🔬 applied physics

Acoustic scattering singularities via quasi-Bound states in the continuum

This paper theoretically and experimentally demonstrates how tuning losses in a non-Hermitian acoustic system via quasi-bound states in the continuum enables the control of scattering singularities, achieving narrowband coherent perfect absorption and unidirectional absorption through critical coupling and exceptional points.

Original authors: Anis Maddi, Mourad Oudich, Aurelien Merkel, Julio A. Iglesias Martínez, Badreddine Assouar

Published 2026-07-16

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CC BY 4.0

Original authors: Anis Maddi, Mourad Oudich, Aurelien Merkel, Julio A. Iglesias Martínez, Badreddine Assouar

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the world of sound not just as noise, but as a river of invisible waves flowing through space. Usually, when these waves hit a wall or a hollow box, they bounce off, pass through, or get lost in a messy jumble of echoes. But scientists have recently discovered a way to play a high-stakes game of "hide and seek" with these sound waves. They use a special kind of physics called non-Hermitian systems, which is a fancy way of saying they intentionally add "loss" or "friction" to the mix. Think of it like a magician who doesn't just make a rabbit disappear, but carefully controls exactly how much of the rabbit's energy leaks out so they can make it vanish on command.

The star players in this story are called "Bound States in the Continuum" (BICs). Picture a sound wave trapped inside a room with no doors or windows; it's stuck there forever, humming away. That's a BIC. But in the real world, perfect traps don't exist. So, scientists use "quasi-BICs" (qBICs), which are like sound waves trapped in a room with a very, very tiny crack in the wall. The sound is mostly stuck, but a tiny bit leaks out. The magic happens when you can control that leak perfectly. If you tune the leak just right to match the sound's natural tendency to fade away inside the room, something amazing occurs: the sound doesn't just bounce back or leak out slowly. Instead, it gets swallowed whole, vanishing completely without a trace. This is called "Coherent Perfect Absorption" (CPA), and it's the acoustic equivalent of a black hole for sound.

In this paper, the researchers at the University of Lorraine in France decided to see if they could turn this theoretical magic into a real-world acoustic trick. They built a special rectangular box with two open pipes sticking out of it, acting as a trap for sound waves. By carefully adjusting the length of the box, they used a phenomenon called "Friedrich–Wintgen interference" to create a quasi-BIC. Think of this interference like two waves crashing into each other in a way that cancels out their ability to escape, effectively sealing the box's "crack" just enough to trap the sound, but not so much that it stays trapped forever.

The team found that by fine-tuning the box's geometry, they could hit a "sweet spot" where the sound waves entering the box were perfectly balanced with the energy leaking out. When they sent in two sound waves with the right timing (a specific phase difference), the box acted like a perfect vacuum for sound. The waves didn't bounce back, and they didn't leak out the other side; they were completely absorbed. In their experiments, they achieved this with a quality factor of 140, meaning the sound stayed trapped and resonated for a long time before being swallowed, creating a very sharp, narrowband absorption effect.

But the researchers didn't stop at just swallowing sound. They also connected two of these special boxes together to create a more complex system. In this setup, they discovered something even stranger called an "Exceptional Point" (EP). Imagine two dancers spinning in sync; at a specific moment, they merge into a single dancer and then vanish. In their system, the mathematical properties of the sound waves (called eigenvalues) merged and vanished simultaneously. This created a one-way street for sound: if you sent a wave from the left, it was absorbed 99% of the time. But if you sent a wave from the right, it bounced right back.

The paper confirms these results through both computer simulations and physical experiments using a 3D-printed plastic box. While the computer models predicted the effect perfectly, the real-world experiment showed a tiny difference because the 3D printing process left the plastic slightly rough, which added a bit more friction than expected. Despite this, the experiment successfully demonstrated the "swallowing" of sound with a quality factor of 140 and the creation of a one-way sound absorber. The researchers show that by mastering these "quasi-traps," we can build acoustic devices that act as incredibly precise filters or one-way sound valves, opening the door to new ways of controlling how sound moves through our world.

Technical Summary: Acoustic scattering singularities via quasi-Bound states in the continuum

Problem Statement
Non-Hermitian systems offer advanced control over wave propagation by exploiting engineered losses, enabling phenomena such as exceptional points (EPs) and coherent perfect absorption (CPA). However, in acoustics, implementing these effects is challenging because conventional acoustic resonances typically suffer from short lifetimes due to radiative and viscothermal dissipation. While Bound States in the Continuum (BICs) can achieve high quality factors ( $Q$ ) by suppressing radiation leakage, they are inherently non-absorbing ( $\gamma_{rad} = 0$ ) and thus cannot function as absorbers. Conversely, conventional CPA implementations often rely on low- $Q$ resonators to match strong radiative leakage, which limits their utility for strong sound confinement or narrowband filtering. There is a need to bridge the gap between high- $Q$ resonances (qBICs) and scattering singularities (CPA and EPs) to achieve narrowband, tunable acoustic absorption.

Methodology
The authors employ a combined theoretical and experimental approach to investigate a two-port rectangular acoustic cavity connected to two radiation channels.

Theoretical Framework: The study utilizes the concept of Friedrich–Wintgen (FW) interference, where the coupling between two distinct cavity modes ( $\psi_{10}$ and $\psi_{01}$ ) near an avoided degeneracy is engineered by tuning the cavity geometry (specifically the length $L_x$ ). This tuning allows for the precise control of radiative decay rates ( $\gamma_{rad}$ ). The system is modeled using a scattering matrix ( $S$ ) and a power matrix ( $\Pi = S^\dagger S$ ). The condition for Coherent Perfect Absorption (CPA) is defined as the vanishing of an eigenvalue of the scattering matrix ( $\lambda_- = r - t = 0$ ), which occurs when intrinsic losses ( $\gamma_{int}$ ) are perfectly balanced by radiative losses ( $\gamma_{rad}$ ).
Numerical Simulation: Simulations were performed using COMSOL Multiphysics to analyze eigenfrequency evolution, $Q$ factors, and pressure field distributions across varying cavity lengths.
Experimental Setup: A 3D-printed cavity made of polylactic acid (PLA) with dimensions $L_x = 90$ mm, $L_y = 94$ mm, and $L_z = 44$ mm was constructed. The cavity was connected to two ducts (29 mm diameter). Scattering coefficients ( $r$ and $t$ ) were measured using an impedance tube (B&K, Type 4206) to validate the theoretical predictions.

Key Contributions and Results

Control of Scattering Singularities via qBICs: The paper demonstrates that quasi-Bound States in the Continuum (qBICs) can be tuned to satisfy the critical coupling condition ( $\gamma_{rad} = \gamma_{int}$ ). By adjusting the cavity length $L_x$ to induce FW interference, the radiative losses are reduced from a high-leakage state to a level that matches intrinsic losses.
Narrowband Coherent Perfect Absorption (CPA):
- Theoretical analysis reveals that at specific cavity lengths (e.g., $L_x \approx 91$ mm and $96.5$ mm), the system achieves CPA with a significantly higher quality factor ( $Q_{CPA} \approx 224$ ) compared to conventional absorbers. This is because the underlying resonance is a qBIC with a maximum potential $Q$ of 467; introducing just enough radiation to reach critical coupling reduces the $Q$ by roughly half, yet it remains high.
- Experimental validation confirmed CPA at $f \approx 1868$ Hz with a measured $Q$ factor of 140. The discrepancy between the experimental $L_x$ (90 mm) and the simulated optimal length (91 mm) is attributed to surface roughness from 3D printing and wall vibrations, which introduce additional effective losses.
- The absorption is highly directional regarding input phase: CPA occurs only when input waves are asymmetric (out-of-phase, $\pi$ shift), leading to strong energy confinement within the cavity. Symmetric (in-phase) inputs excite a radiant mode, resulting in reflection/transmission rather than absorption.
Emergence of an Exceptional Point (EP): By coupling two distinct resonators ( $\Sigma_1$ and $\Sigma_2$ ) through an intermediate channel, the authors demonstrate the formation of an EP. In this configuration, both eigenvalues and eigenvectors of the scattering matrix coalesce and vanish simultaneously. This results in narrowband unidirectional absorption (99% absorption for waves from one side, full reflection from the other).

Significance
The paper establishes a direct connection between qBICs and scattering singularities, offering a route to acoustic devices that feature narrowband resonances with tunable radiative losses. By leveraging the interference mechanisms of qBICs, the authors show that it is possible to achieve critical coupling without sacrificing the high- $Q$ nature of the resonance. This approach overcomes the limitation of conventional CPA systems that rely on low- $Q$ resonators, thereby enabling strong sound confinement and the realization of narrowband filters and absorbers in non-Hermitian acoustic systems. The work provides a theoretical and experimental foundation for manipulating wave propagation through engineered losses in multi-port acoustic systems.

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