Perturbation theory for graphene integrated waveguides: cubic   nonlinearity and third harmonic generation
  We present perturbation theory for analysis of generic third-order nonlinear processes in graphene integrated photonic structures. Optical response of graphene is treated as the nonlinear boundary condition in Maxwell equations. The derived models are applied for analysis of third harmonic generation in a graphene coated dielectric micro-fibre. The efficiency of up to few percent is predicted when using sub-picosecond pump pulses with energies of the order of $0.1$nJ in a sub-millimeter long fibre, when operating near the resonance of the graphene nonlinear conductivity $\hbar\omega=(2/3)E_F$. 
Andrey V. Gorbach, Edouard Ivanov
physics.optics