Lattice-induced sound trapping in biperiodic metasurfaces of acoustic resonators

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 $Γ$-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.