▎ 摘　　要

Due to its unique properties of low mass density, high frequency, high quality-factor and intrinsically small size, graphene has received significant attention and is considered as an ideal material for fabricating nanomechanical systems. In this work, we demonstrate theoretically the coherent optical propagation under different detuning regimes in the graphene resonator-microwave cavity system. In the red detuning, optomechanically induced transparency induced the slow light effect is investigated and the maximum group delay can reach 0.4 ms. In the blue detuning, advancing microwave signal can reach 0.12 ms, and the parametric amplification process can behave as an optical transistor to amplify a weak microwave field via manipulating the pump field. Further, we research the nonlinear effects of four-wave mixing (FWM), and the FWM intensity can be efficiently controlled and modulated by the pump power, such as FWM spectrum can present the phenomenon of normal mode splitting with controlling the pump power. A straightforward optical means for determining the frequency of the resonator by the FWM spectrum is also presented. The graphene optomechanics may indicate applications in quantum information processing.