Ultra-strong optical four-wave mixing signal induced by strong exciton-phonon and exciton-plasmon couplings.

We propose a scheme to generate ultra-strong four-wave mixing (FWM) signal based on a suspended monolayer graphene nanoribbon nanomechanical resonator (NR) coupled to an Au nanoparticle (NP). It is shown that, the FWM spectrum can switch among two-peaked, three-peaked, four-peaked or five-peaked via the modulation of exciton-phonon and exciton-plasmon couplings. This is mainly attributed to the vibrational properties of NR related to the exciton-phonon coupling, and the energy-level splitting of the localized exciton correlated to three classes of resonances consisting of three-photon resonance, Rayleigh Resonance, and AC-Stark atomic resonance. Especially, in a dual-strong coupling regime, the gains for these peaks can be as high as nine orders of magnitude (∼ 109) around the lower bistable threshold due to a combined effect of two couplings. Our findings not only offer an efficient way to measure the vibrational frequency of NR and the exciton-phonon coupling strength but also provide a possibility to fabricate high-performance optoelectronic nanodevices.