Homogenization of Maxwell's equations in periodic composites: boundary effects and dispersion relations.

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.