Excitation of surface plasmon waves in extrinsic graphene is studied using a full-waveelectromagnetic field solver as analysis engine. Particular emphasis is placed on the roleplayed by spatial dispersion due to the finite size of the two-dimensional material at themicro-scale. A simple instructive set up is considered where the near field of a wire antennais held at sub-micrometric distance from a disk-shaped graphene patch. The key-input of thesimulation is the graphene conductivity tensor at terahertz frequencies, being modeled by theBoltzmann 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 conductivityequation is worked out in different levels of approximations, based on the relaxation timeansatz with an additional constraint for particle number conservation. Both drift and diffusioncurrents are shown to significantly contribute to the spatially dispersive anisotropic features ofmicro-scale graphene. More generally, spatial dispersion effects are predicted to influence notonly plasmon propagation free of external sources, but also typical scanning probe microscopyconfigurations. The paper sets the focus on plasmon excitation phenomena induced by nearfield probes, being a central issue for the design of optical devices and photonic circuits.
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