We investigate a dual membrane active–passive cavity where each mechanical membrane individually quadratically coupled to passive and active cavities via two-phonon process. Due to the fact that in the quadratically coupled optomechanical system mean-field approximation fails, hence to analyze the system completely, we switch to a more generalized out of equilibrium approach, namely Keldysh Green’s functional approach. We calculate transmission rate using predetermined full retarded Green’s function, and then numerically examine the effect of the various parameters on the transmission coefficient and discuss the features and physical mechanism behind them in detail. On the basis of the optical responsivity we further extend our study to fast and slow light phenomenon. The results show that our proposed system can not only realize ultra-fast/ultra-slow light under proper choice of cavity parameters but also a realization of the conversion between fast and slow light and vice versa has also been pointed out.

我们研究了双膜主动-被动腔，其中每个机械膜通过双声子过程分别与被动腔和主动腔二次耦合。由于在二次耦合光机械系统中均场逼近失败，因此无法对系统进行完整分析，因此我们改用更为广义的非平衡方法，即Keldysh Green的函数方法。我们使用预定的全延迟格林函数来计算传输速率，然后数值检查各种参数对传输系数的影响，并详细讨论其背后的特征和物理机制。基于光学响应性，我们将研究进一步扩展到快光和慢光现象。