Dispersion of Bulk Waves in a Graphene–Dielectric–Graphene Structure

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.