We present a very efficient recursive method to calculate the effective optical response of nanostructured metamaterials made up of particles with arbitrarily shaped cross sections arranged in periodic two-dimensional arrays. We consider dielectric particles embedded in a metal matrix with a lattice constant much smaller than the wavelength. Neglecting retardation our formalism allows factoring the geometrical properties from the properties of the materials. If the conducting phase is continuous the low frequency behavior is metallic. If the conducting paths are nearly bloqued by the dielectric particles, the high frequency behavior is dielectric. Thus, extraordinary-reflectance bands may develop at intermediate frequencies, where the macroscopic response matches vacuum. The optical properties of these systems may be tuned by adjusting the geometry.Sketch of a nanostructured metamaterial slab with a dielectriclike or metallic-like behavior depending on the frequency of the incoming light.

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