Lattice-induced sound trapping in biperiodic metasurfaces of acoustic resonators

TL;DR

This work addresses the challenge of confining acoustic energy in subwavelength metasurfaces by exploiting lattice-induced multipole interference to realize bound states in the continuum (BICs) at the $\\Gamma$-point. It develops a rigorous T-matrix and multipole framework to describe a 2D lattice of spherical resonators, deriving analytical BIC conditions in terms of monopole-quadrupole and dipole-octupole couplings and revealing how a genuine BIC emerges at specific lattice constants and frequencies. The study demonstrates that an infinite square lattice supports a $\\ ext{Γ}$-point BIC through even-parity zonal multipoles (and an analogous odd-parity BIC), and shows how slight detuning transforms the mode into a high-$Q$ quasi-BIC with a Fano lineshape, including realistic considerations of material losses and substrates as well as finite-size arrays. The results offer a practical pathway to ultra-narrow acoustic filters, high-sensitivity sensors, and energy localization using acoustic metasurfaces, bridging fundamental BIC physics and device-scale design.

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 subwavelength lattice 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 the $Γ$-point (in-plane Bloch wave vector $\mathbf{k}_{\parallel} = \mathbf{0}$) in biperiodic lattices of acoustic resonators with one resonator per unit cell. To do so, we expand the pressure field from the lattice into a series of scalar zonal ($m = 0$) spherical multipoles, carried by a normally incident plane wave, and formulate analytical conditions on the resonator's multipole moments under which an eigenmode becomes a BIC. The conditions allow us to determine the lattice constant and frequency values that enable the formation of the axisymmetric BIC due to the destructive interference of radiation from zonal multipole moments of a certain parity, although each moment radiates 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.

Figures (7)

• Figure 1: (a) Sketch of a biperiodic lattice of spherical particles (resonators) with a subwavelength lattice constant of $L$; the structure supports acoustic bound states in the continuum (trapped modes) at the $\Gamma$-point (normal incidence). (b) Formation of the acoustic BIC thank to the destructive interference of scalar zonal multipoles with the same parity (with respect to $\mathbf{r} \to -\mathbf{r}$). The diagrams illustrate the intensity of the pressure field in the far-field region (i.e., $r \gg \lambda_{\rm b}$) generated by a unit cell. The color represents the pressure field phase, while the radius indicates its amplitude.
• Figure 2: Scattering efficiency of a spherical particle as a function of its size parameter and frequency (blue solid) and contributions to scattering from the monopole (dashed orange), dipole (dashed-dotted green), quadrupole (dotted red), and octupole (dashed violet). The maximum multipole degree is $\ell_{\rm max} = 6$, and the other parameters are listed in Sec. \ref{['sec:simulation_lattice']}.
• Figure 3: Even BIC in the metasurface of spherical resonators depicted in Fig. \ref{['fig:sketch']}(a). (a) The lowest singular value of the inverse effective T-matrix in the monopole-quadrupole approximation \ref{['eq_A']}. (b) Transmittance of the lattice $T \equiv |t|^2$ for a normally incident pressure plane wave with $\ell_{\rm max} = 6$ in Eq. \ref{['eq_t']}. The quantities in panels (a) and (b) are plotted as a function of the normalized lattice constant $L/a$ and size parameter $\omega a / c_{\rm b}$ where $a = 50$$\mu$m and $c_{\rm b} = 1500$ m/s (the other parameters are listed in the text). The red circles indicate the lattice constant and the frequency for which the even BIC appears. (c) Effective zonal monopole and quadrupole coefficients for the even BIC. (d) Normalized absolute value of the pressure field generated by the BIC in the $xz$ plane outside the spherical resonators. (e-g) Transmittance of the lattice as a function of frequency for normalized lattice constants (e) $L/a = 1.5$, (f) $L/a = 1.395$, and (g) $L/a = 1.2$. The solid blue and dashed orange curves correspond to the values computed by the T-matrix method (in acoustotreams) and the finite element method (Pressure Acoustics Module, COMSOL Multiphysics™), respectively. (h) $Q$-factor of the quasi-BIC resonance as a function of the normalized lattice constant offset $\Delta L/a = (L/a-L_{\rm BIC}/a)$ where $L_{\rm BIC}/a = 1.395$.
• Figure 4: Influence of material losses in scatterers (resonators) on the quasi-BIC resonance. (a) Transmittance of the lattice $|t|^2$ [see Eq. \ref{['eq_t']}] in the quasi-BIC regime for different values of material loss tangent being 0 (blue), $10^{-3}$ (orange), and $10^{-2}$ (green). The normalized lattice constant is $L/a = 1.5$. (b) The corresponding absorptance $(1-|r|^2 - |t|^2)$ of the lattice. (c) Total $Q$-factor of the quasi-BIC as a function of material loss tangent.
• Figure 5: Influence of a substrate on the quasi-BIC resonance. (a) Transmittance of the lattice $|t|^2$ [see Eq. \ref{['eq_t']}] in the quasi-BIC regime for different substrates. The normalized lattice constant is $L/a = 1.5$. (b) $Q$-factor of the quasi-BIC as a function of the normalized substrate impedance $Z_{\rm sub}/Z_{\rm b}$ with $Z_{\rm b} = 1.497$ MRayl.