Equivalent boundary conditions for a perfectly conducting periodic surface with a cover layer

Using the method of homogenization, effective electromagnetic properties for a two-dimensional, perfectly conducting, periodic rough surface with a thin periodic cover layer are derived. This allows for the development of an equivalent boundary condition for the "effective" fields at such a surface. It is shown that the coefficients in this equivalent boundary condition can be interpreted as electric and magnetic polarizability densities. We apply this boundary condition to calculate the reflection coefficient of H- and E-polarized plane waves incident at a rough, perfectly conducting surface. The reflection coefficients derived here are compared with previous results from the literature for surfaces with no cover layer, demonstrating the accuracy of the new equivalent boundary condition. We also obtain previously known equivalent boundary conditions for a flat perfectly conducting plane with a thin cover layer as a special case of our result. This work is a first step in the derivation of generalized impedance-type boundary conditions for conducting rough interfaces (to be published separately).