Magnetoplasma modes in thin films in the Faraday configuration.

Abstract

We have undertaken a theoretical study of magnetoplasma waves in a thin, semiconducting film bounded in general, by dissimilar dielectric or conducting media. The applied magnetic field and the direction of propagation of the wave are parallel to the interfaces (Faraday geometry). The exact dispersion relation has been derived on the basis of local theory. 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}${q}_{z}$\ensuremath{\ll}1/d, where d is the thickness of the film. There are two modes, the upper one having a negative group velocity (``backward wave''). These modes---magnetoplasma generalizations of the Fuchs-Kliewer modes---approach the asymptotic frequencies given by [${\ensuremath{\epsilon}}_{\mathrm{xx}}$(\ensuremath{\omega})${\ensuremath{\epsilon}}_{\mathrm{zz}}$(\ensuremath{\omega}${)]}^{1/2}$= -${\ensuremath{\epsilon}}_{i}$, where ${\ensuremath{\epsilon}}_{\mathrm{ij}}$(\ensuremath{\omega}) is an element of the dielectric tensor of the semiconductor and ${\ensuremath{\epsilon}}_{i}$ is the dielectric constant of either one of the bounding media. In the symmetric configuration (${\ensuremath{\epsilon}}_{1}$=${\ensuremath{\epsilon}}_{3}$), the two asymptotic frequencies coincide. We have also applied to the general dispersion relation a thin-film approximation, ${q}_{z}$d\ensuremath{\ll}1. This enables us to find analytic solutions for ${q}_{z}$(\ensuremath{\omega}) in two cases: (1) a very thin semiconducting overlayer on a metallic substrate and (2) a very thin, unsupported, magnetoplasma film. In both cases a splitting in the spectrum occurs in the vicinity of the hybrid cyclotron-plasmon frequency, with the creation of a gap.