Extending the Leontovich impedance approximation for electromagnetic fields at a dielectric – metal interface

The Leontovich approximate condition for electromagnetic fields at a dielectric – metal interface, valid for a small surface impedance $\zeta$, is extended to arbitrary values of $\zeta$, thus extending the applicability range of the impedance approach. The exact boundary condition obtained is expanded as an odd power series in $\zeta$, to reveal that the leading-order linear-in-$\zeta$ Leontovich condition differs only by terms $\sim\zeta^{3}$ from the exact equation — implying that not only linear terms but also those $\sim\zeta^{2}$ are correct in describing wave fields in this approximation. The impedance approximation thus turns out to be more accurate than its author himself believed. Approximations of different orders for polariton propagation and wave reflection at the interface between isotropic dielectrics and metals are error analyzed based on the extension obtained. For polariton theory, it is shown that the Leontovich approximation provides sufficient accuracy not only in the infrared but also all over the visible range. In the reflection problem, while reasonable over most of the visible region and over a wide range of incidence angles, this approximation fails in the short-wavelength large-incident-angle range, where it is necessary to go beyond the framework of the Leontovich approximation to substantially improve accuracy.