Frequency Converters for the Terahertz and Infrared Ranges Based on Two-Dimensionally Periodic Graphene Gratings

A method for solving the problem of nonlinear diffraction on two-dimensional periodic gratings of graphene ribbons has been developed. The third-order nonlinear conductivity of graphene under the action of two waves is taken into account, which is determined by the field of the pump wave, for which we use the field on graphene ribbons obtained by solving the linear diffraction problem. Numerical analysis shows the efficiency of nonlinear frequency conversion in the terahertz and infrared ranges when the frequencies of the incident pump and signal waves coincide with the resonant frequencies of the fundamental and higher order modes of surface plasmon polaritons in graphene ribbons.