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Fourier Modal Method and Its Applications in Computational Nanophotonics

Book Description

Most available books on computational electrodynamics are focused on FDTD, FEM, or other specific technique developed in microwave engineering. In contrast, Fourier Modal Method and Its Applications in Computational Nanophotonics is a complete guide to the principles and detailed mathematics of the up-to-date Fourier modal method of optical analysis. It takes readers through the implementation of MATLAB® codes for practical modeling of well-known and promising nanophotonic structures. The authors also address the limitations of the Fourier modal method.

Features

  • Provides a comprehensive guide to the principles, methods, and mathematics of the Fourier modal method
  • Explores the emerging field of computational nanophotonics
  • Presents clear, step-by-step, practical explanations on how to use the Fourier modal method for photonics and nanophotonics applications
  • Includes the necessary MATLAB codes, enabling readers to construct their own code

Using this book, graduate students and researchers can learn about nanophotonics simulations through a comprehensive treatment of the mathematics underlying the Fourier modal method and examples of practical problems solved with MATLAB codes.

Table of Contents

  1. Cover Page
  2. Half Title
  3. Title Page
  4. Copyright
  5. Contents
  6. Preface
  7. 1 Introduction
    1. 1.1 Nanophotonics and Fourier Modal Methods
    2. 1.2 Elements of the Fourier Modal Method
  8. 2 Scattering Matrix Method for Multiblock Structures
    1. 2.1 Scattering Matrix Analysis of Finite Single-Block Structures
      1. 2.1.1 Eigenmode Analysis
      2. 2.1.2 S-Matrix and Coupling Coefficient Operator Calculation of a Single Block
      3. 2.1.3 Field Visualization
        1. 2.1.3.1 Left-to-Right Field Visualization
        2. 2.1.3.2 Right-to-Left Field Visualization
    2. 2.2 Scattering Matrix Analysis of Collinear Multiblock Structures
      1. 2.2.1 Two-Block Interconnection
      2. 2.2.2 N-Block Interconnection with Parallelism
      3. 2.2.3 Half-Infinite Block Interconnection
      4. 2.2.4 Field Visualization
        1. 2.2.4.1 Left-to-Right Field Visualization
        2. 2.2.4.2 Right-to-Left Field Visualization
        3. 2.2.4.3 Energy Conservation
    3. 2.3 MATLAB® Implementation
  9. 3 Fourier Modal Method
    1. 3.1 Fourier Modal Analysis of Single-Block Structures
      1. 3.1.1 Eigenmode Analysis
      2. 3.1.2 S-Matrix and Coupling Coefficient Operator Calculation of Single Block
      3. 3.1.3 Field Visualization
    2. 3.2 Fourier Modal Analysis of Collinear Multiblock Structures
      1. 3.2.1 Two-Block Interconnection
      2. 3.2.2 N-Block Interconnection with Parallelism
      3. 3.2.3 Half-Infinite Block Interconnection
      4. 3.2.4 Field Visualization
        1. 3.2.4.1 Case A: Half-Infinite Homogeneous Space–Multiblock Structure–Half-Infinite Homogeneous Space
        2. 3.2.4.2 Case B: Half-Infinite Homogeneous Space–Multiblock Structure–Half-Infinite Inhomogeneous Space
        3. 3.2.4.3 Case C: Half-Infinite Inhomogeneous Waveguide–Multiblock Structure–Half-Infinite Homogeneous Space
        4. 3.2.4.4 Case D: Half-Infinite Inhomogeneous Waveguide–Multiblock Structure–Half-Infinite Inhomogeneous Space
    3. 3.3 MATLAB® Implementation
    4. 3.4 Applications
      1. 3.4.1 Extraordinary Optical Transmission Phenomenon
  10. 4 A Perfect Matched Layer for Fourier Modal Method
    1. 4.1 An Absorbing Boundary Layer for Fourier Modal Method
      1. 4.1.1 MATLAB® Implementation
    2. 4.2 Nonlinear Coordinate Transformed Perfect Matched Layer for Fourier Modal Method
      1. 4.2.1 Mathematical Model
        1. 4.2.1.1 Split-Field PML
        2. 4.2.1.2 Stretched Nonlinear Coordinate Transformation
      2. 4.2.2 MATLAB® Implementation
    3. 4.3 Applications
      1. 4.3.1 Plasmonic Beaming
      2. 4.3.2 Plasmonic Hot Spot and Vortex
  11. 5 Local Fourier Modal Method
    1. 5.1 Local Fourier Modal Analysis of Single-Super-Block Structures
    2. 5.2 Local Fourier Modal Analysis of Collinear Multi-Super-Block Structures
      1. 5.2.1 Field Visualization
        1. 5.2.1.1 Case A: Half-Infinite Homogeneous Space–Multiblock Structure–Half-Infinite Homogeneous Space
        2. 5.2.1.2 Case B: Semi-Infinite Homogeneous Space–Multiblock Structure–Semi-Infinite Inhomogeneous Space
        3. 5.2.1.3 Case C: Semi-Infinite Inhomogeneous Waveguide–Multiblock Structure–Semi-Infinite Homogeneous Space
        4. 5.2.1.4 Case D: Semi-Infinite Inhomogeneous Waveguide–Multiblock Structure–Semi-Infinite Inhomogeneous Space
    3. 5.3 MATLAB® Implementation
    4. 5.4 Applications
      1. 5.4.1 Field Localization in Photonic Crystals
      2. 5.4.2 Tapered Photonic Crystal Resonator
  12. 6 Perspectives on the Fourier Modal Method
    1. 6.1 Nanophotonic Network Modeling
    2. 6.2 Local Fourier Modal Analysis of Two-Port Block Structures
    3. 6.3 Local Fourier Modal Analysis of Four-Port Cross-Block Structures
    4. 6.4 Generalized Scattering Matrix Method
      1. 6.4.1 Interconnection of Four-Port Block and Two-Port Blocks
    5. 6.5 Concluding Remarks
  13. References
  14. Index