Magnetoplasmons in thin films in the Voigt configuration

We have studied the magnetoplasma modes of a thin film, bounded by two dissimilar dielectrics, the applied magnetic field ${\mathrm{B}}_{0}$ being parallel to the interfaces and the waves propagating in a direction perpendicular to ${\mathrm{B}}_{0}$ (Voigt geometry). On the basis of local theory we have derived the exact dispersion relation that governs the propagation characteristics of both surface and bulk (or waveguide) modes. These waves are p (or TM) polarized and exhibit nonreciprocity with respect to their direction of propagation. An analytic solution for the propagation constant ${q}_{z}$(\ensuremath{\omega}) has been found in the nonretarded limit, valid for \ensuremath{\omega}/c\ensuremath{\ll}\ensuremath{\Vert}${q}_{z}$\ensuremath{\Vert}\ensuremath{\ll}1/d, where d is the thickness of the film. In the limit \ensuremath{\Vert}${q}_{z}$\ensuremath{\Vert}\ensuremath{\rightarrow}\ensuremath{\infty} there are two surface modes whose limiting frequencies are given by ${\ensuremath{\epsilon}}_{\mathrm{zz}}$(\ensuremath{\omega})\ifmmode\pm\else\textpm\fi{}i${\ensuremath{\epsilon}}_{\mathrm{yz}}$(\ensuremath{\omega}) sgn(${q}_{z}$)=-${\ensuremath{\epsilon}}_{j}$, where ${\ensuremath{\epsilon}}_{\mathrm{ij}}$(\ensuremath{\omega}) is an element of the dielectric tensor of the semiconductor, and ${\ensuremath{\epsilon}}_{1}$ and ${\ensuremath{\epsilon}}_{3}$ are the dielectric constants of the bounding media.Moreover, in the nonretarded limit as ${\mathrm{B}}_{0}$ is increased, the upper mode changes its behavior from monotonically decreasing to monotonically increasing; for a simple model of ${\ensuremath{\epsilon}}_{\mathrm{ij}}$(\ensuremath{\omega}) this occurs at a critical value of the cyclotron-frequency to plasma-frequency ratio ${\ensuremath{\omega}}_{c}$/${\ensuremath{\omega}}_{p}$=[${\ensuremath{\epsilon}}_{L}$(${\ensuremath{\epsilon}}_{L}^{2}$/${\ensuremath{\epsilon}}_{j}^{2}$-1)${]}^{1\ensuremath{-}2}$, where ${\ensuremath{\epsilon}}_{L}$ is the background dielectric constant and, for ${q}_{z}$>0 (${q}_{z}$0) the correct choice is j=3 (j=1). Then, for a given propagation direction, the upper surface mode degenerates into a horizontal line, i.e., the corresponding group velocity vanishes. We have also applied to the general dispersion relation a thin-film approximation \ensuremath{\beta}d\ensuremath{\ll}1. This enables us to find an analytic solution in two cases: (1) a very thin semiconducting overlayer on a metallic substrate, giving rise to a splitting in the spectrum in the vicinity of the hybrid cyclotron-plasmon frequency with the creation of a gap; (2) a very thin, unsupported, magnetoplasma film in which case we find four polariton branches.