Electrodynamics of spoof plasmons in periodically corrugated waveguides

States of the electromagnetic field confined near a periodically corrugated surface of a perfect conductor, spoof surface plasmon polaritons (SSPP), are approached systematically based on the developed adaptation of the mode matching technique to the transfer matrix formalism. Within this approach, in the approximation of narrow grooves, systems with arbitrary transversal structure can be investigated straightforwardly, thus lifting the restrictions of the effective medium description and usual implementations of mode matching. A compact expression for the SSPP coupling parameter accounting for the effect of higher Bloch modes is found. The results of the general analysis are applied for studying the effect of dielectric environment on SSPP spectra. It is shown that the effective SSPP plasma frequency is unaffected by the dielectric constant of the medium outside of the grooves and the main effect of sufficiently wide dielectric slabs covering the corrugated surface is described by simple rescaling of the maximal value of the Bloch wavenumber and the coupling parameter. Additionally, in the case of a thin dielectric layer, it is shown that SSPP are sensitive to variation of the thickness of the layer on the sub-wavelength scale.