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.…