1st Edition

Electromagnetic Theory and Applications for Photonic Crystals

Edited By Kiyotoshi Yasumoto Copyright 2006
    464 Pages 255 B/W Illustrations
    by CRC Press

    Photonic technology promises much faster computing, massive parallel processing, and an evolutionary step in the digital age. The search continues for devices that will enable this paradigm, and these devices will be based on photonic crystals. Modeling is a key process in developing crystals with the desired characteristics and performance, and Electromagnetic Theory and Applications for Photonic Crystals provides the electromagnetic-theoretical models that can be effectively applied to modeling photonic crystals and related optical devices.

    The book supplies eight self-contained chapters that detail various analytical, numerical, and computational approaches to the modeling of scattering and guiding problems. For each model, the chapter begins with a brief introduction, detailed formulations of periodic structures and photonic crystals, and practical applications to photonic crystal devices. Expert contributors discuss the scattering matrix method, multipole theory of scattering and propagation, model of layered periodic arrays for photonic crystals, the multiple multipole program, the mode-matching method for periodic metallic structures, the method of lines, the finite-difference frequency-domain technique, and the finite-difference time-domain technique.

    Based on original research and application efforts, Electromagnetic Theory and Applications for Photonic Crystals supplies a broad array of practical tools for analyzing and designing devices that will form the basis for a new age in computing.

    SCATTERING MATRIX METHOD APPLIED TO PHOTONIC CRYSTALS; Daniel Maystre, Stefan Enoch, and Gérard Tayeb
    Introduction
    Scattering Matrix Method
    Combination of Scattering Matrix and Fictitious Sources Methods
    Dispersion Relations of Bloch Modes
    Theoretical and Numerical Studies of Photonic Crystal Properties
    Conclusion
    References
    FROM MULTIPOLE METHODS TO PHOTONIC CRYSTAL DEVICE MODELING; Lindsay C. Botten, Ross C. McPhedran, C. Martijn de Sterke, Nicolae A. Nicorovici, Ara A. Asatryan, Geoffrey H. Smith, Timothy N. Langtry, Thomas P. White, David P. Fussell, and Boris T. Kuhlmey
    Introduction
    Multipole Theory for Finite and Infinite Structures
    Multipole Modeling of Photonic Crystal Fibers
    Radiation Dynamics and the Local Density of States
    Bloch Mode Analysis of Composite PC Devices
    Modeling of Photonic Crystal Devices
    Discussion and Conclusions
    Acknowledgement
    References
    MODELING OF PHOTONIC CRYSTALS BY MULTILAYERED PERIODIC ARRAYS OF CIRCULAR CYLINDERS; Kiyotoshi Yasumoto and Hongting Jia
    Introduction
    Scattering by a Single Cylinder
    Scattering by a Periodic Array of Cylindrical Objects
    Two-Dimensional Scattering from Layered Periodic Arrays
    Three-Dimensional Scattering from Layered Crossed-Arrays
    Modal Analysis of Two-Dimensional Photonic Crystal Waveguides
    Numerical Examples
    Conclusions
    References
    SIMULATION AND OPTIMIZATION OF PHOTONIC CRYSTALS USING THE MULTIPLE MULTIPOLE PROGRAM; Christian Hafner, Jasmin Smajic, and Daniel Erni
    Introduction and Overview
    Introduction to Photonic Crystal Simulation
    Basics of the Multiple Multipole Program
    Handling Periodic Symmetries While Using Periodic Boundary Conditions
    Advanced MMP and MAS Eigenvalue Solvers
    Computation of Waveguide Modes in Photonic Crystals
    Computation of Waveguide Discontinuities
    Sensitivity Analysis of Photonic Crystal Devices
    Optimization Based on the Sensitivity Analysis
    Achromatic 90° Bend
    Filtering T-Junction
    Conclusions and Outlook
    Acknowledgement
    References
    MODE-MATCHING TECHNIQUE APPLIED TO METALLIC PHOTONIC CRYSTALS; Hongting Jia and Kiyotoshi Yasumoto
    Introduction
    Analysis of a Metallic Array Composed of Rectangular Cylinders
    Analysis of Photonic Crystals Consisting of Metallic Cylinders with Arbitrary Cross Section
    Analysis of Metallic Photonic Crystals for a General Incidence
    Scattering Analysis of Crossed Photonic Crystals Consisting of Arbitrarily Shaped Cylinders
    Diffraction from a Conductive Slab Cut Periodically by Rectangular Holes
    Scattering Analysis of a Conductive Slab Cut Periodically by Rectangular Holes in an Arbitrary Direction
    Conclusion
    Acknowledgement
    References
    THE METHOD OF LINES FOR THE ANALYSIS OF PHOTONIC BANDGAP STRUCTURES; Reinhold Pregla and Stefan F. Helfert
    Introduction
    Basic Theory
    Impedance/Admittance Transformation
    Determination of Floquet Modes
    Determining the Band Structures of Photonic Crystals
    Junctions in Photonic Crystal Waveguides
    Numerical Results
    Conclusion
    Acknowledgement
    References
    APPLICATIONS OF THE FINITE-DIFFERENCE FREQUENCY-DOMAIN MODE SOLUTION METHOD TO PHOTONIC CRYSTAL STRUCTURES; Chin-Ping Yu and Hung-Chun Chang
    Introduction
    The FDFD Model
    Modal Analysis of Photonic Crystal Fibers
    The FDFD Method for Analysis of Photonic Band Structures
    Calculation of 2D PC Band Diagrams
    Modal Analysis of Planar PC Waveguides
    Conclusion
    Acknowledgements
    References
    FINITE-DIFFERENCE TIME-DOMAIN METHOD APPLIED TO PHOTONIC CRYSTALS; Hiroyoshi Ikuno and Yoshihiro Naka
    Introduction
    Method of Solution
    Photonic Crystal Straight Waveguide
    Fundamental Optical Circuit Devices Using Photonic Crystals
    Wavelength Multi/Demultiplexer
    Conclusion
    References
    INDEX

    Biography

    Kiyotoshi Yasumoto