Frequency-dependent impedance and surface waves on the boundary of a stratified dielectric medium

We analyse waves propagating along the interface between half-spaces filled with a perfect dielectric and a Lorentz material. We show that the corresponding interface condition leads to a generalization of the classical Leontovich condition on the boundary of a dielectric half-space. We study when this condition supports propagation of (dispersive) surface waves. We derive the related dispersion relation for waves along the boundary of a stratified half-space and determine the relationship between the loss parameter, frequency and wavenumber for which interfacial waves exist. This article is part of the theme issue 'Modelling of dynamic phenomena and localization in structured media (part 1)'.