▎ 摘　　要

In this paper, the phase-matching condition, the excited electric field formula, and the nonlinear susceptibility tensor elements conditions required for excitation of surface plasmon polaritons (SPPs) on flat graphene are derived. The second-order nonlinearity is utilized for compensation of the free-space and SPPs wave vectors mismatch. In order to excite SPPs on graphene, the phase matching condition is investigated for the second-order effects including the difference frequency generation (DFG), the second harmonic generation (SHG), and the sum-frequency generation (SFG). In addition, since the incident waves polarizations play an important role in the excitation of the SPPs, the realization of the susceptibility tensor elements conditions, the effect of TE, TM, not polarized and perpendicularly polarized incident waves are investigated using the Green's function theory. (C) 2017 Elsevier B.V. All rights reserved.