Effective optical response of metamaterials

We use a homogenization procedure for Maxwell's equations in order to obtain in the local limit the frequency-dependent macroscopic dielectric-response tensor ? ij M (?) of metamaterials made of a matrix with inclusions of any geometrical shape repeated periodically with any lattice structure. We illustrate the formalism calculating ? ij M (?) for several structures. For dielectric rectangular inclusions within a conducting material we obtain an anisotropic response that may change from conductorlike at low ? to dielectriclike with resonances at large ?, attaining a very small reflectance at intermediate frequencies which can be tuned through geometrical tailoring. A simple explanation allowed us to predict and confirm similar behavior for other shapes, even isotropic, close to the percolation threshold. 2009 The American Physical Society