Retrieval of metamaterial constitutive parameters through a generalization of the Bloch theory

In this work a novel method for the retrieval of the constitutive parameters of metamaterials is presented. The proposed approach, which is well suited for the important class of metamaterials consisting of a stack of planar periodic surfaces, accounts for both spatial and time dispersivity. The homogenization procedure is new and systematic, and it provides a complete characterization of the effective homogenous medium by retrieving all the entries of both the permittivity and the permeability tensors. Numerical results are presented to demonstrate how the proposed approach can be used to obtain dispersion relations and an accurate prediction of the scattering from a finite metamaterial slab.