Effective boundary conditions for rough surfaces with a thin cover layer

We present an expression for an effective boundary condition for a rough periodic surface with a thin cover layer. This boundary condition was derived from an asymptotic technique known as homogenization. It is shown that the coefficients in this effective 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 on a rough perfectly conducting surface. The reflection coefficients obtained here are compared to results in the literature, which demonstrate the accuracy of the effective boundary condition. We also specialize our result to obtain an effective boundary condition for a flat perfectly conducting plane with a thin cover layer.