Impedance boundary conditions and effective surface impedance of inhomogeneous metal

Abstract

We present nonperturbative results for the effective impedance of strongly inhomogeneous metals valid in the frequency region in which the local impedance (Leontovich) boundary conditions are applicable. The inhomogeneity is due to the properties of the metal and/or the surface roughness. If the surface of an inhomogeneous metal is flat, the effective surface impedance associated with the reflection of an averaged electromagnetic wave is equal to the value of the local impedance tensor averaged over the surface inhomogeneities. This result is exact within the accuracy of the Leontovich boundary conditions. As an example, we calculate the effective impedance for a flat surface with a strongly inhomogeneous periodic strip-like local surface impedance. For strongly rough surfaces a similar approach allows us to calculate the ohmic losses and the shift of the reflected wave, if we know the magnetic vector in the vicinity of the perfect conductor of the same geometry. One-dimensional rough surfaces are examined. Particular attention is paid to the influence of the evanescent waves generatedand the difference between the elements of the effective impedance tensor relating to different polarizations of the incident wave. The effective impedance tensor associated with a one-dimensional lamellar grating is calculated.