Theoretical Research On Some Phenomena In An Optomechanical System With The Membrane-cavity Coupling

In the past few decades,the optomechanical system of light and matter interaction has received great attention from scientists.The typical optomechanical system is composed of a fixed cavity mirror and a movable cavity mirror.When the system is driven by a pump laser,the radiation pressure of light will make the movable cavity mirror vibrate(The oscillating cavity mirror can be approximated as a mechanical harmonic resonator),which induces a small change of the cavity length.As a result,the cavity and the resonator are coupled together,thus forming a optomechanical system.In the past decade,cavity optomechanics has made great progress due to the fabrication of high-quality mechanical resonators.Many significant advances have been made in this emerging field,including the optical bistability,sideband effects,optomechanically induced transparency and quantum ground state cooling,and so on.In this paper,we have studied the optical bistability,multi-stability and four-wave mixing effect in a three-mode optomechanical system with a membrane resonator.We studide the three-mode cavity optomechanical system,where an oscillating membrane of perfect reflection is inserted between two fixed mirrors of partial transmission.Firstly,we study the optical bistability and multistability effects in an optomechanical system with the membrane-cavity coupling.If the left pump power is input and the right pump power is closed,the optical bistability phenomenon occurs only in the left cavity.If the right pump power is input and the left pump power is closed,the bistable phenomenon occurs only in the right cavity.If the left and right pump power is entered simultaneously,bistable phenomena will occur simultaneously both in the left and right cavities.In addition,through the study of decay rate,coupling constant and detuning,we found that they can regulate the behavior of optical bistability in the left and right cavities.Second,by adjusting the right input pump power,the cavity will change from bistability to multi-bistability.These phenoms are important and have not been reported in the related references as far as we know.The last,we further illustrated the OB appeared in the cavity by the effective potential as a function of the position.Secondly,we study the four wave mixing effect in a three-mode optomechanical system.We find that a high efficiency of the four wave mixing process can be achieved and it is easy to control the four wave mixing by adjusting intensities of the left(right)pump field,the left(right)probe field,the decay rate and the coupling strength.When the right probe field is turned on,however,we can observe that the four wave mixing intensity peak in the left cavity increases if the two probe fields are entered at the same time.Finally,we make a brief summary of the full text.