Extreme Sound Confinement From Quasibound States in the Continuum

Extreme confinement of incident acoustic waves remains challenging due to the conflict between reflection elimination and weak dissipation. In this study, by realizing a Friedrich-Wintgen quasibound state in the continuum (quasi-BIC), we demonstrate that sound confinement with an arbitrarily high quality factor becomes possible. The proposed proof-of-concept system consists of two slightly detuned resonators sharing a single-port radiating channel and supports a quasi-BIC. When operating with balanced low radiative and dissipative decay rates, it allows frequency-selective trapping of the incoming sound waves. The effect is experimentally and numerically validated as evidenced by the observation of an ultranarrow reflection dip (zero reflection at 420.8 Hz) along with intensive field enhancement (24.5 dB). We also show that the quality factor can be further improved by simultaneously reducing the detuning and the intrinsic loss. Our work breaks through the barrier in obtaining extreme sound confinement and may offer opportunities for the development of acoustic sensors, filters, and harvesters.

Figure 1

Sound confinement via a BIC. (a) Unity reflection in a lossless resonant cavity. Blue blocks represent rigid structures. $p_i$ and $p_r$ represent the incident and reflected waves. (b) Zero reflection for a lossy cavity (perfect absorber). (c) Friedrich-Wintgen quasi-BIC-induced wave confinement in two detuned resonators (cavities) with tiny intrinsic losses. $p_r^A(B)$ represents the reflected waves from the Cavity $A(B)$. Upper panels are the schematic illustrations of the corresponding systems below. $S_i^{+}$ and $S_r^{-}$ represent the incident and reflected waves. $a_{N(L)}$ and ${\gamma }_{N(L)}$ denote the mode amplitude and the radiative decay rate of the lossless (or lossy) system. ${\mathrm{\Gamma }}_L$ is the dissipative decay rate of the lossy system.

Figure 2

Acoustic quasi-BIC achieved via two detuned resonant cavities. (a) 3D-printed sample with a width ($w$) of $38.5$ mm and a height ($h$) of 54 mm. The length of cavity $A$ is fixed to $l_A=180$ mm. $b$ is the wall thickness, which is set to 4.5 mm. To fit the experimental impedance tube, the two cavities are assembled into a cylindrical adaptor with a radius ($R$) of 50 mm. (b) Calculated reflection amplitude as a function of the cavities’ length difference, $\mathrm{\Delta }l$, and frequency, $\omega /2\pi$. ${\gamma }_A=0.190{\omega }_A$ and ${\gamma }_B=0.191{\omega }_B$, $\mathrm{\Gamma }/{\omega }_0=3.13\times {10}^{-3}$ are extracted from full wave simulations [47]. (c) Calculated reflection amplitude (upper panel) and phase (lower panel) as functions of $\omega /2\pi$ and $\mathrm{\Gamma }/{\omega }_0$. The length of cavity $B$ is selected as 194 mm. White lines refer to the resonant frequencies of individual cavity $A$ (${\omega }_A/2\pi =435.8$ Hz) and cavity $B$ (${\omega }_B/2\pi =406.8$ Hz).

Figure 3

Experimental demonstration. (a) Experimental setup. Points 1–3 are, respectively, situated at the positions $20$, $85$, and 130 mm above the inner bottom of cavity A. (b) Reflection factor (blue) and pressure amplification (red) at point 1. Circles, lines, and forks, respectively, represent the experimental, simulated, (frequency domain) and calculated (impedance-based model) results. (c),(d) Pressure amplifications at points 2–3. (e) Impedance measurements and analysis. Top: acoustic impedances of cavities $A$ (blue lines) and $B$ (red lines). $x_{A(B)}$ and $y_{A(B)}$ represent the resistance and resistance of cavity $A(B)$. Middle: acoustic impedance of the overall coherent system. The solid line and circles represent the theoretical and experimental coherent resistance ($x_{AB}$). The dotted line and triangles represent the theoretical and experimental coherent reactance ($y_{AB}$). Bottom: absorption coefficients of the coherent system (green), individual cavity $A$ (blue) and $B$ (red).

Figure 4

Time-domain simulation. (a),(b), Time-dependent sound-pressure fluctuations at point 4 and point 1. Point 4 is located at the position 200 mm above the cavity opening [47]. $T_0$ is the time period of the incident waves.