  Localized plasmons in metallic nanostructures have been widely used to
enhance nonlinear optical effects due to their ability to concentrate and
enhance light down to extreme-subwavelength scales. As alternatives to noble
metal nanoparticles, graphene nanostructures can host long-lived plasmons that
efficiently couple to light and are actively tunable via electrical doping.
Here we show that doped graphene nanoislands present unique opportunities for
enhancing nonlinear optical wave-mixing processes between two externally
applied optical fields at the nanoscale. These small islands can support
pronounced plasmons at multiple frequencies, resulting in extraordinarily high
wave-mixing susceptibilities when one or more of the input or output
frequencies coincide with a plasmon resonance. By varying the doping charge
density in a nanoisland with a fixed geometry, enhanced wave mixing can be
realized over a wide spectral range in the visible and near infrared. We
concentrate in particular on second- and third-order processes, including sum
and difference frequency generation, as well as on four-wave mixing. Our
calculations for armchair graphene triangles composed of up to several hundred
carbon atoms display large wave mixing polarizabilities compared with metal
nanoparticles of similar lateral size, thus supporting nanographene as an
excellent material for tunable nonlinear optical nanodevices.
