Effective medium theory of negative index composite metamaterials

TL;DR

This paper develops an effective medium theory for negative index composite metamaterials, revealing how their homogenization depends on geometry and the harmonic mean of dielectric constants, leading to abrupt property variations.

Contribution

It introduces a novel approach to homogenizing negative index metamaterials by relating it to 1D single negative stacks and analyzing the harmonic mean of dielectric constants.

Findings

Homogenization depends on the harmonic mean of dielectric constants.

Sensitivity to geometrical parameters causes abrupt variations in properties.

The theory explains the role of layer arrangement in negative index behavior.

Abstract

In the homogenization of composite metamaterials the role played by the relative positions of the wires and resonators is not well understood, though essential. We present a general argument which shows that the homogenization of such metamaterials can be seen as the homogenization of 1D single negative stacks. The sensitivity to the geometrical parameters is due to the fact that light sees the harmonic mean of the dielectric constant when propagating parallel to the layers. Since the dielectric constant is not positive definite the harmonic mean is not bounded and presents abrupt variations. We discuss applications of this remarkable phenomenon.