5. 11.5 Quantum Detection
      1. 11.5.1 Direct Detection
      2. 11.5.2 Coherent Detection
        1. 11.5.2.1 Beam Splitter
        2. 11.5.2.2 Coherent Detection Signal to Noise
        3. 11.5.2.3 Balanced Homodyne Detection
    6. 11.6 Quantum Squeezed Light
      1. 11.6.1 Single-Mode Squeezed States
      2. 11.6.2 Squeezed Light Experiments
    7. 11.7 Multimode Quantum States
      1. 11.7.1 Entangled Quantum States
      2. 11.7.2 Entanglement via SPDC
        1. 11.7.2.1 Type I Phase Matching
        2. 11.7.2.2 Type II Phase Matching
      3. 11.7.3 Two-Mode Parametric Squeezing
      4. 11.7.4 Quantum Optical Phase Conjugation
      5. 11.7.5 HOM Interferometer
    8. Problems
    9. References
    10. Books
    11. Selected Articles
    12. Amplifiers and Attenuators
    13. Squeezed Light
    14. EPR and Tests of Quantum Mechanics
  21. Appendix A: Complex Notation
  22. Appendix B: Sellmeier Equations
  23. Appendix C: Programming Techniques
  24. Appendix D: Exact Solutions to the Coupled Amplitude Equations
  25. Appendix E: Optical Fibers—Slowly Varying Envelope Equations
  26. Index

Product information

  • Title: Fundamentals of Nonlinear Optics, 2nd Edition
  • Author(s): Peter E. Powers, Joseph W. Haus
  • Release date: April 2017
  • Publisher(s): CRC Press
  • ISBN: 9781498736862