激光的产生，使得腔光力系统的研究逐渐深入。双机械薄膜腔光力系统相比较于典型腔光力系统，使用了双机械薄膜，并重点引入相位进行研究。此系统不仅具有传统腔光力系统的优势，还能利用参数调控来研究更多样的光力诱导透明、光力诱导放大、慢光效应等光学特性。研究光力诱导透明来实现对微小质量的精细测量，研究慢光效应可用于对快慢光的操控。随着不断探索和研究，可以获得更新颖的应用价值。本论文具体研究内容分为以下几步：

第一步，建立双机械薄膜腔光力系统物理模型，先写出腔光力系统的哈密顿量，利用幺正变换，得到更便于研究的新哈密顿量形式，之后得到各算符的海森堡-朗之万运动方程并进行求解，最后得到一组与腔光力系统相关的方程，用于分析腔光力学系统的各种物理特性。

第二步，研究双机械薄膜腔光力系统的光力诱导透明现象。根据输入-输出形式研究发现，在光力耦合存在时，若是两个机械薄膜频率不一致会出现两个透明窗口，频率一致会出现一个透明窗口。之后分别讨论腔光力系统参数对于光力诱导透明现象的影响。结果表明，改变耦合系数、强泵浦场功率和腔体耗散会导致透明窗口宽度改变；调控强泵浦场与弱探测场的相位差可以实现吸收和放大的转化；调控驱动场相位可以实现光力诱导透明和光力诱导放大转化；当衰减系数过大时，光力诱导透明特性不再保留。最后通过透明窗口位置的改变实现对微小质量的精细测量。

第三步，研究双机械薄膜腔光力系统的慢光效应。在光力耦合存在时，若是两个机械薄膜频率不一致会出现两次超快色散，频率一致会出现一次超快色散。超快色散会导致群延迟，通过延迟时间公式，计算延迟时间，可以看出在两次透明窗口处可以得到最大的延迟时间。之后分别讨论腔光力系统参数对于慢光效应的影响。结果表明，改变耦合系数、强泵浦场功率和腔体耗散会导致群延迟时间改变；调控强泵浦场相位与弱探测场的相位差和驱动场相位可以实现慢光和快光的转化；当机械薄膜衰减系数过大时，慢光效应消失，回归至无光力耦合存在时的状态。

The generation of lasers has gradually deepened the research on cavity optomechanica systems. Compared with typical cavity optomechanical system, the cavity optomechanical system in this thesis use double mechanical membranes and the researches focusing on phase parameter is introduced. This system not only has the advantages of the traditional cavity optomechanical system, but also can be used to study various optical characteristics such as optomechanically induced transparency, optomechanically induced amplification, slow light effect and so on. Optomechanically induced transparency is studied to realize the precise measurement of small mass, and the slow light effect is studied to realize the control of fast and slow light. With continuous exploration and research, even more novel application value can be obtained. The specific research content of this paper is divided into the following steps:

The first step is to establish the physical model of the cavity optomechanical system with double mechanical membranes, Starting from the Hamiltonian of the cavity optomechanical system, a more convenient Hamiltonian form by using unitary transformation is used. Then, the  Heisenberg-Langevin equations of each operator are obtained and solved. Finally, a set of equations related to the cavity optomechanical system are obtained for analysis of various physical characteristics.

The second step is to study optomechanically induced transparency in the cavity optomechanical system with double mechanical membranes. According to the input-output formula, it is found that two transparent windows will appear when the frequencies of two mechanical membranes are inconsistent, and one transparent window will appear if the frequencies of two mechanical membranesare consistent. Then the effect of the cavity optomechanical system parameters on the optomechanically induced transparency is discussed respectively. The results show that the width of transparent window can be changed by coupling coefficient, strong pump field power and cavity dissipation. The conversion of absorption and amplification can be realized by adjusting the phase difference between the strong pump field and the weak probe field. Optomechanically induced transparency and Optomechanically induced amplification can be achieved by adjusting the phase of the driving field. optomechanically induced transparency is no longer retained when the exhausting coefficient is too large. Finally, the micro mass can be measured precisely by changing the position of transparent window.

The third step is to study the slow light effect of the cavity optomechanical system with double mechanical membranes. In the presence of optomechanical coupling, two ultrafast dispersions curves will occur when the frequencies of two mechanical membranes are inconsistent, and one ultrafast dispersions will occur when the frequencies are consistent, which will lead to group delay. By analysing the delay time through the syatem formula, it can be seen that the maximum group delay time can be obtained at the two transparent windows. Then the influence parameter of cavity optomechanical system on the slow light effect is discussed respectively. The results show that the group delay time can be changed by changing the coupling coefficient, strong pump field power and cavity dissipation. The conversion of slow light and fast light can be realized by adjusting the phase difference between strong pump field and weak probe field and the phase of driving field. When the exhausting coefficient of the mechanical membranes is too large, the slow light effect disappears and presents to be absent from the optomechanical coupling.