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