Modeling and analysis of transient processes in open resonant structures : new methods and techniques /

Modeling and analysis of transient processes in open resonant structures : new methods and techniques /

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Bibliographic Details
Author / Creator:Sirenko, Y. K.
Imprint:New York ; London : Springer, c2007.
Description:xiv, 353 p. : ill. 23 cm.
Language:English
Series:Springer series in optical sciences. v. 122
Subject:
Electromagnetic waves -- Scattering -- Mathematical models.
Electromagnetic waves -- Scattering -- Mathematical models.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/6215143
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Other authors / contributors:Yashina, N. P.
Stròˆm, Staffan.
ISBN:0387308784 (hbk.)
9780387308784 (hbk.)
Notes:Includes bibliographical references and index.
Table of Contents:
  • Preface
  • 1. Numerical Analysis of Transient Processes: Fundamental Results of the Theory, Methods, and Problems
  • 1.1. Introduction
  • 1.2. Main Equations and Fundamental Results of the Theory
  • 1.2.1. Maxwell Equations
  • 1.2.2. Wave and Telegraph Equations
  • 1.2.3. The Borgnis Functions
  • 1.2.4. Domains of Analysis, Boundary, and Initial Conditions
  • 1.2.5. Formulation of Initial Boundary Value Problems: Generalized Functions and Generalized Solutions
  • 1.2.6. Fundamental Results of the Theory
  • 1.3. Methods of Solving Initial Boundary Problems on the Basis of Spatio-Frequency Representations
  • 1.3.1. The Laplace and Fourier Integral Transformation Methods
  • 1.3.2. Natural Resonances and the Singularity Expansion Method
  • 1.4. Time-Domain Methods
  • 1.4.1. The Finite-Difference Method
  • 1.4.2. The Integral Equation Method
  • 1.4.3. The Directional Decomposition Method (Also Called the Invariant Imbedding or the Wave-Splitting Method)
  • 1.4.4. The Method of Separation of Variables and Other Analytic Methods
  • 2. Waveguides and Periodic Structures: Exact Absorbing Conditions on Virtual Boundaries in Cross-Section of Regular Waveguiding Structures
  • 2.1. Introduction
  • 2.2. Compact Waveguide Units: 2-D Scalar Problems in Cartesian Coordinates
  • 2.2.1. Transformation of the Evolutionary Basis for a Signal in a Regular Plane-Parallel Waveguide
  • 2.2.2. Nonlocal Absorbing Conditions
  • 2.2.3. Local Absorbing Conditions
  • 2.3. Axially Symmetrical Waveguide Units: 2-D Scalar Problems in Cylindrical Coordinates
  • 2.3.1. Statement of Model Initial Boundary Value Problems and Their General Solutions
  • 2.3.2. Exact Absorbing Conditions
  • 2.4. Vector Problems of the Theory of Open Waveguide Resonators
  • 2.4.1. General Theoretical Questions
  • 2.4.2. Exact Absorbing Conditions in Vector Initial Boundary Value Problems
  • 2.5. Problems of the Electromagnetic Theory of Gratings
  • 2.5.1. Scalar Problems for a Perfect Reflecting Grating
  • 2.5.2. The Transport Operator Specifying Spatio-Temporal Signal Transformations in the Floquet Channel and Exact Conditions for Outgoing Waves
  • 2.5.3. The Conditions Truncating the Analysis Domain in Vector Problems of the Electromagnetic Theory of Gratings
  • 3. Compact Inhomogeneities in Free Space: Virtual Coordinate Boundaries in Scalar and Vector Problems of Wave Scattering Theory
  • 3.1. Introduction
  • 3.2. Exact Conditions for Artificial Boundaries in Cylindrical (Polar) Coordinates
  • 3.2.1. Transformation of the Evolutionary Basis for a Diverging Cylindrical Wave
  • 3.2.2. Radiation Conditions and Nonlocal Absorbing Conditions
  • 3.3. Exact Conditions for Artificial Boundaries in Cartesian Coordinates: The Problem of Comer Points and Its Solution
  • 3.3.1. Truncation of the Analysis Domain Down to a Band in the Plane of the Variables g = {{y, z}}
  • 3.3.2. The Comer Points: Correct Formulation of the Inner Initial Boundary Value Problems in the Exact Local Absorbing Conditions
  • 3.4. Vector Problems: Spherical Coordinates
  • 3.4.1. Statement of the Problems and Preliminary Derivations
  • 3.4.2. Nonlocal Radiation Conditions for the Borgnis Functions
  • 3.4.3. Exact Radiation Conditions for the Components of the Electric Field Vector
  • 3.5. Axially Symmetric Problems: Spherical and Cylindrical Coordinates
  • 3.5.1. Formulation of the Initial Boundary Value Problems and Some General Statements
  • 3.5.2. Exact Radiation Conditions for the Artificial Spherical Boundary
  • 3.5.3. Some Peculiarities Arising in Implementation of Exact Absorbing Conditions in a Rectangular Grid of Coordinates g = {{[rho], z}}
  • 4. The Simplest Modifications of the Exact ABCs Approach and the Associated Numerical Tests
  • 4.1. Introduction
  • 4.2. Radiators with Infinite Flanges
  • 4.2.1. Statement of the Initial Boundary Value Problems
  • 4.2.2. Exact Absorbing Conditions in the Radiation Zone of an Axially Symmetric Structure
  • 4.2.3. Exact Absorbing Conditions in Cross-Sections of the Feeding Waveguides
  • 4.3. Wave Radiation from a Plane-Parallel Waveguide of Arbitrary Aperture
  • 4.3.1. Truncation of the Analysis Domain Down to a Half-Plane and a Band
  • 4.3.2. The Problem of the Corner Points and the Exact Absorbing Conditions on a Rectangular Coordinate Boundary
  • 4.3.3. Conditions for the Artificial Boundary L in the Cross-Section of a Plane-Parallel Waveguide
  • 4.4. The Problems of Strong and Remote Field Sources
  • 4.4.1. Waveguide Open Resonators: 2-D Scalar Problems
  • 4.4.2. Compact Discontinuities in R[superscript 2] Space: Formulation of Modified Problems in Terms of Secondary Field U[superscript s] (g, t)
  • 4.4.3. Determination of the Given Sources Field
  • 4.5. Evolutionary Basis of Outgoing Waves in the Domains [subscript L]Q with Homogeneous and Inhomogeneous Filling
  • 4.6. Numerical Tests of the New Exact Conditions
  • 4.6.1. A Finite-Difference Scheme with Exact ABCs at the Coordinate Boundary in the Floquet Channel
  • 4.6.2. A Finite-Difference Scheme with Exact ABCs for 2-D Problems in Polar Coordinate Systems
  • 4.6.3. Absorbing Conditions on the Boundaries with Corner Points
  • 4.6.4. Spherical Conditions in Axially Symmetric Problems
  • 5. Transform Operators in Space of Signal's Evolutionary Basis: A Time-Domain Analogue of the Generalized Scattering-Matrix Method
  • 5.1. Introduction
  • 5.2. Evolutionary Signal Basis and Transform Operators
  • 5.2.1. The Field of Given Sources in Hollow Waveguide of Arbitrary Cross-Section
  • 5.2.2. Key Statements
  • 5.2.3. Operator Method for Problems of Cascades of Elementary Discontinuities
  • 5.3. Canonical Problems of the Time Domain
  • 5.3.1. Formulation of the Problems
  • 5.3.2. Thin Diaphragms: Exact Solution of the Initial Boundary Value Problems by the Mode-Matching Method
  • 5.3.3. Residue Calculation Method and Analytical Regularization Method for Canonical Problems in the Time Domain
  • 5.3.4. Inhomogeneities Preserving Mode Structure of the Field
  • 5.4. Algorithms for Calculating Transient Characteristics of Resonant Inhomogeneities
  • 5.5. Signals in the Floquet Channel: The Transform Operators and Some Canonical Initial Boundary Value Problems
  • 5.5.1. The Basic Definitions
  • 5.5.2. Stripe Grating and a Grating of Thick Half-Planes: Solution of Initial Boundary Value Problems by Using the Mode-Matching Method
  • 6. Open Periodic Resonators and Waveguides: Novel Results in Electromagnetic Theory of Gratings
  • 6.1. Introduction
  • 6.2. Essential Qualitative Results in the Spectral Theory of Gratings
  • 6.2.1. Formulation of Boundary Value Problems and Principal Definitions
  • 6.2.2. Grating as an Open Periodic Resonator
  • 6.2.3. Grating as an Open Periodic Waveguide
  • 6.2.4. Natural Resonances and Transient Processes in Open Periodic Structures: Examples for Analysis
  • 6.3. Dynamic Patterns of Spectral Points in the Frequency Domain
  • 6.3.1. Specific Properties of the Dynamics of Elements of the Spectral Sets: Effects of Existence of Super-High-Q Oscillations and Surface Waves in Periodic Structures with Open Energy Radiation Channels
  • 6.3.2. Gallery of Anomalous Spatio-Frequency Transformations of Electromagnetic Field
  • 6.4. Gratings in Transient Wave Fields: Establishing of Regularities
  • 6.4.1. Scattering of Narrowband Signals: Dynamical Images of Spectral Points in the Time Domain
  • 6.4.2. Wideband Signal Scattering
  • 6.4.3. Visualization of Transient Fields: Reflecting Gratings
  • 6.5. Pulse Deformations by Free Propagation in Regular Sections of the Floquet Channels
  • 6.5.1. Deformation of Narrowband Signals
  • 6.5.2. Propagation and Deformation of Wideband Pulses
  • 7. Model Synthesis of Resonance Quasi-Optical Devices: Dispersive Open Resonators, Absorbing Coatings, and Pattern-Forming Structures
  • 7.1. Introduction
  • 7.2. Model Synthesis of Structures Including Grating Dispersive Elements (Frequency Domain)
  • 7.2.1. Optimization of the Absorbing Properties of Coatings
  • 7.2.2. Pattern-Forming Grating Structures
  • 7.2.3. Mode Selection in Open Resonators with Mirrors Made of Gratings
  • 7.3. Inverse Problems in Electromagnetic Theory of Gratings (Frequency Domain)
  • 7.3.1. General Statements
  • 7.3.2. Uniqueness Theorems
  • 7.3.3. Arbitrary Profile Reflective Grating: Visualization Problem
  • 7.3.4. Synthesis of Reflective Gratings
  • 7.4. Open Dispersive Resonators
  • 7.4.1. Open Resonators of Classical Configurations: Computational Experiments in the Time Domain
  • 7.4.2. Dispersive Open Resonators with Grating Mirrors
  • 7.5. Transient Processes in the Near Zone of Pulsed Waves Radiators
  • 7.5.1. The Luneburg Lens
  • 7.5.2. Radiation from Open Periodic Waveguides
  • References
  • Appendix. List of Symbols and Abbreviations
  • Index
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