High-Quality Resonances in Quasi-Periodic Clusters of Scatterers for Flexural Waves

TL;DR

This paper investigates how quasi-periodic arrangements of scatterers on elastic plates can produce high-quality resonances, useful for wave localization, by applying multiple scattering theory to analyze their resonant modes and quality factors.

Contribution

It introduces the application of multiple scattering theory to quasi-periodic scatterer clusters, revealing their potential for high-Q resonances and wave localization in elastic plates.

Findings

Quasi-periodic structures exhibit a high density of states with high quality factors.

Resonant modes can be efficiently calculated using multiple scattering theory.

High-Q resonances suggest potential for wave localization devices.

Abstract

Multiple scattering theory is applied to the study of clusters of point-like scatterers attached to a thin elastic plate and arranged in quasi-periodic distributions. Two type of structures are specifically considered: the twisted bilayer and the quasi-periodic line. The former consists in a couple of two-dimensional lattices rotated a relative angle, so that the cluster forms a moir\'e pattern. The latter can be seen as a periodic one-dimensional lattice where an incommensurate modulation is superimposed. Multiple scattering theory allows for the fast an efficient calculation of the resonant modes of these structures as well as for their quality factor, which is thoroughly analyzed in this work. The results show that quasi-periodic structures present a large density of states with high quality factors, being therefore a promising way for the design of high quality wave-localization devices.