Surface electromagnetic waves supported by nano conducting layers with inhomogeneities in the conductivity profile

Abstract

Conducting interfaces and nano conducting layers can support surface electromagnetic waves. Uniform charge layers of non-zero thickness and their asymptotic behavior toward conducting interfaces of infinitely small thicknesses, where the thin charge layer is modeled via a surface conductivity σs, are already studied. Here, the possible effects of inhomogeneity in the conductivity profile of the thin conducting layers are investigated for the first time and a new approximate yet accurate enough analytical formulation for mode extraction in such structures is given. In order to rigorously analyze the structure and justify the proposed approximate formulation, the Galerkin’s method with Legendre polynomial basis functions is applied, i.e. the transverse electric field for the TE polarized surface waves and the transverse magnetic field for the TM polarized surface waves are each expanded in terms of Legendre polynomials and then each eigenmode; subjected to appropriate boundary conditions, is sought in the complete space spanned by Legendre basis functions. The proposed approximate solution is then proved to be accurate. In particular, sinusoidal fluctuations are introduced into formerly uniform conductivity profiles and it is numerically demonstrated that surface electromagnetic waves supported by nano conducting layers are not much sensitive to the very shape of conductivity profiles.