Multistability and transparency with quadratically coupled membranes in a hybrid optomechanical system

The optical nonlinear characteristics of a hybrid optomechanical system with a membrane are theoretically investigated. We derive the mean photon number equation and analyse the behaviour of its steady state. By considering the quadratic coupling of the membrane, the optomechanical system is found to exhibit optical multistability. We study the effects of relevant parameters on this optical multistability, showing that both the threshold of optical multistability and the width of the multistability curve can be effectively modulated by adjusting the quadratic optomechanical coupling strength and the cavity decay rate. In addition, we investigate the optomechanically induced transparency and fast-slow light phenomenon of the system. The quadratic coupling strength and cavity decay rate have significant impacts on the optomechanically induced transparency curves. The slow light in the system can be shaped by the quadratic coupling strength.