Abstract
The mathematical model of nonlinear wave mixing (NMW) in multilayer graphene plasmonic nanoribbon structures (PNRSs) consisting of several two-periodic arrays of graphene nanoribbons on dielectric layers was developed based on the solution of the nonlinear diffraction boundary problem for the Maxwell's equations simultaneously with a model of nonlinear graphene surface conductivity of third order nonlinearity using the perturbation method. The possibility to improve the NMW process when the wavelengths λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> of the incident pump and signal waves and wavelength λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> of generated wave at the combination frequency f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> =2 f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -f <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> are all very close to the resonant wavelength λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">res</sub> of multilayer graphene PNRSs and to increase the magnitude of the generated wave by several orders at resonance of surface plasmon polariton (SPPs) modes is shown. It is demonstrated that the NMW efficiency increases with increasing number of graphene nanoribbon arrays and upon decreasing the signal wave frequency detuning and the value of chemical potential. It is shown the insensitivity of NMW efficiency to the incident angles of the pump and signal waves over a wide range of angles. Using the multiband resonances of localized SPPs depending on the geometrical configuration of multilayer graphene PNRSs, their multiband nonlinear spectral response in mid-IR range can be designed.
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