▎ 摘　　要

In this paper, we propose a nonlinear plasmonic structure in which ABA-stacked trilayer graphene deposited on a silicon random grating. Due to the randomness of grating, Anderson localization phenomenon for surface plasmon polaritons waves leads to the appearance of many narrow dips in the transmission spectrum. For the first time, the effects of nonlinearity on the disorder-induced resonance states are investigated for this random plasmonic structure. To this end, the transmission spectra for both periodic and random structures are calculated at different input intensities of the incident wave. It is demonstrated that the dips in the transmission spectrum are red-shifted with increase in the input intensity of the incident electromagnetic wave. This red-shift of dips is explained using the dispersion curve of the graphene surface plasmons and nonlinear conductivity of graphene. By calculation of bistability curve, it is found that random structure can show the bistability response at frequencies around the different dips. Because there is only one resonance dip in the case of periodic structure, we observe bistability behavior for a few frequencies around the dips. But, using the random structure instead of periodic one allows us to make optical switching in a lot of frequencies. Furthermore, the lower switching-up and higher switching-down thresholds in the random structure are significantly lower than those in the periodic structure. This effect is attributed to the Anderson localization effect and formation of localization centers along the graphene layer. By calculation of electric filed distribution at resonance frequencies, it is confirmed that values of electric fields in the localization centers are higher than the value of electric field in the periodic structure at the same input intensity of incident wave. This stronger field enhancement results in lower bistability thresholds in the random structure compared to the periodic structure. Finally, the tunability of bistability behavior of the proposed random structure is demonstrated with a slight change in the Fermi energy of graphene layer. Therefore, proposed random structure can be a potential candidate for the application in nonlinear devices such as low threshold optical switches.