Generalization of the Leontovich approximation for electromagnetic fields on a dielectric — metal interface

摘要

The Leontovich approximate condition for electromagnetic fields at the dielectric–metal interface, valid for a small surface impedance ξ, is generalized to the case of arbitrary magnitudes of ξ, which provides a broader range of applicability of the impedance approach. The exact boundary condition found is expanded in a series of odd powers of the parameter ξ. Being linear in ξ, the Leontovich condition differs from the exact equation in main order only by terms～ξ~3. Thus, in describing wave fields in this approximation, it is not only linear terms that prove to be correct, but also terms of order ξ~2. The accuracy of an impedance approximation turns out to be higher than its developer himself believed. On the basis of the generalization made, the errors of differentorder approximations are analyzed for the descriptions of polariton propagation and wave reflection near the interface between an isotropic dielectric and metal subinedia. It is shown that in the polariton theory the Leontovich approximation provides a sufficiently high accuracy not only in the infrared range, but also in the whole visible range. In the reflection problem, this approximation is reasonable in most of the visible range within a wide interval of the angles of incidence; however, it is inapplicable when simultaneously the waves are short and the angles of incidence are large. In this domain, the accuracy of the description may be substantially raised only beyond the framework of the Leontovich approximation.