摘要： We propose theoretically a four-mode coupled optomechanical system to explore the optical-response properties of an optical trimer system consisting of a passive cavity, a no-loss-gain cavity, and an active cavity coupled with a mechanical oscillator. In the study, the passive cavity is driven by an external laser so that the stability of the coupled system depends strongly on the gain-to-loss ratio and the photon tunneling between the adjacent cavities. We ?nd that in the regime near the stable-unstable critical point, the resonance absorption of the optical trimer system changes quickly with the increasing gain of the active cavity. In contrast, when the mechanical oscillator is coupled to the passive cavity, the center absorption peak is split and a phenomenon of optomechanically induced transparency appears. Consequently, two additional resonance peaks in the absorption pro?le are induced by the optomechanical coupling, which hinges on the tunneling between the optical cavities and also on the gain of the active cavity. The dependence of the width of the transparency window on the optomechanical coupling and the driving strength is also discussed in detail. The results obtained here indicate that the optical properties of the trimer system can be manipulated by coupling a mechanical oscillator to the system and therefore have a potential application in quantum optics and quantum information processing.