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 B₀ being parallel to the interfaces and the waves propagating in a direction perpendicular to B₀ (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 qz({ω}) has been found in the nonretarded limit, valid for {ω}/c{}{}qz{}{}1/d, where d is the thickness of the film. In the limit {}qz{}{→}{∞} there are two surface modes whose limiting frequencies are given by εzz({ω})±{}iεyz({ω}) sgn(qz)=-εⱼ, where εᵢⱼ({ω}) is an element of the dielectric tensor of the semiconductor, and ε₁ and ε₃ are the dielectric constants of the bounding media.Moreover, in the nonretarded limit as B₀ is increased, the upper mode changes its behavior from monotonically decreasing to monotonically increasing; for a simple model of εᵢⱼ({ω}) this occurs at a critical value of the cyclotron-frequency to plasma-frequency ratio ωc/ωₚ=[εL(εL²/εⱼ²-1)]^1-2, where εL is the background dielectric constant and, for qz>0 (qz0) 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 {β}d{}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.