Merging multiple polarization singularities is a powerful strategy to create higher-order topological charges in photonic systems, yet previous works have primarily focused on merging identical singularity types, often requiring complex lattice symmetries or higher-order bands. The hybrid merging of distinct singularity types, such as bound states in the continuum (BICs) and non-BIC singularities, remains an unexplored frontier. Here, we demonstrate the systematic construction of higher-order merging BICs in conventional photonic crystal slabs by engineering the coalescence of accidental BICs with a quadratic degeneracy point. In a C4v-symmetric lattice, we realize a merging BIC with a topological charge of +3. By subsequently breaking the symmetry to C2v, we further engineer a +2 charged BIC on the resulting nondegenerate bands. This work establishes a versatile and controllable methodology for topological charge manipulation, significantly expanding the capacity for nonlocal vortex beam generation.
Su et al. (Thu,) studied this question.