The localization of waves in two-dimensional (2D) clusters of scatterers arranged in relatively twisted lattices is studied by multiple scattering theory. It is found that, for a given frequency, it is always possible to find localized modes for a discrete set of rotation angles, analogous to the so-called “magic angles” recently found in 2D materials such as graphene. Similarly, for small rotations of the lattices, a large number of resonant frequencies is found, the position of which depends strongly on the rotation angle. Moreover, for angles close to those that make the two lattices commensurable, a single mode appears that can be easily tuned by the rotation angle. Unlike other twisted materials, where the properties of the bilayers are mainly explained in terms of the dispersion relation of the individual lattices, the specific angles in these clusters happen because of the formation of dipolar scatterers due to the relative rotation between the two lattices, therefore enhancing their interaction. While the presented results are valid for any type of wave, the specific case of flexural waves in thin elastic plates is numerically studied and the different modes found are comprehensively explained in terms of the interaction between pairs of scatterers. The analysis presented here shows that these structures are promising candidates for the inverse design of tunable wave-trapping devices for classical waves.

中文翻译：

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扭曲声子晶体板中波的偶极局域化

利用多重散射理论研究了在相对扭曲的晶格中分布的二维（2D）散射体簇中的波的局域性。已经发现，对于给定的频率，总是有可能找到一组离散的旋转角度的局部模式，类似于最近在2D材料（例如石墨烯）中发现的所谓的“魔角”。类似地，对于晶格的小旋转，发现了大量的共振频率，其位置在很大程度上取决于旋转角度。此外，对于接近使两个晶格可比较的角度，出现一个可以通过旋转角度轻松调整的单一模式。与其他扭曲材料不同，双层材料的性能主要是根据各个晶格的色散关系来解释的，这些簇中的特定角度是由于两个晶格之间的相对旋转而形成偶极散射体而产生的，因此增强了它们的相互作用。虽然给出的结果对任何类型的波均有效，但对薄弹性板中挠曲波的具体情况进行了数值研究，并根据散射体对之间的相互作用全面解释了发现的不同模式。此处进行的分析表明，这些结构是经典波可调谐陷波设备逆设计的有希望的候选者。数值研究了弹性薄板中挠曲波的具体情况，并根据散射体对之间的相互作用全面解释了发现的不同模式。此处进行的分析表明，这些结构是经典波可调谐陷波设备逆设计的有希望的候选者。数值研究了薄弹性板中弯曲波的具体情况，并根据散射体对之间的相互作用全面解释了发现的不同模式。此处进行的分析表明，这些结构是经典波可调谐陷波设备逆设计的有希望的候选者。