Non-asymptotic homogenization of 3-D periodic structures

Abstract

A two-scale non-asymptotic homogenization procedure is shown to yield very accurate results for transmission and reflection of electromagnetic waves by 3D periodic structures. On the fine scale, information about the fields is carried by a basis of Bloch waves traveling in different directions; the corresponding coarse-scale basis functions are generalized plane waves. The coarse-scale fields are constructed in such a way that (i) Maxwell's interface boundary conditions and (ii) dispersion relations in the bulk are rendered as accurately as possible. Illustrative examples are presented for 3D dielectric and plasmonic structures.