Nonlocal effective medium model for multilayered metal-dielectric metamaterials

We study layered metal-dielectric structures, which can be considered as a simple example of nanostructured metamaterials. We analyze the dispersion properties of such structures and demonstrate that they show strong optical nonlocality due to excitation of surface plasmon polaritons. We derive a model of a nonlocal effective medium for describing the effects of strong spatial dispersion in the multilayered metal-dielectric metamaterials. We obtain analytical expressions for the components of the effective permittivity tensor which depend on the wave vector and reveal that spatial dispersion effects exist in both directions across and along the layers.