A Modification of the Hybrid Projection Method for Analysis of Doubly Periodic Structures with Inhomogeneous Magneto-Dielectric Elements

We consider the problem of plane electromagnetic wave scattering on two-dimensional periodic structures composed of magneto-dielectric elements, which are inhomogeneous in both longitudinal and transverse directions and arranged on a homogeneous magneto-dielectric substrate. A modification of the hybrid projection method is developed for numerical analysis of the structure with accounting for the feature of the elements of the latter. The method includes projection of the Maxwell equations for the fields in the structure on transverse vector orthonormal functions, projection matching of the fields on the boundaries of the region containing the elements of the structure, and application of one-dimensional finite-element method reducing the problem to a system of linear algebraic equations.