Sirenko / Velychko Electromagnetic Waves in Complex Systems

Selected Theoretical and Applied Problems
1. Auflage 2016
ISBN: 978-3-319-31631-4
Verlag: Springer Nature Switzerland
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 91, 459 Seiten

Reihe: Springer Series on Atomic, Optical, and Plasma Physics

This book gives guidance to solve problems in electromagnetics, providing both examples of solving serious research problems as well as the original results to encourage further investigations. The book contains seven chapters on various aspects of resonant wave scattering, each solving one original problem. All of them are unified by the authors' desire to show advantages of rigorous approaches at all stages, from the formulation of a problem and the selection of a method to the interpretation of results. The book reveals a range of problems associated with wave propagation and scattering in natural and artificial environments or with the design of antennas elements. The authors invoke both theoretical (analytical and numerical) and experimental techniques for handling the problems. Attention is given to mathematical simulations, computational efficiency, and physical interpretation of the experimental results. The book is written for students, graduate students and young researchers.

Yuriy Sirenko Since 1974, he has held several research and academic positions at A.Ya. Usikov Institute of Radiophysics and Electronics of National Academy of Sciences of Ukraine (IRE NASU), Kharkiv, Ukraine, where he has been a head of the Mathematical Physics Department since 1988. He is also an invited professor at L.N.Gumilyov Eurasian National University, Astana, Kazakhstan since 2013. He also was a professor at V.N.Karazin Kharkiv National University, Kharkiv, Ukraine (1989-1997). He is an author of 8 books and more than 200 research papers. The Candidate of Science Degree (Ph.D. degree equivalent) in physics and mathematics he got from the Kharkiv National University in 1978. The Doctor of Science Degree in physics and mathematics he got from the Kharkiv National University in 1988. He is recognized as an expert in the fields of radio physics and mathematical physics. He has also experience in teaching fundamental and applied mathematics and modern methods in computational electrodynamics. Research interests Wave scattering theory, analytical and numerical techniques for wave motion simulation, resonance phenomena, spectral theory of open structures, operator theory and its applications. Semi-analytical methods for solving diffraction problems of the resonant theory of gratings and the spectral theory for open periodic and waveguide resonators have been developed. Efficient semi-analytical and numerical methods for the analysis of transient processes under resonance conditions in gratings and waveguides have been elaborated.    Grants, awards 1998 - 1999 Research and Teaching Personal Grant of the International Science Foundation 1996 - 1999 Research Grant of Royal Academy of Science, Sweden. 1993 Research Personal Grant of the International Science Foundation. 1989 State Prize in the Field of Science and Engineering, Ukraine.

Lyudmyla Velychko has more than 30 years of research experience in the areas of radio physics and applied mathematics. Since 1982, she has been with A.Ya.Usikov Institute of Radiophysics and Electronics of the National Academy of Sciences of Ukraine, Kharkiv, Ukraine. Since 2000, she has been a Senior Researcher at the Mathematical Physics Department there. The Candidate of Science Degree (Ph.D. degree equivalent) in physics and mathematics she got from A.Ya.Usikov Institute of Radiophysics and Electronics of the National Academy of Sciences of Ukraine in 1996 with the thesis title 'Inverse diffraction problems for plane periodic gratings'. She is an author of more than 50 research journal and conference papers and a book chapter. Research interests Electromagnetic theory of gratings; simulation and analysis of resonant wave scattering in the time domain. Development of methods for solving inverse problems in electrodynamic theory of gratings. Elaboration of algorithms for analysis and model synthesis of plane pattern-forming and efficiently absorbing structures. Simulation and analysis of resonant phenomena in open structures of complex geometry by time domain and frequency domain methods combined.     

Autoren/Hrsg.

Sirenko, Yuriy

Velychko, Lyudmyla

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;Contributors;14
4;1 New Analytical Solutions of Selected Electromagnetic Problems in Wave Diffraction Theory;15
4.1;Abstract;15
4.2;1.1 Introduction;15
4.3;1.2 Wave Propagation Near an Irregular Impedance Structure;17
4.3.1;1.2.1 Wave Propagation Over a Plane Surface of Variable Conductivity;17
4.3.2;1.2.2 A Field of Linear Magnetic Current in a Plane Waveguide with Smoothly Varying Impedance of Its Walls;21
4.3.2.1;1.2.2.1 Reduction of the Problem to an Integral Equation;21
4.3.2.2;1.2.2.2 Solution of the Integral Equation;24
4.3.2.3;1.2.2.3 Residue Series Representation;28
4.3.2.4;1.2.2.4 Transformation of Eigenmodes on the Waveguide Junction;31
4.4;1.3 The Cycle Slipping Phenomenon and the Degeneracy of Waveguide Modes;35
4.4.1;1.3.1 Introduction;35
4.4.2;1.3.2 Problem Formulation and Solution;38
4.4.3;1.3.3 The Watson Transformation;45
4.4.4;1.3.4 A Numerical Experiment;49
4.5;1.4 Pulsed Radiation from a Line Electric Current Near a Planar Interface;54
4.5.1;1.4.1 Problem Formulation;55
4.5.2;1.4.2 Reduction to Single Integrals;58
4.5.3;1.4.3 The Field in the First Medium;62
4.5.4;1.4.4 The Field in the Second Medium;65
4.5.5;1.4.5 Discussion and Conclusion;66
4.6;1.5 Transition Radiation of a Longitudinal Magnetic Dipole in the Case of Diffuse Interface;68
4.6.1;1.5.1 Problem Formulation and Solution;68
4.6.2;1.5.2 The Criterion of the Interface ‘Sharpness’;75
4.7;1.6 The Biisotropic Epstein Transition Layer;77
4.7.1;1.6.1 Equations for the Electromagnetic Field in a Biisotropic Medium;77
4.7.2;1.6.2 Problem Formulation and Solution;79
4.7.3;1.6.3 Analysis of the Reflected and Transmitted Fields;82
4.8;1.7 Negative Refraction in Isotropic Double-Negative Media;85
4.8.1;1.7.1 Negative Refraction Phenomenon in Homogeneous Double-Negative Media;85
4.8.2;1.7.2 A Model of Smoothly Inhomogeneous Flat-Layered Double Negative Medium. Solution of the Problem of Transmission of a Plane Wave;87
4.8.3;1.7.3 Analysis of the Expressions for Fields;90
4.9;1.8 Distorting Coatings as an Alternative to Masking Coatings;92
4.9.1;1.8.1 Transformation Optics, Masking Coatings, Distorting Coatings;92
4.9.2;1.8.2 Radical Distortion of Radar Image by Applying a Special Coating on the Metamaterial Surface;93
4.10;1.9 Conclusion;97
4.11;References;99
5;2 Dyadic Green’s Function for Biaxial Anisotropic Media;105
5.1;Abstract;105
5.2;2.1 Introduction;105
5.3;2.2 Formulation of the Problem;106
5.4;2.3 Initial Representation for Dyadic Green’s Function;107
5.5;2.4 Transformation of the Original Representation. Singular Part of Dyadic Green’s Function;108
5.6;2.5 Regular Part of Dyadic Green’s Function;110
5.7;2.6 The Physical Solution;112
5.8;2.7 Conclusion;115
5.9;References;116
6;3 Operator Fresnel Formulas in the Scattering Theory of Waveguide Modes;117
6.1;Abstract;117
6.2;3.1 Introduction;117
6.3;3.2 The Mode-Matching Technique in the Problem of a Waveguide Step-like Discontinuity;120
6.3.1;3.2.1 The Classical Mode-Matching Technique: An Example of Application;120
6.3.2;3.2.2 The Mode-Matching Technique in the Problem of a Step Discontinuity in a Waveguide: Standard Approach;122
6.3.3;3.2.3 New Formulation of the Problem of Scattering of Waveguide Modes;128
6.4;3.3 Matrix Operator Formalism in the Scalar Mode Analysis;128
6.5;3.4 Generalized Mode-Matching Technique in the Step Discontinuity Problem;133
6.5.1;3.4.1 Derivation of the Operator Fresnel Formulas;133
6.5.2;3.4.2 Reciprocity Principle and Energy Conservation Law in the Operator Form;137
6.5.3;3.4.3 Correctness of the Matrix-Operator Model;141
6.6;3.5 Justification of the Truncation Technique for Solving Operator Equations;143
6.6.1;3.5.1 Construction of Projection Approximations for the Fresnel Formulas;144
6.6.2;3.5.2 Unconditional Convergence of the Truncation Technique;147
6.6.3;3.5.3 Rate of Convergence of the Approximations of Scattering Operators;149
6.7;3.6 Mittra Rule for Scattering Operators;153
6.8;3.7 Novel Matrix Models for the Problem of a Step Discontinuity in a Waveguide;157
6.9;3.8 The Conservation Laws in Operator Form for Two Classes of Mode Diffraction Problems;162
6.10;3.9 Universality of the Operator Fresnel Formulas;169
6.10.1;3.9.1 Step-Like Discontinuity in a Waveguide;169
6.10.2;3.9.2 Generalized Operator Fresnel Formulas for Resonant Discontinuities;171
6.11;3.10 Matrix Scattering Operators;173
6.11.1;3.10.1 Properties of Reflection and Transmission Operators;173
6.11.2;3.10.2 Basic Operator Properties of the Generalized Scattering Matrix;178
6.12;3.11 Conclusion;186
6.13;Appendix A: Vectors and Their Spaces;189
6.13.1;Vectors in the Hilbert Spaces l_{2}, \tilde{l}_{2} and \tilde{\tilde{l}}_{2};189
6.13.2;Vectors in the Hilbert Space h_{N} \equiv l_{2}^{N}, N \ge 2;191
6.13.3;Operator Vectors in the Space {\hbox{V}}_{N} \equiv \left( {l_{2} \to l_{2} } \right)^{N}, N \ge 2;192
6.13.4;Pontryagin Space \Pi_{\nu } with Indefinite Metric;192
6.14;Appendix B: Infinite Systems of Linear Algebraic Equations;193
6.14.1;Early Results of the Theory;193
6.14.2;Completely Regular Systems;194
6.14.3;Regular Systems;194
6.14.4;Quasi-regular Systems;195
6.14.5;Matrix Contractions;196
6.14.6;The Schur Test and the Young Inequality. Hilbert Matrices;196
6.14.7;Compact (Completely Continuous) Operators;197
6.14.8;The Kojima and Toeplitz Matrix Operators;197
6.15;Appendix C: Operator Forms of the Energy Conservation Law Under Time Reversal;198
6.16;References;199
7;4 Two-Dimensionally Periodic Gratings: Pulsed and Steady-State Waves in an Irregular Floquet Channel;201
7.1;Abstract;201
7.2;4.1 Introduction;201
7.3;4.2 Fundamental Equations, Domain of Analysis, Initial and Boundary Conditions;203
7.4;4.3 Time Domain: Initial Boundary Value Problems;206
7.5;4.4 Exact Absorbing Conditions for the Rectangular Floquet Channel;208
7.6;4.5 Some Important Characteristics of Transient Fields in the Rectangular Floquet Channel;211
7.7;4.6 Transformation Operator Method;216
7.7.1;4.6.1 Evolutionary Basis of a Signal and Transformation Operators;216
7.7.2;4.6.2 Equations of the Operator Method in the Problems for Multilayered Periodic Structures;220
7.8;4.7 Some Important Properties of Steady-State Fields in the Rectangular Floquet Channel;222
7.8.1;4.7.1 Excitation by a TM-Wave;222
7.8.2;4.7.2 Excitation by a TE-Wave;226
7.8.3;4.7.3 General Properties of the Grating’s Secondary Field;227
7.8.4;4.7.4 Corollaries of the Reciprocity Relations and the Energy Conservation Law;229
7.9;4.8 Elements of Spectral Theory for Two-Dimensionally Periodic Gratings;231
7.9.1;4.8.1 Canonical Green Function;231
7.9.2;4.8.2 Qualitative Characteristics of the Spectrum;233
7.10;4.9 Conclusion;237
7.11;References;237
8;5 The Exact Absorbing Conditions Method in the Analysis of Open Electrodynamic Structures;239
8.1;Abstract;239
8.2;5.1 Introduction;239
8.3;5.2 Circular and Coaxial Waveguides;242
8.3.1;5.2.1 Formulation of the Model Problem;242
8.3.2;5.2.2 Radiation Conditions for Outgoing Waves;244
8.3.3;5.2.3 Nonlocal Exact Absorbing Conditions;249
8.3.4;5.2.4 Local Exact Absorbing Conditions;251
8.3.5;5.2.5 Equivalence Theorem;255
8.4;5.3 Compact Axially Symmetric Structures;259
8.4.1;5.3.1 Formulation of the Model Problem;259
8.4.2;5.3.2 Radiation Conditions for Outgoing Waves;260
8.4.3;5.3.3 Far-Field Zone Problem, Extended and Remote Sources;268
8.4.4;5.3.4 Virtual Feed Lines in Compact Open Structures;273
8.5;5.4 Characteristics of Steady-State and Transient Fields in Axially Symmetric Structures;277
8.5.1;5.4.1 Frequency-Domain Prototypes for Initial Boundary Value Problems;277
8.5.2;5.4.2 Electrodynamic Characteristics of Open Axially Symmetric Structures;279
8.5.3;5.4.3 Spectral Characteristics of Open Resonators;283
8.6;5.5 Plane Models for Open Electrodynamic Structures;289
8.6.1;5.5.1 The Key Problem;289
8.6.2;5.5.2 Exact Absorbing Conditions for Parallel-Plate Waveguides;291
8.6.3;5.5.3 Exact Absorbing Conditions for Cylindrical Virtual Boundary in Free Space;297
8.6.4;5.5.4 Exact Absorbing Conditions for Rectangular Virtual Boundary in Free Space;300
8.6.5;5.5.5 Frequency-Domain Formalism and Main Characteristics of Open Plane Structures;305
8.7;5.6 3-D Vector Models;306
8.7.1;5.6.1 Exact Absorbing Conditions for Regular Hollow Waveguides;308
8.7.2;5.6.2 Radiation Conditions and Exact Absorbing Conditions for Spherical Virtual Boundary in Free Space;314
8.7.3;5.6.3 TM-Excitation: Frequency-Domain Characteristics;320
8.7.4;5.6.4 TE-Excitation: Frequency-Domain Characteristics;324
8.8;5.7 Accurate and Efficient Calculations;325
8.8.1;5.7.1 General Questions;325
8.8.2;5.7.2 Nonlocal or Local Conditions?;326
8.8.3;5.7.3 The Blocked FFT-Based Acceleration Scheme;328
8.8.4;5.7.4 Efficiency and Accuracy of the Blocked FFT-Based Acceleration Scheme. Numerical Results;331
8.8.5;5.7.5 Test Problems;334
8.9;5.8 Conclusion;336
8.10;References;338
9;6 High-Power Short Pulses Compression: Analysis and Modeling;341
9.1;Abstract;341
9.2;6.1 Introduction;341
9.3;6.2 Exact Absorbing Conditions Method: 2-D Case;343
9.3.1;6.2.1 Planar Structures;343
9.3.2;6.2.2 Axially Symmetric Structures;351
9.4;6.3 Energy Accumulation in Direct-Flow Waveguide Compressors;357
9.4.1;6.3.1 Slot Switches;357
9.4.2;6.3.2 Active Compressors Based on Circular and Coaxial Waveguides;362
9.4.3;6.3.3 Distributed Switches and Active Compressors Based on Rectangular Waveguides;366
9.5;6.4 Radiation of High-Power Short Pulses;372
9.5.1;6.4.1 Radiation of Compressed Pulses by Simple Antennas;374
9.5.2;6.4.2 Novel Antenna Array Design with Combined Compressor/Radiator Elements;381
9.6;6.5 Compression of Frequency-Modulated Electromagnetic Pulses in Hollow Waveguides;385
9.6.1;6.5.1 Transport Operators for Regular Waveguides;387
9.6.2;6.5.2 Pulse Compression in Regular Waveguides;389
9.7;6.6 Conclusion;396
9.8;References;397
10;7 Diffraction Radiation Phenomena: Physical Analysis and Applications;400
10.1;Abstract;400
10.2;7.1 Introduction;400
10.3;7.2 Periodic Structures and Dielectric Waveguides: Analysis Techniques;402
10.3.1;7.2.1 Plane Models for Infinite Gratings: Time-Domain Representations;402
10.3.2;7.2.2 Plane Models for Infinite Gratings: Frequency-Domain Representations;407
10.3.3;7.2.3 Infinite Gratings as Open Resonators or Open Waveguides;410
10.3.4;7.2.4 Some Further Comments;410
10.4;7.3 Diffraction Radiation Phenomena;413
10.4.1;7.3.1 Reflecting Gratings in the Field of a Density-Modulated Electron Flow;413
10.4.2;7.3.2 Finite Gratings: Plane and Axially Symmetric Models;421
10.4.3;7.3.3 Near-Field to Far-Field Conversion by Finite Periodic Structures. Plane Models;424
10.4.4;7.3.4 Near-Field to Far-Field Conversion by Finite Periodic Structures. Axially Symmetric Models;429
10.5;7.4 Synthesis of Diffraction Antenna Components and Units;436
10.5.1;7.4.1 Synthesis of Radiators with Predetermined Amplitude-Phase Field Distribution on the Aperture;436
10.5.2;7.4.2 Maintenance of Antenna Operability on Coupling Level;442
10.6;7.5 The Low-Side-Lobe Planar Antenna;445
10.6.1;7.5.1 Radiator’s Characteristics;445
10.6.2;7.5.2 Antenna Design;448
10.6.3;7.5.3 Experimental Data;451
10.7;7.6 Conclusion;453
10.8;References;453
11;Index;456