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 epsilon(M)(ij)(omega) of metamaterials made of a matrix with inclusions of any geometrical shape repeated periodically with any lattice structure. We illustrate the formalism calculating epsilon(M)(ij)(omega) for several structures. For dielectric rectangular inclusions within a conducting material we obtain an anisotropic response that may change from conductorlike at low omega to dielectriclike with resonances at large omega, 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.