Effect of second-order coupling on optical bistability in a hybrid optomechanical system

We theoretically investigate an optomechanical system consisting of two coupled cavities, a bare optomechanical cavity and a traditional one. An optical parametric amplifier (OPA) is placed inside the traditional cavity. Optomechanical cavity has an oscillating mirror and a fixed one. In addition to the first order coupling between mechanical resonator of the system and the radiation pressure of optomechanical cavity, we consider a second order interaction between them. The evaluation of the system’s behavior shows bistability in the mean photon number of optomechanical cavity. Our results show that, the second order coupling leads to degenerate solutions for the equation of mean photon number of optomechanical cavity. We see that the strength of SOC can change the domain of bistability region of optomechanical cavity. Also, properties of the field driving OPA have remarkable effects on the stability of optomechanical cavity. Moreover, we show that the domain of bistability region can be modified by changing of optical properties of the system. Graphical abstract