A Homogenization Technique for Obtaining Generalized Sheet-Transition Conditions for a Metafilm Embedded in a Magnetodielectric Interface

Using the multiple-scale homogenization method, we derive generalized sheet-transition conditions for electromagnetic fields at the surface of a metafilm. The scatterers that compose the metafilm are of arbitrary shape and are embedded between two different magnetodielectric media. The parameters in these boundary conditions are interpreted as effective electric and magnetic surface susceptibilities, which themselves are related to the geometry of the scatterers that constitute the metafilm.