Observation of Extreme Anisotropic Sensitivity at Topological Bound States in the Continuum

Bound states in the continuum (BICs) are exceptional resonances with extremely high sensitivity and thus inherently fragile. Introducing topological concepts can fortify BICs against perturbations; however, existing topological BICs (TBICs) often rely on intricate strategies. Here, we explore the universality of TBICs governed by symmetry. Different symmetries naturally segregate wave states into uncoupled Hilbert subspaces, enabling independent topological band structure engineering in each subspace. This results in rich topological features, including TBICs, topological Fano resonance, and even exotic TBICs (eTBICs). Intriguingly, eTBICs inherit core attributes from both topological states and BICs, thereby exhibiting counterintuitive behavior-both strong immunity and high sensitivity. We conceptually and experimentally demonstrate this using an acoustic monolayer topological waveguide, uncovering exotic behavior in the transmission spectrum where the bulk is "muted" and the eTBIC is identified with extreme anisotropic sensitivity. Our findings may enrich the research implications of both topological physics and BICs.