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 ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mi>Q</a:mi> </a:math> 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 <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi mathvariant="normal">Γ</b:mi> </b:math> point (in-plane Bloch wave vector <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:msub> <d:mi mathvariant="bold">k</d:mi> <d:mo>∥</d:mo> </d:msub> <d:mo>=</d:mo> <d:mn mathvariant="bold">0</d:mn> </d:mrow> </d:math> ) 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 ( <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>m</g:mi> <g:mo>=</g:mo> <g:mn>0</g:mn> </g:mrow> </g:math> ) 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- <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mi>Q</h:mi> </h:math> quasi-BIC regimes, which can be excited by a plane wave at normal incidence.