Magnetoplasmon-polaritons in a two-dimensional electron system with a back gate

Magnetoplasmon-polariton excitations in a two-dimensional (2D) electron system with a back gate are theoretically studied. The back gate is a metal layer that is parallel to the layer of 2D electrons and is separated from them by a dielectric substrate serving as a waveguide. In the absence of a magnetic field, the interaction of 2D plasmons with the modes of the waveguide limited by the gate from one side results in the formation of a family of waveguide plasmon-polariton modes. The two lowest of these modes are TM modes and have a gapless dispersion relation. As known, a static magnetic field $\mathbf{B}$ perpendicular to the plane of the system hybridizes different modes. The spectra and magnetodispersion of the found 2D modes are determined. The classification of all modes as longitudinal and transverse (ЕЬ–ЕУ classification), which is usually valid only in the absence of $\mathbf{B}$, is recovered in the limit of high fields B. The magnetic field dependence of the cutoff frequencies of the considered modes significantly affects the results. Even a low magnetic field opens a frequency gap proportional to the magnetic field magnitude $\mathbf{B}$ in the spectrum of one of the lowest magnetoplasmon-polariton modes. As the magnetic field increases, the gap is saturated and the mode becomes waveguide.