title: Homogenization of Maxwell's equations in periodic composites: boundary effects and dispersion relations.
abstract: We consider the problem of homogenizing the Maxwell equations for periodic composites. The analysis is based on Bloch-Floquet theory. We calculate explicitly the reflection coefficient for a half space and derive and implement a computationally efficient continued-fraction expansion for the effective permittivity. Our results are illustrated by numerical computations for the case of two-dimensional systems. The homogenization theory of this paper is designed to predict various physically measurable quantities rather than to simply approximate certain coefficients in a partial differential equation.
authors.affiliation: Department of Radiology and Graduate Group in Applied Mathematics and Computational Science, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA. vmarkel@mail.med.upenn.edu
authors.forename: Vadim A
authors.initials: VA
authors.lastname: Markel
authors.forename: John C
authors.initials: JC
authors.lastname: Schotland
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004574:Electromagnetic Fields; D008962:Models, Theoretical