Difference frequency generation of surface plasmon-polaritons in Landau quantized graphene

We develop a rigorous quantum-mechanical theory of the nonlinear optical process of difference frequency generation of surface plasmon-polaritons in Landau-quantized graphene. Although forbidden in the electric-dipole approximation, the second-order susceptibility is surprisingly high, equivalent to the bulk magnitude above 10-3 m/V. We consider the graphene monolayer as a nonlinear optical component of a monolithic photonic chip with integrated pump fields. The nonlinear power conversion efficiency of the order of tens of μW/W2 is predicted from structures of 10-100μm size. We investigate a variety of waveguide configurations to identify the optimal geometry for maximum efficiency.