Comparison of different numerical models for volumetric metamaterials

In this paper we present a comparison of two different techniques for the modeling of volumetric metamaterials realized by stacked periodic surfaces, where the unit cell may contain a patch or a slot element. Both the techniques considered are based on the definition of an equivalent admittance for the single layer, however they differ in the approach used to derive the effective parameters of the metamaterial. In a first case, electric and magnetic polarizabilities of the unit cell are extracted and then substituted into the Clausius-Mossotti equations to find the bulk effective permittivity and permeability. In the second case, the interactions between adjacent layers are taken into account by exploiting the Bloch theory and the effective parameters are defined by imposing that the homogenized medium supports the same modal structure of the volumetric metamaterial.