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.

The authors hope that reader will find that discussed physical and applied results are presented in an illuminating way. Thus, for example, some figures in Chapter 4 are accompanied by .exe-files with self-playing animation. They allow to watch in dynamics the space-time transformations of electromagnetic field close to finite and infinite periodic structures. The archive with these files is open for downloading at http://www.ire.kharkov.ua/downloads/Figures_EXE_Files.zip

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 authors are representatives of a series of large European scientific and educational centers: Royal Institute of Technology, Stockholm, Sweden (Staffan Ström, the editor and the co-author of Chapter 4); Blaise Pascal University, Clermont-Ferrand, France (Jean Chandezon and Gerard Granet – Chapter 3); Usikov Institute of Radio Physics and Electronics of the National Academy of Sciences of Ukraine, Kharkov, Ukraine (Petr Melezhik – Sections 2.2, 2.4, 2.5; Anatoliy Poyedinchuk – Sections 2.1, 2.2, 2.4, 2.5, 3.6; Yuriy Sirenko – the editor, the author and co-author of Chapters 1, 4 and Section 2.3; Yuriy Tuchkin – Sections 2.1, 2.6; and Nataliya Yashina – Chapter 4 and Sections 2.4, 2.5, 3.6); Lund University, Lund, Sweden (Daniel Sjöberg – Chapter 5).

In this book, they are united by their profound interest in periodic structures, an area whose study has always been associated with burning scientific and engineering problems for the last one and a half hundred years.