Electromagnetic Waves in Complex Systems (eBook)

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.     

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