Observation of acoustic Friedrich-Wintgen bound state in the continuum with bridging near-field coupling

Bound states in the continuum (BICs) have attracted increasing interest in recent years owing to their intriguing physical characteristics such as the infinitely high quality factor ($Q$ factor) and the enhanced wave-matter interaction. In this study, we report the theoretical and experimental observation of a Friedrich-Wintgen BIC with bridging near-field coupling in an asymmetric two-state acoustic system. Through the temporal coupled-mode theory, we comprehensively elucidate the role of bridging near-field coupling in constructing Friedrich-Wintgen BICs. Then, we present a two-state system consisting of two asymmetric cavities with a bridging tube. By tuning the diameter and position of the bridging tube, we can effectively modulate the near-field coupling effect of the presented system and achieve a Friedrich-Wintgen BIC. Furthermore, the presented system is modulated to deviate from the BIC, which provides a quasi-BIC and allows for a high-$Q$ perfect absorption when the radiation and dissipation of the quasi-BIC-supporting system achieve the critical coupling condition. The experimental results validate the theoretical and simulation results, demonstrating both the existence of a BIC and a quasi-BIC-based perfect absorption. Our work opens up an avenue to investigate acoustic Friedrich-Wintgen BICs with bridging near-field coupling in asymmetric systems, which enriches the field of acoustic BICs and offers opportunities for the development of acoustic devices with high $Q$ factor and asymmetric wave control.

Figure 1

Concept of tuning the near-field coupling of a two-state system to construct Friedrich-Wintgen BICs. (a),(b) Schematic of the near-field and far-field interactions among two resonant modes (a) and the corresponding two-state system composed of two acoustic resonators with a bridge connection and sharing the same radiation field. (c) Conceptional demonstration of radiation quality factor ${\log }_{10}(Q_{\mathrm{rad}1})$ of the presented two-state system as functions of $\kappa$ and ${\omega }_2/{\omega }_1$. In the analysis, the parameters are set ${\gamma }_1=0.2{\omega }_1$, ${\gamma }_2=0.04{\omega }_2$. (d) Conceptional demonstration of radiation quality factor ${\log }_{10}(Q_{\mathrm{rad}1})$ of the presented two-state system as functions of $\kappa$ and ${\gamma }_2/{\gamma }_1$. In the analysis, the parameters are set ${\omega }_1=1\mathrm{Hz}$, ${\omega }_2=1.2\mathrm{Hz}$.

Figure 2

Eigenvalues and radiation quality factors of the presented two-state system. (a),(b) The real part (a) and imaginary part (b) of the eigenvalues of the two-state system with varying $\kappa$. (c) Radiation quality factors of the two-state system with varying $\kappa$. The parameters are set to ${\omega }_2/{\omega }_1=1.2$ and ${\gamma }_2/{\gamma }_1=0.24$.

Figure 3

Observation of the FW BIC via a two-cavity system. (a) Schematic of the experimental sample. The wall thickness is set to 5.5 mm. (b) Reflection amplitudes ($\left|r\right|$) of the two-cavity system as functions of $d_a$ and $\omega /2\pi$. The tube distance $l_h$ is fixed to 146 mm. (c) Reflection amplitudes ($\left|r\right|$) of the two-cavity system as functions of $l_h$ and $\omega /2\pi$. The tube diameter $d_a$ is fixed to 27 mm. (d) Simulation results of eigenfrequency, pressure field (indicated by colors), and acoustic-intensity field (indicated by green arrows) of the two-cavity system with $d_a$ = 27 mm and $l_h$ = 146 mm.

Figure 4

Experimental validation of the FW BIC. (a) Experimental setup. (b) Experimental and simulation reflection amplitudes ($\left|r\right|$) for the two-cavity system with diameters $d_a$ of 2.2 mm, 8.4 mm, and 27 mm. The tube distance $l_h$ is fixed to 146 mm. (c) Experimental and simulation reflection amplitudes ($\left|r\right|$) for the two-cavity system with the tube distances $l_h$ of 50 mm, 90 mm, and 146 mm. The tube diameter $d_a$ is fixed to 27 mm.

Figure 5

Acoustic perfect absorption. (a) Simulation results of eigenfrequency, pressure field (indicated by colors), and acoustic intensity field (indicated by green arrows) of the presented two-cavity system with $d_a=27\mathrm{mm}$ and $l_h=50\mathrm{mm}$. (b) The theoretical, experimental, and simulation absorption coefficients at $d_a=27\mathrm{mm}$ and $l_h=50\mathrm{mm}$. Sim. ($H$) and Sim. ($E$) indicates that the simulations consider the walls as acoustically hard boundaries and elastic boundaries, respectively. The theoretical results are calculated with the temporal coupled-mode theory. The resonant frequencies in the experimental, simulation, and theoretical results are 717, 727, and 726 Hz, respectively. The working bandwidth (FWHM) in experimental, simulation, and theoretical results are 17 Hz (from 709 to 726 Hz), 17 Hz (from 719 to 736 Hz), and 26 Hz (from 715 to 741 Hz), respectively. The $Q$ factors in experimental, simulation, and theoretical results are 42.2, 42.8, and 27.9, respectively.

Figure 6

Conceptional demonstration of ${\log }_{10}(\left|\mathrm{Im}({\sigma }_1)\right|)$ of the presented two-state system corresponding to Figs. 1 and 1.

Figure 7

(a) Conceptional demonstration of radiation quality factor ${\log }_{10}(Q_{\mathrm{rad}2})$ of the presented two-state system as functions of $\kappa$ and ${\omega }_2/{\omega }_1$. The parameters are set to ${\gamma }_1=0.2{\omega }_1$, ${\gamma }_2=0.04{\omega }_2$. (b) Conceptional demonstration of radiation quality factor ${\log }_{10}(Q_{\mathrm{rad}2})$ of the presented two-state system as functions of $\kappa$ and ${\gamma }_2/{\gamma }_1$. The parameters are set to ${\omega }_1=1\mathrm{Hz}$, ${\omega }_2=1.2\mathrm{Hz}$.

Figure 8

Four specific conditions ($l_h=100\mathrm{mm}$, $l_h=110\mathrm{mm}$, $l_h=112\mathrm{mm}$, and $l_h=125\mathrm{mm}$) in Fig. 3 and the corresponding reflection coefficients. The green stars mark the peaks (dips) in the reflection curves, where the corresponding pressure fields are shown in the right panels.

Figure 9

The near-field coupling factors ($\kappa$) of the two-cavity system as function of $d_a$ (a) and as function of $l_h$ (b). The tube distance $l_h$ is fixed to 146 mm for (a), and the tube diameter $l_h$ is fixed to 27 mm for (b).

Figure 10

Reflection curves in the conditions of $d_a$ from 8.4 to 27 mm referring to Fig. 4.