A systematic approach to determining the constitutive parameters of metamaterials in the context of transformation electromagnetics

A novel systematic method for the retrieval of the constitutive electromagnetic parameters of metamaterials is presented. The analysis is focused on the important class of metamaterials consisting of a stack of planar periodic structures. A complete characterization of the effective medium is obtained by retrieving all the components of the permeability and permittivity tensors and accounting for both spatial and time dispersion. The capability of characterizing the anisotropy is especially useful in the implementation via metamaterials of the results of transformation electromagnetics, which requires a full control of all the components of the constitutive dyadic parameters. Numerical results are presented to demonstrate how the retrieved parameters can be used to obtain an accurate prediction of the scattering from a finite metamaterial slab.