Excitation of discrete and continuous spectrum for a surface conductivity model of graphene

Abstract

Excitation of the discrete (surface-wave/plasmon propagation mode) and continuous (radiation modes) spectrum by a point current source in the vicinity of graphene is examined. The graphene is represented by an infinitesimally thin, local, and isotropic two-sided conductivity surface. The dynamic electric field due to the point source is obtained by complex-plane analysis of Sommerfeld integrals, and is decomposed into physically relevant contributions. Frequencies considered are in the GHz through mid-THz range. As expected, the TM discrete surface wave (surface plasmon) can dominate the response along the graphene layer, although this depends on the source and observation point location and frequency. In particular, the TM discrete mode can provide the strongest contribution to the total electric field in the upper GHz and low THz range, where the surface conductivity is dominated by its imaginary part and the graphene acts as a reactive (inductive) sheet.