The Leontovich boundary conditions and calculation of effective impedance of inhomogeneous metal

Abstract

We bring forward rather simple algorithm allowing us to calculate the effective impedance of inhomogeneous metals in the frequency region where the local Leontovich (the impedance) boundary conditions are justified. The inhomogeneity is due to the properties of the metal or/and the surface roughness. Our results are nonperturbative ones with respect to the inhomogeneity amplitude. They are based on the recently obtained exact result for the effective impedance of inhomogeneous metals with flat surfaces. One-dimension surfaces inhomogeneities are examined. Particular attention is paid to the influence of generated evanescent waves on the reflection characteristics. We show that if the surface roughness is rather strong, the element of the effective impedance tensor relating to the p- polarization state is much greater than the input local impedance. As examples, we calculate: i) the effective impedance for a flat surface with strongly nonhomogeneous periodic strip-like local impedance; ii) the effective impedance associated with one-dimensional lamellar grating. For the problem (i) we also present equations for the forth lines of the Pointing vector in the vicinity of the surface.