Controllable optical bistability in a three-mode optomechanical system with a membrane resonator

We study the optical bistability (OB) in a three-mode cavity optomechanical system, where an oscillating membrane of perfect reflection is inserted between two fixed mirrors of partial transmission. By investigating the behavior of steady state solutions, we find that the left and right cavities will exhibit the bistable behavior simultaneously in this optomechanical system by adjusting the left and right coupling fields. In addition, one can control the OB threshold and the width of the OB curve via adjusting the coupling strength, the detuning, and the decay rate. Moreover, we further illustrate the OB appearing in the cavity by the effective potential as a function of the position.