论文标题
连续体中的结合状态在散射器的圆形簇中
Bound states in the continuum in circular clusters of scatterers
论文作者
论文摘要
在这项工作中，我们研究了弯曲波在高度对称的散射群中的定位。结果表明，当散射器经常放置在圆周的周长中时，共振的质量因素会随着簇中的散射数量而大大增加。还发现，在连续极限中，也就是说，当散点子数量倾向于无限时，质量因子是无限的，因此模式属于连续性或BIC中所谓的绑定状态的类别，并且发现了谐振频率的分析表达。这些模式具有不同的多极对称性，我们表明，对于高多极阶，模式倾向于定位在圆周的边界，因此形成了具有异常高质量因子的Whishpering Gallery模式。进行数值实验，以检查这些模式在不同类型的疾病下的鲁棒性，并从远处研究它们的激发。尽管我们将研究重点放在弯曲波上，但这项工作中提出的方法可以应用于其他经典波，例如电磁波或声波，因此是基于有限散射器的有限簇设计高质量谐振器的一种合格方法。
In this work, we study the localization of flexural waves in highly symmetric clusters of scatterers. It is shown that when the scatterers are placed regularly in the perimeter of a circumference the quality factor of the resonances strongly increases with the number of scatterers in the cluster. It is also found that in the continuous limit, that is to say, when the number of scatterers tends to infinite, the quality factor is infinite so that the modes belong to the class of the so called bound states in the continuum or BICs, and an analytical expression for the resonant frequency is found. These modes have different multipolar symmetries, and we show that for high multipolar orders the modes tend to localize at the border of the circumference, forming therefore a whishpering gallery mode with an extraordinarily high quality factor. Numerical experiments are performed to check the robustness of these modes under different types of disorder and also to study their excitation from the far field. Although we have focused our study to flexural waves, the methodology presented in this work can be applied to other classical waves, like electromagnetic or acoustic waves, being therefore a promissing approach for the design of high quality resonators based on finite clusters of scatterers.
