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Localized plasmons in metallic nanostructures have been widely used toenhance nonlinear optical effects due to their ability to concentrate andenhance light down to extreme-subwavelength scales. As alternatives to noblemetal nanoparticles, graphene nanostructures can host long-lived plasmons thatefficiently couple to light and are actively tunable via electrical doping.Here we show that doped graphene nanoislands present unique opportunities forenhancing nonlinear optical wave-mixing processes between two externallyapplied optical fields at the nanoscale. These small islands can supportpronounced plasmons at multiple frequencies, resulting in extraordinarily highwave-mixing susceptibilities when one or more of the input or outputfrequencies coincide with a plasmon resonance. By varying the doping chargedensity in a nanoisland with a fixed geometry, enhanced wave mixing can berealized over a wide spectral range in the visible and near infrared. Weconcentrate in particular on second- and third-order processes, including sumand difference frequency generation, as well as on four-wave mixing. Ourcalculations for armchair graphene triangles composed of up to several hundredcarbon atoms display large wave mixing polarizabilities compared with metalnanoparticles of similar lateral size, thus supporting nanographene as anexcellent material for tunable nonlinear optical nanodevices.

Plasmon-enhanced nonlinear wave mixing in nanostructured graphene