Effective Dielectric Response of Metamaterials

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.

16 pages 7 figures. Accepted in Phys. Rev. B (2009-06-08)