Modeling and Analysis of Transient Processes in Open Resonant Structures: New Methods and Techniques / Edition 1

by Yuriy K. Sirenko, Staffan Strïm, Nataliya P. Yashina

Overview

The focus of electromagnetic theory is initial boundary value and boundary value problems for the Maxwell equations. Those are the initial models, from which, by applying mathematical methods, we should extract physical results. The modern computer-aided research process can be divided into several stages: qualitative mathematical analysis of the initial problem, the development of algorithms and implementation of the problem in software, problem-oriented computational - periments, and physical interpretation of the results. The success of the study depends in many aspects on whether sufficiently high standards of investigation can be maintained at all these stages and whether there is an “intellectual core” in these investigations that enables us to gain new scientific knowledge [1]. As an exampleofasuccessfulimplementationofsuchanapproachthathassettledalo- standing conflict between theory and experiment, we can cite the development of thetheoryofresonantwavescatteringinthefrequencydomain. Theseresultshave been reported (see [2–16] and the bibliographies contained in those references), andtheyhaveservedasabasisforthedevelopmentofanumberofessentiallynew functional units and devices in millimeter and submillimeter radio engineering, vacuum electronics, and solid-state electronics, optics, and spectroscopy. The modern theory of transient electromagnetic—elds is still lacking achie- ments that may be compared with those existing in the frequency domain, neither by the profoundness of the study, nor by the intensity of the study of electrom- netic phenomena and, as a result, by their applications. However, the process of accumulation of potentialities for a breakthrough is a process still going on.

Product Details

ISBN-13:	9780387308784
Publisher:	Springer New York
Publication date:	11/14/2006
Series:	Springer Series in Optical Sciences , #122
Edition description:	2007
Pages:	353
Product dimensions:	6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Preface     V
Numerical Analysis of Transient Processes: Fundamental Results of the Theory, Methods, and Problems     1
Introduction     1
Main Equations and Fundamental Results of the Theory     2
Maxwell Equations     2
Wave and Telegraph Equations     4
The Borgnis Functions     6
Domains of Analysis, Boundary, and Initial Conditions     8
Formulation of Initial Boundary Value Problems: Generalized Functions and Generalized Solutions     10
Fundamental Results of the Theory     14
Methods of Solving Initial Boundary Problems on the Basis of Spatio-Frequency Representations     17
The Laplace and Fourier Integral Transformation Methods     17
Natural Resonances and the Singularity Expansion Method     21
Time-Domain Methods     24
The Finite-Difference Method     24
The Integral Equation Method     30
The Directional Decomposition Method (Also Called the Invariant Imbedding or the Wave-Splitting Method)     33
The Method of Separation of Variables and Other Analytic Methods     35
Waveguides and Periodic Structures: Exact Absorbing Conditions on Virtual Boundaries in Cross-Section of Regular Waveguiding Structures     38
Introduction     38
Compact Waveguide Units: 2-D Scalar Problems in Cartesian Coordinates     40
Transformation of the Evolutionary Basis for a Signal in a Regular Plane-Parallel Waveguide     40
Nonlocal Absorbing Conditions     43
Local Absorbing Conditions     46
Axially Symmetrical Waveguide Units: 2-D Scalar Problems in Cylindrical Coordinates     49
Statement of Model Initial Boundary Value Problems and Their General Solutions     49
Exact Absorbing Conditions     52
Vector Problems of the Theory of Open Waveguide Resonators     54
General Theoretical Questions     54
Exact Absorbing Conditions in Vector Initial Boundary Value Problems     58
Problems of the Electromagnetic Theory of Gratings     60
Scalar Problems for a Perfect Reflecting Grating     60
The Transport Operator Specifying Spatio-Temporal Signal Transformations in the Floquet Channel and Exact Conditions for Outgoing Waves     62
The Conditions Truncating the Analysis Domain in Vector Problems of the Electromagnetic Theory of Gratings     65
Compact Inhomogeneities in Free Space: Virtual Coordinate Boundaries in Scalar and Vector Problems of Wave Scattering Theory     69
Introduction     69
Exact Conditions for Artificial Boundaries in Cylindrical (Polar) Coordinates      71
Transformation of the Evolutionary Basis for a Diverging Cylindrical Wave     71
Radiation Conditions and Nonlocal Absorbing Conditions     73
Exact Conditions for Artificial Boundaries in Cartesian Coordinates: The Problem of Comer Points and Its Solution     74
Truncation of the Analysis Domain Down to a Band in the Plane of the Variables g = {lcub}y, z{rcub}     74
The Comer Points: Correct Formulation of the Inner Initial Boundary Value Problems in the Exact Local Absorbing Conditions     77
Vector Problems: Spherical Coordinates     81
Statement of the Problems and Preliminary Derivations     81
Nonlocal Radiation Conditions for the Borgnis Functions     85
Exact Radiation Conditions for the Components of the Electric Field Vector     91
Axially Symmetric Problems: Spherical and Cylindrical Coordinates     93
Formulation of the Initial Boundary Value Problems and Some General Statements     93
Exact Radiation Conditions for the Artificial Spherical Boundary     95
Some Peculiarities Arising in Implementation of Exact Absorbing Conditions in a Rectangular Grid of Coordinates g = {lcub}[rho], z{rcub}     97
The Simplest Modifications of the Exact ABCs Approach and the Associated Numerical Tests     99
Introduction     99
Radiators with Infinite Flanges      102
Statement of the Initial Boundary Value Problems     102
Exact Absorbing Conditions in the Radiation Zone of an Axially Symmetric Structure     103
Exact Absorbing Conditions in Cross-Sections of the Feeding Waveguides     105
Wave Radiation from a Plane-Parallel Waveguide of Arbitrary Aperture     107
Truncation of the Analysis Domain Down to a Half-Plane and a Band     107
The Problem of the Corner Points and the Exact Absorbing Conditions on a Rectangular Coordinate Boundary     111
Conditions for the Artificial Boundary L in the Cross-Section of a Plane-Parallel Waveguide     113
The Problems of Strong and Remote Field Sources     114
Waveguide Open Resonators: 2-D Scalar Problems     115
Compact Discontinuities in R[superscript 2] Space: Formulation of Modified Problems in Terms of Secondary Field U[superscript s] (g, t)     118
Determination of the Given Sources Field     120
Evolutionary Basis of Outgoing Waves in the Domains [subscript L]Q with Homogeneous and Inhomogeneous Filling     123
Numerical Tests of the New Exact Conditions     127
A Finite-Difference Scheme with Exact ABCs at the Coordinate Boundary in the Floquet Channel     127
A Finite-Difference Scheme with Exact ABCs for 2-D Problems in Polar Coordinate Systems     136
Absorbing Conditions on the Boundaries with Corner Points     140
Spherical Conditions in Axially Symmetric Problems     143
Transform Operators in Space of Signal's Evolutionary Basis: A Time-Domain Analogue of the Generalized Scattering-Matrix Method     148
Introduction     148
Evolutionary Signal Basis and Transform Operators     149
The Field of Given Sources in Hollow Waveguide of Arbitrary Cross-Section     149
Key Statements     152
Operator Method for Problems of Cascades of Elementary Discontinuities     156
Canonical Problems of the Time Domain     158
Formulation of the Problems     159
Thin Diaphragms: Exact Solution of the Initial Boundary Value Problems by the Mode-Matching Method     162
Residue Calculation Method and Analytical Regularization Method for Canonical Problems in the Time Domain     166
Inhomogeneities Preserving Mode Structure of the Field     169
Algorithms for Calculating Transient Characteristics of Resonant Inhomogeneities     172
Signals in the Floquet Channel: The Transform Operators and Some Canonical Initial Boundary Value Problems     175
The Basic Definitions     175
Stripe Grating and a Grating of Thick Half-Planes: Solution of Initial Boundary Value Problems by Using the Mode-Matching Method     177
Open Periodic Resonators and Waveguides: Novel Results in Electromagnetic Theory of Gratings     181
Introduction     181
Essential Qualitative Results in the Spectral Theory of Gratings     182
Formulation of Boundary Value Problems and Principal Definitions     182
Grating as an Open Periodic Resonator     185
Grating as an Open Periodic Waveguide     192
Natural Resonances and Transient Processes in Open Periodic Structures: Examples for Analysis     198
Dynamic Patterns of Spectral Points in the Frequency Domain     203
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     203
Gallery of Anomalous Spatio-Frequency Transformations of Electromagnetic Field     211
Gratings in Transient Wave Fields: Establishing of Regularities     231
Scattering of Narrowband Signals: Dynamical Images of Spectral Points in the Time Domain     231
Wideband Signal Scattering     240
Visualization of Transient Fields: Reflecting Gratings     244
Pulse Deformations by Free Propagation in Regular Sections of the Floquet Channels     255
Deformation of Narrowband Signals     256
Propagation and Deformation of Wideband Pulses      264
Model Synthesis of Resonance Quasi-Optical Devices: Dispersive Open Resonators, Absorbing Coatings, and Pattern-Forming Structures     270
Introduction     270
Model Synthesis of Structures Including Grating Dispersive Elements (Frequency Domain)     272
Optimization of the Absorbing Properties of Coatings     272
Pattern-Forming Grating Structures     278
Mode Selection in Open Resonators with Mirrors Made of Gratings     282
Inverse Problems in Electromagnetic Theory of Gratings (Frequency Domain)     287
General Statements     287
Uniqueness Theorems     290
Arbitrary Profile Reflective Grating: Visualization Problem     293
Synthesis of Reflective Gratings     301
Open Dispersive Resonators     308
Open Resonators of Classical Configurations: Computational Experiments in the Time Domain     309
Dispersive Open Resonators with Grating Mirrors     316
Transient Processes in the Near Zone of Pulsed Waves Radiators     324
The Luneburg Lens     325
Radiation from Open Periodic Waveguides     328
References     334
List of Symbols and Abbreviations     346
Index     351