Modern Theory of Gratings, 2010
Resonant Scattering: Analysis Techniques and Phenomena
Springer Series in Optical Sciences Series, Vol. 153

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 theanalysis 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.

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 HomogenizedParameters.- Results for Sample Structures.- Conclusions.- References.- Appendix. The List of the Symbols and Abbreviations.