We present perturbation theory for analysis of generic third-order nonlinear processes in graphene-integrated photonic structures. The optical response of graphene is treated as the nonlinear boundary condition in Maxwell's equations. The derived models are applied for analysis of third-harmonic generation in a graphene-coated dielectric microfiber. An efficiency of up to a few percent is predicted when using subpicosecond pump pulses with energies of the order of 0.1 nJ in a submillimeter-long fiber when operating near the resonance of the graphene nonlinear conductivity ℏω=(2/3)EF.
Gorbach, A. V., & Ivanov, E. (2016). Perturbation theory for graphene-integrated waveguides: Cubic nonlinearity and third-harmonic generation. Physical Review A, 94(1), 1-10. . https://doi.org/10.1103/PhysRevA.94.013811