Bound states in the continuum in circular clusters of scatterers

TL;DR

This paper investigates the formation of bound states in the continuum (BICs) in symmetric circular clusters of scatterers, showing that increasing the number of scatterers enhances the quality factor, leading to highly localized whispering gallery modes.

Contribution

It provides an analytical expression for BIC resonant frequencies in circular scatterer clusters and demonstrates the robustness and potential applications of these modes across different wave types.

Findings

Quality factor increases with the number of scatterers.

Infinite scatterers lead to infinite quality factor BICs.

Modes localize at the cluster border for high multipolar orders.

Abstract

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.