Waveguided modes in a planar structure "graphene - thin semiconductor film - graphene"

We investigated optical-range waveguide modes propagating in a semiconductor film sandwiched between two graphene plates. The mode characteristics were shown to depend on the chemical potential of graphene and the film thickness. Based on the numerical analysis, we obtained dispersion relations for the first waveguide modes, frequency dependences of their group and phase velocities, and the distribution of the energy flux density in the structure. We discovered the presence of spectral bands characterized by small phase and negative group velocities of the waveguide modes. The possibility of tuning the waveguide mode by changing the chemical potential of graphene and the thickness of the semiconductor film was established.