Researchers report a way to reach and measure a sound pattern confined inside a fully open acoustic structure. In the laboratory setup, nonlinear demodulation created localized audio-frequency virtual sources and was used to access a symmetry-protected bound state in the continuum, or BIC, without adding a radiative channel. In ordinary language, the BIC is a protected wave pattern that remains confined even though the structure is open.
The work is a laboratory study of a designed acoustic metasurface. Its central question was whether this nonlinear route could provide far-field access while still allowing measurement of the confined field and the resonance's quality factor.
Building and modelling the resonator
The modeled device was a rigid surface made from an infinite periodic array of repeating unit cells. Each cell contained four identical boreholes arranged in a square. That geometry was used to create the symmetry-protected acoustic mode under study.
To calculate the structure's bands and eigenmodes, the researchers used mode matching, enforcing continuity of pressure and normal velocity at the interface. They then used COMSOL finite-element simulations to validate the reduced configuration and its calculated symmetry-protected BIC eigenmode.
For the experiment, four ultrasonic-array modulation signals were driven with alternating phases. Nonlinear demodulation at the metamirror apertures generated localized audio-frequency virtual sources carrying that imposed phase pattern.
What the measurements found
The measured and simulated mode shapes agreed overall. Their reported mean relative error was 0.098, giving the researchers a direct comparison between the pattern calculated for the BIC and the pressure field observed in the experiment.
The frequency measurements were processed with hard time gating, a way of suppressing the incident-field contribution so the scattered response could be isolated. After gating, the broad incident spectrum was reduced to two dominant scattered-field peaks, at 2.013 kHz and 1.959 kHz.
The reported quality factor was 128 in the fully open acoustic environment. Quality factor is the study's measure of how sharply the resonance is concentrated in frequency. The paper did not report a confidence interval or a repeated-device estimate.
What the result does, and does not, show
The paper is careful about a separate measurement often read too broadly: its reported field enhancement is system-level, not a direct measure of intrinsic BIC enhancement. The incident and nonlinear scattered fields had different effective source strengths and were not equivalent excitations, so the result cannot by itself establish how strongly the BIC amplifies energy inside the structure.
A model-based intersection estimated the system's air-loss factor at 3.9 times 10 to the minus 3. That estimate depends on assuming that no radiative channel was opened, and residual radiative leakage was not independently measured. The number therefore describes a model-dependent estimate, not a direct leakage measurement.
The second resonance in the spectrum was not treated as a genuine BIC. It was assigned an estimated quality factor of 96.41 and described as a geometric feature of the enlarged experimental unit cell, rather than a separate physical mechanism.
Taken together, the results show a reported laboratory route to the target mode in this acoustic design. They do not turn the system-level enhancement into a measurement of intrinsic BIC amplification, and the reported quality factor remains a setup result without a confidence interval or repeated-device estimate.
Preprint status
The document is an arXiv version 1 preprint dated 28 Sep 2026. Its acknowledgements list support from MCIN/AEI, Generalitat Valenciana and the European Union, including the DYNAMO project.
Paper data and sources
Original title: Far-field excitation of symmetry-protected bound states in the continuum by nonlinear virtual sources
Authors: Marc Martí-Sabaté, Yijie Zhang, Shengming Sun et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-09-28
DOI: Not available
Original paper · Full text