Modern Theory of Gratings: Resonant Scattering: Analysis Techniques and Phenomena

ISBN-13: 9781441911995 / Angielski / Twarda / 2009 / 408 str.

Yuriy K. Sirenko; Staffan Stram

Opis

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.

Spis treści

Preface

Chapter 1. Basic Statements

1.1. The Formulation of Boundary Value and Initial Boundary Value Problems in the Theory of Diffraction Gratings

1.1.1. Main Equations

1.1.2. Domains of Analysis, Boundary and Initial Conditions

1.1.3. Time Domain: Initial Boundary Value Problems

1.1.4. Frequency Domain: Boundary Value Problems

1.2. The General Physical Picture: Main Definitions and Consequences from Conservation Laws and Reciprocity Theorems

1.2.1. The Diffraction Problems for Plane Waves

1.2.2. The Simplest Physical Consequences from the Poynting Theorem and the Lorentz Lemma

1.3. The Spectral Theory of Gratings

1.3.1. Introduction

1.3.2. The Grating as an Open Periodic Resonator

1.3.3. The Grating as an Open Periodic Waveguide

1.3.4. Some Physical Results of Spectral Theory

Chapter 2. Analytic Regularization Methods

2.1. General Description and Classification of the Analytic Regularization Methods: History, Provenance and Survey

2.2. The Riemann-Hilbert Problem Method and its Generalization

2.2.1. Classical Dual Series Equations and the Riemann-Hilbert Problem

2.2.2. Classical Dual Series Equations with "Matrix Perturbation"

2.2.3. Dual Series Equations with the Non Unit Coefficient of Conjugation

2.2.4. The System of Dual Series Equations and Riemann-Hilbert Vector Problem

2.3. Inversion of Convolution-Type Matrix Operators in Equation Systems of the Mode Matching Technique

2.3.1. Knife Gratings: Systems of First Kind Equations and Analytic Regularization of the Problem

2.3.2. Matrix Scheme of Analytic Regularization Procedure

2.4. Electromagnetic Wave Diffraction by Gratings in Presence of a Chiral Isotropic Medium

2.4.1. Field Presentation in Chiral Medium

2.4.2. Formulation of the Problem

2.4.3. The Systems of Dual Series Equations

2.4.4. An Algebraic System of the Second Kind

2.4.5. Numerical Analysis for Grating and Chiral Half-Space

2.4.6. Strip Grating with Layered Medium

2.4.7. Electromagnetic Properties of a Strip Grating with Layered Medium in the Resonant Frequency Range

2.5. Resonant Scattering of Electromagnetic Waves by Gratings and Interfaces between Anisotropic Media and Metamaterials

2.5.1. Resonant Wave Scattering by a Strip Grating Loaded with a Metamaterial Layer

2.5.2. The Plane Wave Diffraction from a Strip Grating with Anisotropic Medium

2.6. Diffraction of Quasi-Periodic Waves by Obstacles with Cylindrical Periodical Wavy Surfaces

2.6.1. The Dirichlet Diffraction Problem

2.6.2. Reduction of the Dirichlet BVP to the Integral Equations

2.6.3. Investigation of the Differential Properties of the Integral Equation Kernel

2.6.4. Additive Splitting of the Integral Equation Kernel into a Sum of Main Singular Part and Some More Smooth Function

2.6.5. Reduction of the Integral Equation to an Infinite System of Linear Algebraic Equations of the First Kind

2.6.6. Construction of an Infinite System of Linear Algebraic Equations of the Second Kind

2.6.7. The Neumann Diffraction Problem

Chapter 3. C-Method: From the Beginnings to Recent Advances

3.1. Introduction

3.2. Classical C-Method

3.2.1. Modal Equations in Cartesian Coordinates and Quasi-Periodic Green Function

3.2.2. New Coordinate System

3.2.3. Modal Equation in the Translation Coordinate System

3.3. Diffraction of a Plane Wave by a Modulated Surface Grating

3.3.1. Posing the Problem

3.3.2. Tangential Component of a Vector Field at a Coordinate Surface

3.3.3. Boundary Conditions

3.4. Adaptive Spatial Resolution

3.4.1. Trapezoidal Grating

3.4.2. Lamellar Grating and Adaptive Spatial Resolution

3.5. Curved Strip Gratings

3.6. Several Issues of Spectral Theory Relevant to C-method Formalism

3.6.1. The Diffraction Problem Formulation for Real Valued Frequencies

3.6.2. Diffraction Problem for Complex Valued Frequencies

3.6.3. Spectral Problem and its Solution. Some Physical Results

Chapter 4. Modeling and Analysis of Transients in Periodic Structures: Fully Absorbing Boundaries for 2-D Open Problems

4.1. Infinite Gratings: Exact Absorbing Conditions for Plane Parallel Floquet Channel

4.1.1. Transformation of the Evolutionary Basis of a Signal in a Regular Floquet Channel

4.1.2. Nonlocal Absorbing Conditions

4.1.3. Local Absorbing Conditions

4.1.4. The Problems of Large and Remote Field Sources

4.2. Finite Gratings: Exact Conditions for Rectangular Artificial Boundaries

4.2.1. Statement of the problems

4.2.2. Truncation of the Analysis Domain Down to a Band

4.2.3. The Corner Points: Proper Formulation of the Inner Initial Boundary Value Problems in the Exact Local Absorbing Conditions

4.2.4. The Far Zone Problem: Radiation Conditions for Outgoing Cylindrical Waves and Exact Conditions for Artificial Boundaries in Polar Coordinates

4.3. Time-Domain Methods in the Study of Gratings and Compact Grating Structures as Open Resonators

4.3.1. Spatial-Frequency Representations of Transient Fields and Preliminary Qualitative Analysis

4.3.2. A Choice of the Field Sources in Numerical Experiments

4.3.3. Compact Grating Structures

4.4. Infinite Gratings: Resonant Wave Scattering

4.4.1. Electrodynamical Characteristics of Gratings

4.4.2. Semi-Transparent Gratings

4.4.3. Reflective Gratings

4.4.4. Gratings in a Pulsed Wave Field

4.5. 2-D Models of Compact Grating Structures: Spatio-Frequency and Spatio-Temporal Field Transformations

4.5.1. Basic Definitions and Numerical Tests of New Exact Conditions

4.5.2. Finite and Infinite Periodic Structures: Similarities and Differences

4.5.3. Radiating Apertures with Quasi-Periodic Field Structure

4.5.4. Resonant Antennas with Semi-Transparent Grating Mirrors

4.5.5. 2-D Models of Phased Arrays

Chapter 5. Finite Scale Homogenization of Periodic Bianisotropic Structures

5.1. Fundamental Ideas

5.2. Some Mathematical Properties of Maxwell’s Operator

5.2.1. Vacuum Case

5.2.2. Material Case

5.2.3. Lossless Media: Eigenvalue Decomposition

5.2.4. Dispersive Media: Singular Value Decomposition

5.3. Estimates of the Eigenvalues and Singular Values in the Low Frequency Limit

5.4. Reduced Number of Degrees of Freedom in the Low Frequency Limit

5.5. Computation of Homogenized Parameters

5.5.1. Lossless Case

5.5.2. Dispersive Case

5.6. Results for Sample Structures

5.6.1. Laminated Media

5.6.2. Validity of Classical Homogenization

5.6.3. Results for a Chiral Structure

5.7. Conclusions

References

Appendix. The List of the Symbols and Abbreviations

Blurb

Diffraction gratings are one of the most popular objects of analysis in electromagnetic theory. The requirements of applied optics and microwave engineering lead to many new problems and challenges for the theory of diffraction gratings, which force us to search for new methods and tools for their resolution. In Modern Theory of Gratings, the authors present results of the electromagnetic theory of diffraction gratings that will constitute the base of further development of this theory, which meet the challenges provided by modern requirements of fundamental and applied science.

This volume covers:

• spectral theory of gratings (Chapter 1) giving reliable grounds for physical analysis of space-frequency and space-time transformations of the electromagnetic field in open periodic resonators and waveguides;
• authentic analytic regularization procedures (Chapter 2) that, in contradistinction to the traditional frequency-domain approaches, fit perfectly for the analysis of resonant wave scattering processes;
• parametric Fourier method and C-method (Chapter 3) oriented to the effective numerical analysis of transformation properties of periodic interfaces and multilayer conformal arrays;
• new rigorous methods for analysis of special-temporal transformations of electromagnetic field that are based on the construction and incorporation into the standard finite-difference computational schemes the so-called exact absorbing boundary conditions (Chapter 4);
• new solution variants to the homogenization problem (Chapter 5) – the central problem arising in the synthesis of metamaterials and metasurfaces;
• new physical and applied results (Chapters 2 to 5) about pulsed and monochromatic wave resonant scattering by periodic structures, including structures loaded on dielectric layers or chiral and left-hand medium layers, etc.

Modern Theory of Gratings is intended for researchers and postgraduate students in computational electromagnetics and optics, theoretical and applied radio physics. The material is also suitable for undergraduate courses in physics, computational physics and applied mathematics.