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Computational Photonics

Book Description

A comprehensive manual on the efficient modeling and analysis of photonic devices through building numerical codes, this book provides graduate students and researchers with the theoretical background and MATLAB programs necessary for them to start their own numerical experiments. Beginning by summarizing topics in optics and electromagnetism, the book discusses optical planar waveguides, linear optical fiber, the propagation of linear pulses, laser diodes, optical amplifiers, optical receivers, finite-difference time-domain method, beam propagation method and some wavelength division devices, solitons, solar cells and metamaterials. Assuming only a basic knowledge of physics and numerical methods, the book is ideal for engineers, physicists and practising scientists. It concentrates on the operating principles of optical devices, as well as the models and numerical methods used to describe them.

Table of Contents

  1. Cover
  2. Half Title
  3. Title Page
  4. Copyright
  5. Table of Contents
  6. Preface
  7. 1 Introduction
    1. 1.1 What is photonics?
    2. 1.2 What is computational photonics?
    3. 1.3 Optical fibre communication
    4. 1.4 Biological and medical photonics
    5. 1.5 Photonic sensors
    6. 1.6 Silicon photonics
    7. 1.7 Photonic quantum information science
    8. References
  8. 2 Basic facts about optics
    1. 2.1 Geometrical optics
    2. 2.2 Wave optics
    3. 2.3 Problems
    4. Appendix 2A: MATLAB listings
    5. References
  9. 3 Basic facts fromelectromagnetism
    1. 3.1 Maxwell’s equations
    2. 3.2 Boundary conditions
    3. 3.3 Wave equation
    4. 3.4 Time-harmonic fields
    5. 3.5 Polarized waves
    6. 3.6 Fresnel coefficients and phases
    7. 3.7 Polarization by reflection from dielectric surfaces
    8. 3.8 Antireflection coating
    9. 3.9 Bragg mirrors
    10. 3.10 Goos-Hänchen shift
    11. 3.11 Poynting theorem
    12. 3.12 Problems
    13. 3.13 Project
    14. Appendix 3A: MATLAB listings
    15. References
  10. 4 Slab waveguides
    1. 4.1 Ray optics of the slab waveguide
    2. 4.2 Fundamentals of EM theory of dielectric waveguides
    3. 4.3 Wave equation for a planar wide waveguide
    4. 4.4 Three-layer symmetrical guiding structure (TE modes)
    5. 4.5 Modes of the arbitrary three-layer asymmetric planar waveguide in 1D
    6. 4.6 Multilayer slab waveguides: 1D approach
    7. 4.7 Examples: 1D approach
    8. 4.8 Two-dimensional (2D) structures
    9. 4.9 Problems
    10. 4.10 Projects
    11. Appendix 4A: MATLAB listings
    12. References
  11. 5 Linear optical fibre and signal degradation
    1. 5.1 Geometrical-optics description
    2. 5.2 Fibre modes in cylindrical coordinates
    3. 5.3 Dispersion
    4. 5.4 Pulse dispersion during propagation
    5. 5.5 Problems
    6. 5.6 Projects
    7. Appendix 5A: Some properties of Bessel functions
    8. Appendix 5B: Characteristic determinant
    9. Appendix 5C: MATLAB listings
    10. References
  12. 6 Propagation of linear pulses
    1. 6.1 Basic pulses
    2. 6.2 Modulation of a semiconductor laser
    3. 6.3 Simple derivation of the pulse propagation equation in the presence of dispersion
    4. 6.4 Mathematical theory of linear pulses
    5. 6.5 Propagation of pulses
    6. 6.6 Problems
    7. Appendix 6A: MATLAB listings
    8. References
  13. 7 Optical sources
    1. 7.1 Overview of lasers
    2. 7.2 Semiconductor lasers
    3. 7.3 Rate equations
    4. 7.4 Analysis based on rate equations
    5. 7.5 Problems
    6. 7.6 Project
    7. Appendix 7A: MATLAB listings
    8. References
  14. 8 Optical amplifiers and EDFA
    1. 8.1 General properties
    2. 8.2 Erbium-doped fibre amplifiers (EDFA)
    3. 8.3 Gain characteristics of erbium-doped fibre amplifiers
    4. 8.4 Problems
    5. 8.5 Projects
    6. Appendix 8A: MATLAB listings
    7. References
  15. 9 Semiconductor optical amplifiers (SOA)
    1. 9.1 General discussion
    2. 9.2 SOA rate equations for pulse propagation
    3. 9.3 Design of SOA
    4. 9.4 Some applications of SOA
    5. 9.5 Problem
    6. 9.6 Project
    7. Appendix 9A: MATLAB listings
    8. References
  16. 10 Optical receivers
    1. 10.1 Main characteristics
    2. 10.2 Photodetectors
    3. 10.3 Receiver analysis
    4. 10.4 Modelling of a photoelectric receiver
    5. 10.5 Problems
    6. 10.6 Projects
    7. Appendix 10A: MATLAB listings
    8. References
  17. 11 Finite difference time domain (FDTD) formulation
    1. 11.1 General formulation
    2. 11.2 One-dimensional Yee implementation without dispersion
    3. 11.3 Boundary conditions in 1D
    4. 11.4 Two-dimensional Yee implementation without dispersion
    5. 11.5 Absorbing boundary conditions (ABC) in 2D
    6. 11.6 Dispersion
    7. 11.7 Problems
    8. 11.8 Projects
    9. Appendix 11A: MATLAB listings
    10. References
  18. 12 Beam propagationmethod (BPM)
    1. 12.1 Paraxial formulation
    2. 12.2 General theory
    3. 12.3 The 1 + 1 dimensional FD-BPM formulation
    4. 12.4 Concluding remarks
    5. 12.5 Problems
    6. 12.6 Project
    7. Appendix 12A: Details of derivation of the FD-BPM equation
    8. Appendix 12B: MATLAB listings
    9. References
  19. 13 Some wavelength division multiplexing (WDM) devices
    1. 13.1 Basics of WDM systems
    2. 13.2 Basic WDM technologies
    3. 13.3 Applications of BPM to photonic devices
    4. 13.4 Projects
    5. Appendix 13A: MATLAB listings
    6. References
  20. 14 Optical link
    1. 14.1 Optical communication system
    2. 14.2 Design of optical link
    3. 14.3 Measures of link performance
    4. 14.4 Optical fibre as a linear system
    5. 14.5 Model of optical link based on filter functions
    6. 14.6 Problems
    7. 14.7 Projects
    8. Appendix 14A: MATLAB listings
    9. References
  21. 15 Optical solitons
    1. 15.1 Nonlinear optical susceptibility
    2. 15.2 Main nonlinear effects
    3. 15.3 Derivation of the nonlinear Schrödinger equation
    4. 15.4 Split-step Fourier method
    5. 15.5 Numerical results
    6. 15.6 A few comments about soliton-based communications
    7. 15.7 Problems
    8. Appendix 15A: MATLAB listings
    9. References
  22. 16 Solar cells
    1. 16.1 Introduction
    2. 16.2 Principles of photovoltaics
    3. 16.3 Equivalent circuit of solar cells
    4. 16.4 Multijunctions
    5. Appendix 16A: MATLAB listings
    6. References
  23. 17 Metamaterials
    1. 17.1 Introduction
    2. 17.2 Veselago approach
    3. 17.3 How to create metamaterial?
    4. 17.4 Some applications of metamaterials
    5. 17.5 Metamaterials with an active element
    6. 17.6 Annotated bibliography
    7. Appendix 17A: MATLAB listings
    8. References
  24. Appendix A Basic MATLAB
    1. A.1 Working session with m-files
    2. A.2 Basic rules
    3. A.3 Some rules about good programming in MATLAB
    4. A.4 Basic graphics
    5. A.5 Basic input-output
    6. A.6 Numerical differentiation
    7. A.7 Review questions
    8. References
  25. Appendix B Summary of basic numericalmethods
    1. B.1 One-variable Newton’s method
    2. B.2 Muller’s method
    3. B.3 Numerical differentiation
    4. B.4 Runge-Kutta (RK) methods
    5. B.5 Solving differential equations
    6. B.6 Numerical integration
    7. B.7 Symbolic integration in MATLAB
    8. B.8 Fourier series
    9. B.9 Fourier transform
    10. B.10 FFT in MATLAB
    11. B.11 Problems
    12. References
  26. Index