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Abstract-The paper is devoted to the study of the interaction of the electromagnetic waves with the structure composed of perfectly conducting strip grating, situated on the plane boundary of metamaterial with effective permittivity, depending on the frequency of the wave of excitation. The rigorous solution to the relevant diffraction boundary value problem is developed. The extensive numerical experiments, performed with a help of corresponding algorithm constructed, allowed to establish several regularities in the complicated process of interaction of electromagnetic waves with grating on dispersive metamaterial. The efficient association of analytical and numerical study has provided the understanding of the nature of resonant phenomena appearing in this process.

Abstract-The goal of the present paper is two folded. The first, the methodological one, is the complementation of well established in diffraction theory of gratings C method with certain elements of spectral theory and the development of interactive numerical algorithm that made feed back conjunction between diffraction and spectral problems. As a natural result the second goal appeared: the appearing of such tool for numerical experiments resulted in profound qualitative and quantitative study of rather peculiar phenomena in resonant scattering from periodic surface. Special attention has been paid to the investigation of electromagnetic waves diffraction from periodic boundaries of material with single and double negative parameters.

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The extension of C method, combined with idea of Tikhonov's regularization is proposed. The regularizing algorithm for numerical solution of electromagnetic wave diffraction by the boundary of dielectric media is developed. This algorithm is based on the solution of the system linear algebraic equations of C method as subject of regularizing method of A. N. Tikhonov. The numerical calculations of scattered field in the case of E-polarization are presented. The efficiency and reliability of the method for the solution of the problems of boundary shape reconstruction have been proved and demonstrated numerically for several situations.