Characterizing Metasurfaces/Metafilms: The Connection Between Surface Susceptibilities and Effective Material Properties

A metafilm is a type of metasurface, a two-dimensional equivalent of a metamaterial, and is essentially a surface distribution of electrically small scatterers arranged in a judiciously chosen pattern. In previous work, we have shown that the most appropriate way to characterize a metafilm is by its effective electric and magnetic surface susceptibilities, and we discussed methods for retrieving these surface susceptibilities. Nevertheless, some researchers have continued to characterize metasurfaces in terms of bulk effective material properties. In this letter, we first clarify sign conventions (and nomenclature) used for surface susceptibilities and correct sign errors in previous publications. We then discuss the connection between the surface susceptibilities of a metafilm and effective material properties of a thin material slab. The two subtle but important aspects discussed here are: 1) the interpretation of a thin material slab by its surface susceptibilities, and 2) the equating of a metafilm (which has its own unique surface susceptibilities) to a thin material slab with effective material properties.