Homogenization of waveguide-based metamaterials by energy averaging

Abstract

We develop a homogenization technique based on electromagnetic energy averaging that is suitable for waveguide-based metamaterials. We first derive general homogenization formulations using Maxwell's equations and the Poynting theorem, and then apply the technique to a common waveguide-based metamaterial implementation consisting of layered media, yielding simple expressions for the effective permittivity and effective permeability of the waveguide based on energy-density-weighted averages of the local permittivity of the layers. Examples are presented in which we evaluate the effective parameters of ultrathin metal-clad waveguides sustaining a single surface-plasmon polariton mode, using realistic material parameters and geometries that have been recently explored in the literature.