Bound states in the continuum and topological phase singularities in an acoustic Gires-Tournois interferometer setting

Photonic bound states in the continuum (BICs) have been identified as vortex polarization singularities within the momentum space, revealing their captivating topological traits. In contrast, the topological characteristics of acoustic BICs remain largely unexplored. In this paper, we delve into the behavior of BICs within an acoustic Gires-Tournois interferometer (GTI) setting. The underlying physics of BICs formation is illuminated through rigorous analyses of the structure's eigenfields, combining theoretical insights with numerical simulations. Leveraging our eigenfield analyses, we establish that BICs are associated with phase singularities in the out-of-plane radiation, represented by phase winding numbers that act as topological indices, thereby conferring robustness against perturbations in the system's structural parameters. Additionally, we introduce a temporal coupled-wave theory to dissect the phase interplay between total reflection fields and resonant radiation fields under the influence of incident waves. Harnessing this relationship enables the extraction of resonant radiation-field phase information from measured total reflection fields, offering experimental validation that acoustic BICs constitute topological phase singularities. Ultimately, both numerical and experimental results indicate that the acoustic GTI is capable of sustaining phase resonances with high-quality factors and group delays, suggesting significant potential for applications in dispersion engineering.