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Excitation of surface plasmon waves in extrinsic graphene is studied using afull-wave electromagnetic field solver as analysis engine. Particular emphasisis placed on the role played by spatial dispersion due to the finite size ofthe two-dimensional material at the micro-scale. A simple instructive set up isconsidered where the near field of a wire antenna is held at sub-micrometricdistance from a disk-shaped graphene patch. The key-input of the simulation isthe graphene conductivity tensor at terahertz frequencies, being modeled by theBoltzmann transport equation for the valence and conduction electrons at theDirac points~(where a linear wave-vector dependence of the band energies isassumed). The conductivity equation is worked out in different levels ofapproximations, based on the relaxation time ansatz with an additionalconstraint for particle number conservation. Both drift and diffusion currentsare shown to significantly contribute to the spatially dispersive anisotropicfeatures of micro-scale graphene. More generally, spatial dispersion effectsare predicted to influence not only plasmon propagation free of externalsources, but also typical scanning probe microscopy configurations. The paperset the focus on plasmon excitation phenomena induced by near field probes,being a central issue for the design of optical devices and photonic circuits.

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