Electromagnetic wave scattering by rectangular-cell double-periodic magneto-dielectric gratings

The problem of electromagnetic waves scattering by a double-periodic grating is solved by the new method based on the rigorous volume integro-differential equations. The Galerkin method is applied to reduce this volume integro-differential equation to set of second-order differential ones with constant coefficients in functionals. Numerical solution was obtained for the simplest double-periodic magneto-dielectric rectangular-cell grating as an example of a structure with translational symmetry