Spatial dispersion effects upon local excitation of extrinsic plasmons in a graphene micro-disk

Abstract

Excitation of surface plasmon waves in extrinsic graphene is studied using a full-wave electromagnetic field solver as analysis engine. Particular emphasis is placed on the role played by spatial dispersion due to the finite size of the two-dimensional material at the micro-scale. A simple instructive set up is considered where the near field of a wire antenna is held at sub-micrometric distance from a disk-shaped graphene patch. The key-input of the simulation is the graphene conductivity tensor at terahertz frequencies, being modeled by the Boltzmann transport equation for the valence and conduction electrons at the Dirac points~(where a linear wave-vector dependence of the band energies is assumed). The conductivity equation is worked out in different levels of approximations, based on the relaxation time ansatz with an additional constraint for particle number conservation. Both drift and diffusion currents are shown to significantly contribute to the spatially dispersive anisotropic features of micro-scale graphene. More generally, spatial dispersion effects are predicted to influence not only plasmon propagation free of external sources, but also typical scanning probe microscopy configurations. The paper set the focus on plasmon excitation phenomena induced by near field probes, being a central issue for the design of optical devices and photonic circuits.