Quasi-analytical models for metamaterial homogenization

This work presents a quasi-analytical approach to the homogenization of metamaterials realized by the superposition of identical periodic planar surfaces. It is based on the definition of an equivalent admittance matrix for the single layer, combined with the application of the Bloch theory for the analysis of the periodically loaded equivalent transmission line modeling the layered structure. Different theoretical definitions of equivalence are discussed in connection with practical applications of the homogenization concept. It is shown that the uniqueness of the equivalent homogeneous medium depends on the final objective of the homogenization procedure, i.e. on the specific metamaterial behavior to be mimicked.