Electronically Tunable Broadband THz Frequency Multipliers Based on Multilayer Nonlinear Graphene Metasurfaces

A numerical method for modeling of nonlinear effects in the multilayer metasurfaces of rectangular graphene nanoribbons was developed based on the solution of nonlinear diffraction problem for Maxwell's equations, complemented by the model of the nonlinear graphene surface conductivity. The numerical analysis taking into account the third order conductivity of graphene in the presence of high intensity THz field shows an efficient frequency multiplication mechanism in the condition of resonance of the surface plasmon-polariton waves and standing waves due to reflection from dielectric separation layers and graphene ribbon arrays. The normalized power of third-harmonic wave, emitted in the forward (transmission) and the backward (reflection) directions by multilayer graphene nanoribbons metasurfaces as a function of frequency of the incident waves of s- and p-polarization were calculated. It is shown, how the efficiency of third harmonic generation at the resonant frequency depends on the structural parameters of THz frequency multipliers such as the periodicity of arrays, geometrical sizes of graphene nanoribbons, the thickness of dielectric layers and the change in its dielectric permeability, the variation in the graphene chemical potential.