Averaged transition conditions for electromagnetic fields at a metafilm

This paper derives generalized sheet transition conditions (GSTCs) for the average electromagnetic fields across a surface distribution of electrically small scatterers characterized by electric and magnetic polarization densities. We call such an arrangement of scatterers a metafilm-the two-dimensional (2-D) equivalent of a metamaterial. The derivation is based on a replacement of the discrete distribution of scatterers by a continuous one, resulting in a continuous distribution of electric and magnetic polarization densities in the surface. This is done in a manner analogous to the Clausius-Mossotti-Lorenz-Lorentz procedure for determining the dielectric constant of a volume distribution of small scatterers. The result contains as special cases many particular ones found throughout the literature. The GSTCs are expected to have wide application to the design and analysis of antennas, reflectors, and other devices where controllable scatterers are used to form a smart surface.