Analysis and optimization of matching two-dimensionally periodic dielectric structures with cone-shaped cavities

Abstract

The problem of scattering of plane electromagnetic waves by two-dimensionally periodic dielectric structures with cone-shaped cavities placed on a homogeneous dielectric substrate is considered. A modified hybrid projection method for solving this problem, which combines the coupled-wave method (incomplete Galerkin method), the projection field matching on domains’ boundaries, and the one-dimensional finite-element method, is proposed. The modified method enables one to avoid the use of the excessive number of unknown expansion coefficients, typical for the previous versions. The method is used for calculating the effective permittivity of a dielectric layer of finite thickness with cylindrical holes and for optimizing the parameters of conical cavities providing the matching of a dielectric half-space for various incidence angles.