Modern Theory of Gratings [recurso electrónico] : Resonant Scattering: Analysis Techniques and Phenomena / edited by Yuriy K. Sirenko, Staffan Ström.

Preface -- Basic Statements -- The Formulation of Boundary Value and Initial Boundary Value Problems in the Theory of Diffraction Gratings -- The General Physical Picture: Main Definitions and Consequences from Conservation Laws and Reciprocity Theorems -- The Spectral Theory of Gratings -- Analytic Regularization Methods -- General Description and Classification of the Analytic Regularization Methods: History, Provenance and Survey -- The Riemann-Hilbert Problem Method and its Generalization -- Inversion of Convolution-Type Matrix Operators in Equation Systems of the Mode Matching Technique -- Electromagnetic Wave Diffraction by Gratings in Presence of a Chiral Isotropic Medium -- Resonant Scattering of Electromagnetic Waves by Gratings and Interfaces between Anisotropic Media and Metamaterials -- Diffraction of Quasi-Periodic Waves by Obstacles with Cylindrical Periodical Wavy Surfaces -- C-Method: From the Beginnings to Recent Advances -- Introduction -- Classical C-Method -- Diffraction of a Plane Wave by a Modulated Surface Grating -- Adaptive Spatial Resolution -- Curved Strip Gratings -- Several Issues of Spectral Theory Relevant to C-method Formalism -- Modeling and Analysis of Transients in Periodic Structures: Fully Absorbing Boundaries for 2-D Open Problems -- Infinite Gratings: Exact Absorbing Conditions for Plane Parallel Floquet Channel -- Finite Gratings: Exact Conditions for Rectangular Artificial Boundaries -- Time-Domain Methods in the Study of Gratings and Compact Grating Structures as Open Resonators -- Infinite Gratings: Resonant Wave Scattering -- 2-D Models of Compact Grating Structures: Spatio-Frequency and Spatio-Temporal Field Transformations -- Finite Scale Homogenization of Periodic Bianisotropic Structures -- Fundamental Ideas -- Some Mathematical Properties of Maxwell’s Operator -- Estimates of the Eigenvalues and Singular Values in the Low Frequency Limit -- Reduced Number of Degrees of Freedom in the Low Frequency Limit -- Computation of Homogenized Parameters -- Results for Sample Structures -- Conclusions -- References -- Appendix. The List of the Symbols and Abbreviations.

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.

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