Electromagnetic characteristics of a doubly-periodic magnetodielectric layer bounded by two media (low frequency approximation)

The problem of electromagnetic wave propagation in a doubly-periodic magnetodielectric layer bounded by two uniform infinite media is solved by a new method based on rigorous integro-differential equations. The Galerkin method is applied to reduce these equations to a set of second-order differential ones with constant coefficients in functionals. An analytic solution is given to the problem of propagation of low-frequency electromagnetic wave along and through the layer with arbitrary distribution of dielectric permittivity and magnetic permeability over the period. Based on such "one-mode" approximation we derive simple expressions for the propagation constants and fields in all the regions