Acoustic scattering singularities via quasi-Bound states in the continuum

Abstract

Non-Hermitian systems enable advanced control of wave propagation by exploiting engineered losses. This introduces an additional degree of freedom that permits the emergence of exceptional points (EPs). In this letter, we theoretically and experimentally demonstrate the control of scattering singularities in a non-Hermitian acoustic system using quasibound states in the continuum (qBICs). Through Friedrich Wintgen interference, the losses of a two port cavity are tuned until achieving critical coupling, yielding narrowband coherent perfect absorption (CPA) with a quality factor of 140. Additionally, by coupling two distinct resonators, we observe the emergence of an EP, where both eigenvalues simultaneously coalesce and vanish, resulting in narrowband unidirectional absorption. Our results establish a connection between qBICs and scattering singularities, and offer a route toward acoustic devices featuring narrowband resonances and tunable radiative losses.

Figures (5)

• Figure 1: Interplay between qBICs and absorption in two-port scattering problems with input $(a_1,a_2)$ and output $(b_1,b_2)$ waves. (a) Resonator $\Sigma_1$ with resonance frequency $f_0$, radiative $\gamma_{rad}$ and intrinsic $\gamma_{int}$ decay rates. A conventional resonator under critical coupling conditions yields CPA when $\gamma_{int}=\gamma_{rad}$ but typically with a moderate or low $Q$ factor. Once a qBIC is employed, the critical coupling condition can be satisfied with significantly lower $\gamma_{rad}$, resulting in narrowband absorption. (b) EP combining qBIC resonance and absorption using a system of coupled resonators $\Sigma_1$ and $\Sigma_2$. In this configuration, the eigenvalues and eigenvectors simultaneously vanishes, resulting in a unidirectional absorber. Waves impinging from the left are fully absorbed while waves propagating from the right are fully reflected.
• Figure 2: Formation of a qBIC in an acoustic cavity. (a) Cavity of dimension $L_x$, $L_y$ and $L_z$ with two radiation channels. (b) Resonance frequencies for varying cavity length $L_x$. The dashed lines represents the resonance frequencies $f_{01}$ and $f_{10}$ in the absence of coupling. (c) $Q$ factors for varying $L_x$. Insets (i--iii) represents the pressure field magnitude (mode shapes) for $L_x = 93.6\,\text{mm}$, $L_x = 91\,\text{mm}$, and $L_x = 80\,\text{mm}$.
• Figure 3: Realization of CPA using qBIC resonance. (a) Eigenvalue $\vert \lambda_{-} \vert^2$ as a function of the cavity length $L_x$ and frequency, where $\lambda_-=t-r$. The red markers denote the points where CPA is realized via qBIC formation. The inset shows the eigenvalue for the lower red point ($L_x=91$ mm). (b,c) Pressure distribution for asymmetrical (+,-) and symmetric input waves (+,+), with $L_x=91$ mm. An asymmetrical input results in CPA with strong field localization inside the cavity, whereas a symmetrical input radiates strongly in the channels.
• Figure 4: Experimental validation of CPA using a qBIC resonator. (a) 3D printed cavity of inner dimensions $L_x=90$mm, $L_y=94$mm and $L_z=44$ connected to two channels of inner diameter $29$mm. (b-d) Magnitude of the scattering parameters: (b) reflection coefficient $r$, (c) transmission coefficient $t$, and (d) the eigenvalue $\vert \lambda_{-}\vert^2$. The blue and red colours represent the experimental and numerical results, respectively. The cross marker corresponds to the point where $r= t$.
• Figure 5: Emergence of an EP and unidirectional absorption using a qBIC. (a) Sketch of the coupled system. (b) Experimental setup using two acoustic resonators. The experimental results are presented as follow: (c) Magnitude of the scattering coefficient. (d) Absorption coefficient for left $\alpha^m=1-\vert t\vert^2 -\vert r^m\vert^2$ and right impinging waves $\alpha^p=1-\vert t\vert^2 -\vert r^p\vert^2$. (e) Real and imaginary part of the eigenvalues of the scattering matrix.