Periodic surface of materials with single and double negative parameters: absorption resonances

Here, we present the study of electromagnetic waves interaction with material with single and double negative parameters having periodic surface, based on rigorous solution to corresponding boundary value problem. It is well known and proved by numerous cases that the most profound and efficient study of electromagnetic waves interaction with objects and especially the objects possessing resonant properties, can be performed by the interactive and complementary study of diffraction and spectral problem solution. Here, we use the solution to diffraction problem for periodic surface obtained by C formalism associated with regularization that is described. For the spectral problem solution the analytical continuation (within the frames of the theory of analytic functions) of the solutions to diffraction problem for the boundary between two dielectric media into the domain of complex valued frequencies is considered. The reason and benefits of such continuation consist in the fact that singularities (poles, branching points and etc.) of the diffraction problem solution, appearing after such continuation into the domain of complex frequencies, define and predetermine completely the diffraction field features, obtained in the physical (at real frequencies) domain of parameters.