Generalized Sheet Transition Conditions for a Metascreen-A Fishnet Metasurface

We used a multiple-scale homogenization method to derive generalized sheet transition conditions (GSTCs) for electromagnetic fields at the surface of a metascreen-a metasurface with a "fishnet" structure. These surfaces are characterized by periodically spaced arbitrary-shaped apertures in an otherwise relatively impenetrable surface. The parameters in these GSTCs are interpreted as effective surface susceptibilities and surface porosities, which are related to the geometry of the apertures that constitute the metascreen. We emphasize the subtle but important difference between the GSTCs required for metascreens and those required for metafilms [a metasurface with a "cermet" structure, i.e., an array of isolated (nontouching) scatterers]. Finally, we demonstrate the validity of the surface parameters derived here by comparing results for metascreens composed of either circular or square apertures with those of other approaches.