On the calculation of ohmic losses at the metallic surface with sharp edges

Abstract

We discuss the applicability of the perturbation theory in electrodynamic problems where the local Leontovich (the impedance) boundary conditions are used to calculate the ohmic losses at the metallic surface. As an example, we examine a periodic grating formed from semi- infinite rectangular plates exposed to the s-polarized electromagnetic wave. Two different ways for calculation of the ohmic losses are presented: (i) the calculation of the reflection coefficient obtained with the aid of the perturbation theory (the impedance is the small parameter) and (ii) the direct calculation of the energy flux through the metallic surface, when to get the answer only the tangential magnetic field at the surface of a perfect conductor of the same geometry has to be known. The results (i) and (ii) differ noticeably. The same difficulty is inherent in all the problems where the metallic surface has rectangular grooves. We show that the standard first order perturbation theory is not applicable since beginning from a number n even the first corrections to the modal functions $ϕ_{n}$ used to calculate the fields, are of the same order as the zero order modal functions (the impedance is equal to zero). Basing on the energy conservation law we show that the accurate value for the ohmic losses is obtained with the aid of the approach (ii).