We explore the optical response of a multimode optomechanical system with quadratic coupling to a weak probe field, where the cavity is driven by a strong control field and the two movable membranes are, respectively, excited by weak coherent mechanical driving fields. We study the two cases that the two movable membranes are degenerate and nondegenerate. For the degenerate case, it is shown that only one transparency window occurs and the transition between optomechanically induced transparency and Fano resonance can be realized by tuning the cavity-control field detuning. For the nondegenerate case, two transparency windows are observed and the absorption spectrum can switch between a single Fano resonance and double Fano resonances. Furthermore, we show that the output probe field can be greatly amplified or completely suppressed due to the complex interference effect by tuning the amplitude and phase of the mechanical driving fields. Our results can be extended to the optomechanical system with multiple membranes, which enables us to control the light propagation more flexibly.

中文翻译：

---

具有二次耦合的多模光机系统中的光机诱导的透明度，放大和Fano共振

我们探索了与弱探针场二次耦合的多模光学机械系统的光学响应，其中腔由强控制场驱动，两个可移动膜分别由弱相干机械驱动场激发。我们研究了两个可移动膜退化和未退化的两种情况。对于退化的情况，表明仅出现一个透明窗口，并且可以通过调整腔控制场失谐来实现光机械感应的透明和Fano共振之间的过渡。对于非简并的情况，观察到两个透明窗口，并且吸收光谱可以在单个Fano共振和双Fano共振之间切换。此外，我们表明，通过调整机械驱动场的幅度和相位，由于复杂的干扰效应，可以大大放大或完全抑制输出探测场。我们的结果可以扩展到具有多个膜的光机械系统，这使我们能够更灵活地控制光的传播。