We investigate theoretically the generation of nonlinear dissipative structures in optomechanical (OM) systems containing discrete arrays of mechanical resonators. We consider both hybrid models in which the optical system is a continuous multimode field, as it would happen in an OM cavity containing an array of micro-mirrors, and also fully discrete models in which each mechanical resonator interacts with a single optical mode, making contact with Ludwig & Marquardt [Phys. Rev. Lett. 101, 073603 (2013)]. Also, we study the connections between both types of models and continuous OM models. While all three types of models merge naturally in the limit of a large number of densely distributed mechanical resonators, we show that the spatial localization and the pattern formation found in continuous OM models can be still observed for a small number of mechanical elements, even in the presence of finite-size effects, which we discuss. This opens new venues for experimental approaches to the subject.

中文翻译：

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离散光机械腔和阵列中的空间定位和图案形成

我们从理论上研究了包含离散机械谐振器阵列的光机械 (OM) 系统中非线性耗散结构的生成。我们考虑两种混合模型，其中光学系统是连续多模场，因为它会发生在包含微镜阵列的 OM 腔中，以及完全离散模型，其中每个机械谐振器与单个光学模式相互作用，使得与 Ludwig & Marquardt [Phys. 牧师莱特。101, 073603 (2013)]。此外，我们研究了两种类型的模型和连续 OM 模型之间的联系。虽然这三种模型在大量密集分布的机械谐振器的限制下自然融合，我们表明，即使存在我们讨论的有限尺寸效应，在连续 OM 模型中发现的空间定位和图案形成仍然可以观察到少量机械元件。这为该主题的实验方法开辟了新的场所。