Electrically Controllable Infrared Frequency Conversion in Nonlinear Multilayer Graphene Ribbon Arrays

Through the developed numerical technique to solve the nonlinear diffraction problem for the Maxwell’s equations simultaneously with a model of the nonlinear graphene surface conductivity the nonlinear frequency conversion (NFC) process in the multilayer graphene ribbon arrays was investigated. A numerical approach was developed using the perturbation method. The results of numerical simulation of nonlinear transmittance T
3
and reflectance R
3
spectra of generated mid-IR wave at combination frequency $f_{3}=2f_{1}-f_{2}$ versus the signal wavelength $\lambda_{2}$ show that the maximum of nonlinear transmittance T
3
peak increase by several orders when the resonance conditions of the surface plasmon-polariton (SPPs) modes in the graphene ribbons are satisfied. With increasing number of layers of graphene nanoribbons the NFC efficiency by multilayer graphene arrays can be increased by several orders of magnitude. It is demonstrated that the NFC process is the wide tunability of frequency of the generated mid-IR waves by tuning the graphene chemical potential and the corresponding pump wavelengths for the SPPs resonance conditions without changing the geometry sizes of arrays. It is shown the highest NFC efficiency when the detuning $\pm\triangle f/f_{1}=(f_{2}-f_{1})/f_{1}$ of the signal wave frequency f
2
relative to the pump wave frequency f
1
approaches to zeros. It is demonstrated the insensitivity to the incident angles of the pump and signal waves over a wide range of angles. The combination of multiple graphene ribbon layers opens ways toward novel reconfigurable nonlinear IR devices: electrically controllable ultracompact IR mixers, efficient nonlinear modulators, shutters, switches.