Lattice-induced sound trapping in biperiodic metasurfaces of acoustic resonators

TL;DR

This paper investigates how lattice interactions in biperiodic acoustic resonator metasurfaces can induce bound states in the continuum (BICs) with high quality factors, using multipole interference and analytical conditions to design and analyze these trapped modes.

Contribution

It introduces an analytical framework for realizing accidental acoustic BICs in biperiodic metasurfaces through multipole interference, supported by numerical validation using the T-matrix method.

Findings

Identification of conditions for BIC formation via multipole interference.

Demonstration of high-Q quasi-BIC regimes in finite arrays.

Analytical design rules for lattice parameters to achieve BICs.

Abstract

A referential example of a physical system that supports bound states in the continuum (BICs) with an infinite quality factor ($Q$ factor) is a metasurface of discrete scatterers (resonators), whose response can be significantly modified by exploiting lattice interactions. In this work, we explore the multipole-interference mechanism for realizing accidental acoustic BICs (trapped modes) at $\Gamma$-point (in-plane Bloch wave vector $\mathbf{k}_{\parallel} = \mathbf{0}$) of biperiodic metasurfaces of acoustic resonators with one resonator per unit cell. To do so, we expand the pressure field from the metasurface into a series of scalar zonal ($m = 0$) spherical multipoles, carried by a normally incident plane wave, and formulate analytical conditions on the resonator multipole moments under which an eigenmode becomes a BIC. The conditions enable us to determine the lattice constant and frequency values that facilitate the formation of an axisymmetric BIC with a specific parity, resulting from destructive interference between zonal multipoles of the same parity, despite each moment radiating individually. By employing the T-matrix method for acoustic metasurfaces, we numerically investigate the BIC resonance in various structures, including finite arrays, and also the transformation of such resonances into high-$Q$ quasi-BIC regimes, which can be excited by a plane wave at normal incidence.