Effective Dielectric Response of Metamaterials

TL;DR

This paper develops a homogenization method to determine the frequency-dependent dielectric response of periodic metamaterials, revealing tunable anisotropic behaviors and low reflectance at specific frequencies.

Contribution

It introduces a formalism for calculating the macroscopic dielectric response of metamaterials with arbitrary shapes and structures, including novel insights into anisotropic and resonant behaviors.

Findings

Anisotropic dielectric response varies with frequency.

Low reflectance achieved at intermediate frequencies.

Behavior tunable through geometrical design.

Abstract

We use a homogenization procedure for Maxwell's equations in order to obtain in the local limit the frequency ($\omega$) dependent macroscopic dielectric response $\epsilon^M(\omega)$ of metamaterials made of natural constituents with any geometrical shape repeated periodically with any structure. We illustrate the formalism calculating $\epsilon^M(\omega)$ for several structures. For dielectric rectangular inclusions within a conducting material we obtained a very anisotropic response which changes along one direction from conductor-like at low $\omega$ to a resonant dielectric-like at large $\omega$, attaining a very small reflectance at intermediate frequencies unrelated to surface plasmon excitation and which can be tuned through geometrycal tayloring. A similar behavior is obtained for other shapes close to the percolation threshold.