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Plasmon-enhanced nonlinear wave mixing in nanostructured graphene

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.