Transformation of surface plasmon polaritons to radiation in graphene in terahertz regime

We demonstrate a concept that allows direct excitation of surface plasmon polaritons (SPPs) by a moving electron bunch above a single layer graphene sheet deposited on a dielectric substrate without any additional coupling requirements. We show that if the two-dimensional current in the graphene is dominated by the third order nonlinear effect when the surface electric field exceeds a moderate strength of ∼5kV/cm, the SPP mode can cross the light line although the group velocity remains much smaller than the speed of light. This effect gives rise to direct transformation of SPPs into radiation. The underlying mechanism of the crossing of the SPP dispersion into the light line is the energy shift of charged particles in the nonlinear regime and the finite transport scattering time in graphene. Both the energy and lifetime of the SPPs increase with the field intensity. The radiation intensity and frequency can be tuned with an AC bias.