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It has recently been demonstrated that difference frequency mixing (DFM) cangenerate surface plasmons in graphene [1]. Here, we present detailedcalculations comparing the contributions to this effect from substrate and fromgraphene nonlinearities. Our calculations show that the substrate (quartz)nonlinearity gives rise to a surface plasmon intensity that is around twelveorders of magnitude smaller than that arising from the intrinsic grapheneresponse. This surprisingly efficient intrinsic process, given thecentrosymmetric structure of graphene, arises almost entirely due to non-localcontributions to the second order optical nonlinearity of graphene.

The Roles of Substrate vs Nonlocal Optical Nonlinearities in the Excitation of Surface Plasmons in Graphene