A discussion on the interpretation and characterization of metafilms/metasurfaces: The two-dimensional equivalent of metamaterials

A metafilm (also referred to as a metasurface) is the surface equivalent of a metamaterial. More precisely, a metafilm is a surface distribution of suitably chosen electrically small scatterers. Metafilms are becoming popular as an alternative to full three-dimensional metamaterials. Unfortunately, many papers in the literature present incorrect interpretations and mischaracterizations of these metafilms. In fact, some of the characterizations presented in the literature result in non-unique parameters for a uniquely defined metafilm. In this paper we discuss an appropriate interpretation and characterization of metafilms and present a correct manner to characterize a metafilm. Additionally, we illustrate the error that results from an incorrect characterization of metafilms. We present various examples to emphasize these points. Finally we present a retrieval approach for determining the uniquely defined quantities (the electric and magnetic susceptibilities of its constituent scatterers) that characterize a metafilm.