A homogenization technique for obtaining generalized sheet transition conditions for an arbitrarily shaped coated wire grating

Using a multiple-scale homogenization method, we derive generalized sheet transition conditions (GSTCs) for an arbitrarily shaped coated wire grating. The parameters in these GSTCs are interpreted as effective electric and magnetic surface susceptibilities and surface porosities of the wire grating. We give expressions for determining these surface parameters for any arbitrarily shaped grating. We show that these GSTCs are a generalized form of the boundary conditions derived earlier by Wainstein and Sivov, who analyzed the case of symmetric, uncoated wire gratings. This work is also a first step in developing GSTCs for more general types of structures such as metasurfaces, metafilms, and metascreens.