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Homogenization of Maxwell's equations in periodic composites: boundary effects and dispersion relations
Vadim A Markel1, John C Schotland
1Department of Radiology and Graduate Group in Applied Mathematics and Computational Science, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA. vmarkel@mail.med.upenn.edu
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.
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