Homogenization of Maxwell's equations in periodic composites

TL;DR

This paper develops a homogenization method for Maxwell's equations in periodic composites using Bloch-Floquet theory, providing explicit formulas and efficient computations for effective permittivity, with numerical validation.

Contribution

It introduces a new homogenization approach that predicts measurable quantities directly, including a continued-fraction expansion for effective permittivity.

Findings

Explicit reflection coefficient calculation for half-space

Efficient continued-fraction expansion for permittivity

Numerical validation in 2D systems

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 PDE.