We investigate the dispersion properties of the first waveguide modes in a dielectric film that is coated with graphene layers having different chemical potential values. The control over the phase and group velocities of the first waveguide mode is considered. Spectral intervals in which the phase velocity of the waveguide modes is small, while their group velocity is negative, are revealed. We show that the dispersion characteristics of the waveguide modes can be rearranged using an external electric field.

In this work for far-infrared range we investigated the dispersion properties of surface plasmon polaritons in a structure «graphene plate-thin semiconductor film graphene plate». It is shown the ability of control the propagation modes by changing the chemical potential on one or both plates. It were received the dispersion relations for waves with TE- and TM-polarization and the distribution of wave field and energy fluxes along the transverse axes relate to propagation wave. It is shown that there is the spectral range, which characterized by negative group velocity.