Modulation Of Four-wave Mixing Of Graphene Nanoribbon Nanomechanical Resonators By Surface Plasmons

Graphene nanoribbon,as an excellent two-dimensional material,is proposed as a powerful candidate for nanomechanical resonators because of their advantages including low mass density,small size,and high quality factor.The study of four-wave mixing properties of the graphene nanoribbon resonators has a large potential in the fields of photonics and optoelectronics.In this paper,a series of research works have been carried out on the four-wave mixing properties of a monolayer graphene nanomechanical resonator system modulated by surface plasmons of a metal nanoparticle.The specific research contents and results are list as follows:(1)We construct a theoretical model consisting of an Au nanoparticle and a graphene nanomechanical resonator,write the Hamiltonian of the system by using the quantum mechanical method,and then we use the Heisenberg equations of motion for operators and the commutation relationship between operators,finally we derive the analytical formulas for the population inversion of exciton and four-wave mixing signal of the system.We study the relationship between these formulas and the excitation conditions and the structural parameters of the system,and explore the conditions for enhancing the optical four-wave mixing properties of the system.(2)We investigate the four-wave mixing effect of an Au nanoparticle/monolayer graphene nanomechanical resonator hybrid system.The results show that the four-wave mixing spectrum can switch among two-peaked,three-peaked,four-peaked and fivepeaked by adjusting the exciton-phonon and exciton-plasmon coupling strengths,which can be ascribed to the energy-level splitting of exciton.In the dual-strong coupling regime,the gains for these peaks can reach as high as 109 near the low bistability threshold due to a strong combination of these two couplings.When only the exciton-plasmon coupling exists,the four-wave mixing spectrum becomes two-peaked structure.When the pumping intensity is weak,the four-wave mixing signal of the system shows a large gain by modulating the distance between the Au nanoparticle and nanoresonator.The four-wave mixing signal will be enhanced by enlarging the pumping intensity.(3)We study the four-wave mixing properties of an Au@SiO2 core-shell nanoparticles/monolayer graphene nanomechanical resonator hybrid system.The results show that,in this core-shell nanosystem,the four-wave mixing signal is gradually enhanced with the increase of d.When the interparticle distance is constant,the four-wave mixing signal will be enhanced by increasing of the thickness of the SiO2 shell.In the strong exciton-plasmon coupling regime,the four-wave mixing signal can be enhanced by enlarging the exciton-phonon coupling strength.Also,the signal can be strengthened via the enhancement effect of SiO2 shell.However,it has a weak impact on the gain for the signal obtained from the exciton-phonon coupling.In the dual-strong coupling regime(i.e.when the exciton-phonon and exciton-plasmon couplings are both strong),the four-wave mixing signal will be enhanced with the increase of the pumping intensity.Similarly,the enhancement for the signal brought from the SiO2 shell is demonstrated again.The shell also does not affect the gain for the signal obtained from the pumping intensity.