Homogenization Processes and Retrieval of Equivalent Constitutive Parameters for Multisurface-Metamaterials

Different procedures are presented for the retrieval of effective constitutive parameters of metamaterial structures realized by multilayer lossless periodic structures. These structures are modeled as Floquet-wave based multiport networks connected by pieces of transmission lines. A generalized Bloch method is then adopted to find the dominant modes of the volumetric homogenized metamaterial. Starting from the results of this analysis, the constitutive tensors of an equivalent homogeneous material are defined. Different levels of equivalence are defined, denoted as "external equivalence," "dispersion equivalence," "single-mode equivalence," and "double-mode equivalence." The corresponding homogenization processes are characterized by an increasing level of completeness (in the description of the metamaterial behavior) and of sophistication (concerning the processing of the full-wave analysis outcomes). The defined homogenization procedure accounts for dispersion in time (frequency) and space (wavenumber), as well as for anisotropy.