Bound states in the continuum (BICs) can confine light with a theoretically infinite Q factor. However, in practical on-chip resonators, scattering loss caused by inevitable fabrication imperfection leads to finite Q factors due to the coupling of BICs with nearby radiative states. Merging multiple BICs can improve the robustness of BICs against fabrication imperfection by improving the Q factors of nearby states over a broad wavevector range. To date, the studies of merging BICs have been limited to fundamental BICs with topological charges ±1. Here we show the unique advantages of higher-order BICs (those with higher-order topological charges) in constructing merging BICs. Merging multiple BICs with a higher-order BIC can further improve the Q factors compared with those involving only fundamental BICs. In addition, higher-order BICs offer great flexibility in realizing steerable off-Γ merging BICs. A higher-order BIC at Γ can split into a few off-Γ fundamental BICs by reducing the system symmetry. The split BICs can then be tuned to merge with another BIC, e.g., an accidental BIC, at an off-Γ point. When the in-plane mirror symmetry is further broken, merging BICs become steerable in the reciprocal space. Merging BICs provide a paradigm to achieve robust ultrahigh-Q resonances, which are important in enhancing nonlinear and quantum effects and improving the performance of optoelectronic devices.

连续体 (BIC) 中的束缚态可以限制具有理论上无限 Q 因子的光。然而，在实际的片上谐振器中，由于 BIC 与附近辐射态的耦合，不可避免的制造缺陷引起的散射损耗导致 Q 因子有限。合并多个 BIC 可以通过在宽波矢范围内提高附近状态的 Q 因子来提高 BIC 对制造缺陷的鲁棒性。迄今为止，合并 BIC 的研究仅限于拓扑电荷为 ±1 的基本 BIC。在这里，我们展示了高阶 BIC（具有高阶拓扑电荷的那些）在构建合并 BIC 方面的独特优势。与仅涉及基本 BIC 的那些相比，将多个 BIC 与高阶 BIC 合并可以进一步提高 Q 因子。此外，高阶 BIC 在实现可控的 off-Γ 合并 BIC 方面提供了极大的灵活性。Γ 处的高阶 BIC 可以通过降低系统对称性拆分为几个非 Γ 基本 BIC。然后可以调整拆分的 BIC 以与另一个 BIC 合并，例如，一个意外的 BIC，在 off-Γ 点。当面内镜对称性进一步破缺时，合并的 BIC 在倒易空间中变得可控。合并 BIC 提供了实现稳健的超高 Q 共振的范例，这对于增强非线性和量子效应以及提高光电器件的性能非常重要。