Khokholkov V. Mathematical models and computing methods for solution of plane linearly polarized electromagnetic wave diffraction problem.

The thesis is dedicated to improving the known mathematical models and to creating new ones to model the phenomenon of scattering a plane electromagnetic wave over one-dimensional structures both in isotropic and gyrotropic media. An investigation has been carried out into the status of the mathematical modeling of the electromagnetic wave scattering phenomenon. An analysis has been made of available mathematical models and methods aimed at investigating this problem. The necessity has been substantiated to develop a novel method that would combine classical and modern approaches to enable computer modeling. On the basis of the known method of redecomposition a new method has been developed to calculate diffraction spectra of the basic (key) model of planar periodic structures, namely, gratings made of perfectly conducting rectangular bars. This novel method has been shown as being more effective, more accurate and faster than other methods. Based on this novel method and with the aid of symbol algebra instruments implemented in Maple Х, new algorithms have been created to make possible the transi-tion from a continuous model to a discrete model. With the aid of the developed algorithms, an investigation has been made into spectral properties of a grating made of infinitely thin wires. So far, these properties have not yet been completely studied, important as such a grating is in the theory of electromagnetic wave scattering over periodic structures. Based of the above algorithms, a solution has been first obtained in the rigorous formulation to the problem of scattering a plane E-polarized wave that is obliquely falling onto a grating made of rectangular bars at the interface between an isotropic medium and a transversely magnetized ferrite. Non-reciprocity of the properties has been shown to take place, even when such a wave is orthogonally falling onto the grating with the ferrite. A software package has been created to enable a comprehensive numerical and computer modeling of the scattering of electromagnetic waves over one-dimensionally periodic rectangular gratings. This software makes it possible to de-termine amplitude spectra of diffraction harmonics and to plot diagrams, using the conditions of phase-matching and surface resonance. The obtained results can be used in methodic developing to measure ferrite magnetized to total saturation. Key words: scattering, diffraction grating, computer modeling, system of linear equations, automation of symbol transformations, polarization, resonant wave passage, gyrotropic medium, ferrite, method.