The paper is focused at the study resonant phenomena arising in the process of electromagnetic waves interaction with metamaterials with periodic surface or with grating. Wide range of numerical experiments is performed on the base of accurate solution to boundary value problems. The peculiarities of diffraction characteristics and eigen waves and eigen frequencies in dispersive and anisotropic media have been revealed. The results, obtained in the study, have to help the understanding of the nature of diverse type of electromagnetic waves resonant transformation by the periodic surface with/of metainaterial.
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