Bound States in the Continuum as Nodal Chain Points of Scattering Matrices

Bound states in the continuum (BICs), exotic resonances with infinite lifetimes embedded in radiation continua, have long been studied for their topological robustness. Meanwhile, nodal lines-degenerate momentum-space manifolds in photonic and electronic band structures-represent another cornerstone of topological physics. Here, we unveil a profound connection between these phenomena by demonstrating that BICs act as topological chain points pinning together nodal lines within scattering-matrix eigenvalue space. Through scattering-matrix eigenphase analysis, we show that BICs enforce robust nodal chain formation in frequency-momentum space, even when system symmetries are broken. Experimentally, we validate this mechanism using a metasurface platform, where angle-resolved phase measurements reveal nodal lines intersecting at a symmetry-protected BIC. Strikingly, breaking mirror symmetry preserves the BIC-pinned nodal chain, highlighting its origin in the intrinsic singular scattering nature of BICs rather than conventional symmetry protection. This Letter establishes scattering matrices as a natural framework to unify BICs and nodal topology, offering new pathways to engineer topologically robust photonic systems resilient to perturbations. Our findings bridge fundamental concepts in topological photonics and open avenues for applications in metasurfaces and light-matter interaction control.