Modern Theory of Gratings

by Sirenko, Yuriy K.; Strom, Staffan; Chandezon, Jean (CON); Granet, Gerard (CON); Melezhik, Petr N. (CON)

• ISBN13: 9781441911995
• ISBN10: 1441911995
• Format: Hardcover
• Copyright: 2009-12-30
• Publisher: Springer Verlag

Summary

The advances in the theory of diffraction gratings and the applications of these results certainly determine the progress in several areas of applied science and engineering. The polarization converters, phase shifters and filters, quantum and solid-state oscillators, open quasi optical dispersive resonators and power compressors, slow-wave structures and patter forming systems , accelerators and spectrometer; that is still far from being a complete list of devices exploiting the amazing ability of periodic structures to perform controlled frequency, spatial, and polarization selection of signals.Diffraction gratings used to be and still are one of the most popular objects of analysis in electromagnetic theory. The further development of the theory of diffraction gratings, in spite of considerable achievements, is still very important presently. The requirements of applied optics and microwave engineering present the theory of diffraction gratings with many new problems which force us to search for new methods and tools for their resolution. Just in such way there appeared recently new fields, connected with the analysis, synthesis and definition of equivalent parameters of artificial materials ' layers and coatings, having periodic structure and possessing features, which can be found in natural materials only in extraordinary or exceptional situations.In this book the authors present results of the electromagnetic theory of diffraction gratings that may constitute the base of further development of this theory which can meet the challenges provided by the most recent requirements of fundamental and applied science.The following issues will be considered in the book Authentic methods of analytical regularization, that perfectly match the requirements of analysis of resonant scattering of electromagnetic waves by gratings; Spectral theory of gratings, providing a reliable foundation for the analysis of spatial ' frequency transformations of electromagnetic fields occurring in open periodic resonators and waveguides;Parametric Fourier method and C-method , that are oriented towards the efficient numerical analysis of transformation properties of fields in the case of arbitrary profile periodic boundary between dielectric media and multilayered conformal arrays;Rigorous methods for analysis of transient processes and time-spatial transformations of electromagnetic waves in resonant situations , based on development and incorporation in standard numerical routines of FDTD of so called explicit absorbing boundary conditions;New approaches to the solution of homogenization problems ' the key problem arising in construction of metamaterials and meta surfaces;New physical results about the resonance scattering of pulse and monochromatic waves by periodic structures, including structures with chiral or left-handed materials;Methods and the results of the solutions of several actual applied problems of analysis and synthesis of pattern creating gratings, power compressors, resonance radiators of high capacity short radio pulses, open electromagnetic structures for the systems of resonant quasi optics and absorbing coatings.

Table of Contents

Basic Statements	p. 1
The Formulation of Boundary Value and Initial Boundary Value Problems in the Theory of Diffraction Gratings	p. 1
Fundamental Equations	p. 1
Domains of Analysis, Boundary and Initial Conditions	p. 3
Time Domain: Initial Boundary Value Problems	p. 5
Frequency Domain: Boundary Value Problems	p. 11
The General Physical Picture: Principal Definitions and Consequences from Conservation Laws and Reciprocity Theorems	p. 15
The Diffraction Problems for Plane Waves	p. 15
The Simplest Physical Consequences from the Poynting Theorem and the Lorentz Lemma	p. 19
The Spectral Theory of Gratings	p. 22
Introduction	p. 22
The Grating as an Open Periodic Resonator	p. 24
The Grating as an Open Periodic Waveguide	p. 28
Some Physical Results of Spectral Theory	p. 33
Analytic Regularization Methods	p. 43
General Description and Classification of the Analytic Regularization Methods: History, Provenance, and Survey	p. 43
The Riemann-Hilbert Problem Method and Its Generalization	p. 56
Classical Dual Series Equations and the Riemann-Hilbert Problem	p. 57
Classical Dual Series Equations with "Matrix Perturbation"	p. 63
Dual Series Equations with the Nonunit Coefficient of Conjugation	p. 73
The System of Dual Series Equations and Riemann-Hilbert Vector Problem	p. 80
Inversion of Convolution-Type Matrix Operators in System of Equations in the Mode Matching Technique	p. 88
Lamellar Gratings: Systems of First-Kind Equations and Analytic Regularization of the Problem	p. 90
Matrix Scheme of Analytic Regularization Procedure	p. 96
Electromagnetic Wave Diffraction by Gratings in Presence of a Chiral Isotropic Medium	p. 102
Field Presentation in Chiral Medium	p. 104
Formulation of the Problem	p. 106
The Systems of Dual Series Equations	p. 107
An Algebraic System of the Second Kind	p. 110
Numerical Analysis for Grating and Chiral Half-Space	p. 115
Strip Grating with Layered Medium	p. 120
Electromagnetic Properties of a Strip Grating with Layered Medium in the Resonant Frequency Range	p. 122
Resonant Scattering of Electromagnetic Waves by Gratings and Interfaces Between Anisotropic Media and Metamaterials	p. 130
Resonant Wave Scattering by a Strip Grating Loaded with a Metamaterial Layer	p. 131
The Plane-Wave Diffraction from a Strip Grating with Anisotropic Medium	p. 145
Diffraction of Quasi-Periodic Waves by Obstacles with Cylindrical Periodical Wavy Surfaces	p. 155
The Dirichlet Diffraction Problem	p. 158
Reduction of the Dirichlet BVP to the Integral Equations	p. 158
Investigation of the Differential Properties of the Integral Equation Kernel	p. 161
Additive Splitting of the Integral Equation Kernel into a Sum of Main Singular Part and Some More Smooth Function	p. 164
Reduction of the Integral Equation to an Infinite System of Linear Algebraic Equations of the First Kind	p. 165
Construction of an Infinite System of Linear Algebraic Equations of the Second Kind	p. 167
The Neumann Diffraction Problem	p. 167
C-Method: From the Beginnings to Recent Advances	p. 173
Introduction	p. 173
Classical C-Method	p. 174
Modal Equations in Cartesian Coordinates and Quasi-periodic Green Function	p. 175
New Coordinate System	p. 177
Modal Equation in the Translation Coordinate System	p. 178
Diffraction of a Plane Wave by a Modulated Surface Grating	p. 180
Formulation of the Problem	p. 180
Tangential Component of a Vector Field at a Coordinate Surface	p. 182
Boundary Conditions	p. 183
Adaptive Spatial Resolution	p. 184
Trapezoidal Grating	p. 185
Lamellar Grating and Adaptive Spatial Resolution	p. 188
Curved Strip Gratings	p. 192
Several Issues of Spectral Theory Relevant to C-Method Formalism	p. 198
The Diffraction Problem Formulation for Real-Valued Frequencies	p. 199
Diffraction Problem for Complex-Valued Frequencies	p. 201
Spectral Problem and Its Solution: Some Physical Results	p. 204
Modeling and Analysis of Transients in Periodic Structures: Fully Absorbing Boundaries for 2-D Open Problems	p. 211
Infinite Gratings: Exact Absorbing Conditions for Plane Parallel Floquet Channel	p. 212
Transformation of Evolutionary Basis of a Signal in a Regular Floquet Channel	p. 213
Nonlocal Absorbing Conditions	p. 216
Local Absorbing Conditions	p. 219
The Problems of Large and Remote Field Sources	p. 224
Finite Gratings: Exact Conditions for Rectangular Artificial Boundaries	p. 227
Statement of the Problems	p. 227
Truncation of the Analysis Domain to a Band	p. 230
The Corner Points: Proper Formulation of the Inner Initial Boundary Value Problems in the Exact Local Absorbing Conditions	p. 232
The Far Zone Problem: Radiation Conditions for Outgoing Cylindrical Waves and Exact Conditions for Artificial Boundaries in Polar Coordinates	p. 236
Time Domain Methods in the Study of Gratings and Compact Grating Structures as Open Resonators	p. 239
Spatial-Frequency Representations of Transient Fields and Preliminary Qualitative Analysis	p. 239
A Choice of the Field Sources in Numerical Experiments	p. 246
Compact Grating Structures	p. 250
Infinite Gratings: Resonant Wave Scattering	p. 258
Electrodynamical Characteristics of Gratings	p. 259
Semitransparent Gratings	p. 262
Reflective Gratings	p. 269
Gratings in a Pulsed Wave Field	p. 277
2-D Models of Compact Grating Structures: Spatio-frequency and Spatio-temporal Field Transformations	p. 285
Basic Definitions and Numerical Tests of New Exact Conditions	p. 285
Finite and Infinite Periodic Structures: Similarities and Differences	p. 291
Radiating Apertures with Quasi-periodic Field Structure	p. 296
Resonant Antennas with Semitransparent Grating Mirrors	p. 305
2-D Models of Phased Arrays	p. 317
Finite Scale Homogenization of Periodic Bianisotropic Structures	p. 335
Fundamental Ideas	p. 336
Some Mathematical Properties of Maxwell's Operator	p. 338
Vacuum Case	p. 340
Material Case	p. 341
Lossless Media: Eigenvalue Decomposition	p. 342
Dispersive Media: Singular Value Decomposition	p. 344
Estimates of the Eigenvalues and Singular Values in the Low-Frequency Limit	p. 345
Reduced Number of Degrees of Freedom in the Low-Frequency Limit	p. 349
Computation of Homogenized Parameters	p. 353
Lossless Case	p. 354
Dispersive Case	p. 355
Results for Sample Structures	p. 356
Laminated Media	p. 356
Validity of Classical Homogenization	p. 358
Results for a Chiral Structure	p. 361
Conclusions	p. 365
Appendix: The List of the Symbols and Abbreviations	p. 367
References	p. 371
Index	p. 383
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