Surface plasmon-polaritons in a two-layer graphene structure with a dielectric barrier layer under various control regimes

The dispersion dependences of a symmetric dielectric waveguide with graphene plates were compared in two regimes of graphene potential control from two sides of the structure. A general dispersion relation was obtained, the numerical analysis of which reveals the possibility of controlling the parameters of amplified surface modes. A numerical analysis of the dispersion relation solutions in the case of symmetry and asymmetry of the control potential on graphene layers has been carried out. A solution has been found that grows in amplitude with time in the region of negative conductivity of graphene in the presence of an inverse population of the levels.