Springer Optical Sciences

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