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.

中文翻译：

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声学 Gires-Tournois 干涉仪设置中的连续体束缚态和拓扑相位奇点


连续体中的光子束缚态（BIC）已被确定为动量空间内的涡旋偏振奇点，揭示了它们迷人的拓扑特征。相比之下，声学 BIC 的拓扑特性在很大程度上仍未得到探索。在本文中，我们深入研究了声学 Gires-Tournois 干涉仪 (GTI) 设置中 BIC 的行为。通过对结构特征场的严格分析，将理论见解与数值模拟相结合，阐明了 BIC 形成的基本物理原理。利用我们的特征场分析，我们确定 BIC 与面外辐射中的相位奇点相关，由充当拓扑索引的相绕组数表示，从而赋予系统结构参数扰动的鲁棒性。此外，我们引入了时间耦合波理论来剖析入射波影响下全反射场和谐振辐射场之间的相位相互作用。利用这种关系可以从测量的全反射场中提取谐振辐射场相位信息，从而提供声学 BIC 构成拓扑相位奇点的实验验证。最终，数值和实验结果表明声学 GTI 能够维持具有高质量因子和群延迟的相位共振，这表明在色散工程中具有巨大的应用潜力。