Impedance-type boundary conditions for a periodic interface between a dielectric and a highly conducting medium

Using the homogenization method, we derive a generalized impedance-type equivalent boundary condition for the electromagnetic (EM) field at a two-dimensional (2-D) periodic highly conducting rough surface with small-scale roughness. The results obtained in this paper generalize ones obtained preciously for the case of a perfectly conducting rough surface. We will show that the coefficients in this equivalent boundary condition can be interpreted in terms of electric and magnetic polarizability densities. We also show that when the roughness dimensions are small compared to a skin depth of the conducting region (a smooth interface), the generalized impedance boundary condition given here reduces to the standard Leontovich (1948, 1985) condition. Results for the reflection coefficient of a plane wave incident onto a 2-D conducting interface are presented. We show the importance of the boundary-layer fields (as used in this study) over that of classical methods when calculating the reflection coefficient from a highly conducting rough interface. This work will lead to an analysis of the effects of surface roughness on power loss in MIMIC circuits.