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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.

The principal goal of the book is to describe new accurate and robust algorithms for open resonant structures with substantially increased efficiency. These algorithms allow the extraction of complete information with estimated accuracy concerning the scattering of transient electromagnetic waves by complex objects. The determination and visualization of the electromagnetic fields, developed for realistic models, simplify and significantly speed up the solution to a wide class of fundamental and applied problems of electromagnetic field theory. The book presents a systematic approach to the study of electromagnetic waves scattering which can be introduced in undergraduate/postgraduate education in theoretical and applied radiophysics and different advanced engineering courses on antenna and wave-guide technology. On a broader level, the book should be of interest to scientists in optics, computational physics and applied mathematics.