Analytical investigation of surface plasmon excitation on a graphene sheet using four-wave mixing

In the present paper, the general conditions for exciting graphene surface plasmon polaritons (GSPPs) on a suspended graphene using nonlinear optics are investigated. The approach uses the Green's function analysis to derive GSPP fields generated under the basis of momentum conservation using four-wave mixing (FWM). Since the incident beam polarization is challenging in the nonlinear excitation of GSPPs, the significant target of this paper has been set to achieve the conditions for the third-order susceptibility tensor and the wave vectors so that the incident beams with varied polarizations are able to excite GSPPs. Nonlinear optics, in particular FWM, is utilized to compensate the mismatch between the free-space and GSPPs wave vectors. In addition, it avoids the need for applying any patterning or lithography on graphene or its substrate.