Bound States in the Continuum with Vectorial Topological Charge.

Bound states in the continuum (BICs) have long been recognized as topological singularities of light, yet their descriptions have relied solely on scalar topological charges that trace a polarization angle rotation, leaving their true vectorial topology unexplored. Here, we apply the concept of a vectorial topological charge (VTC) to BICs, resolving this fundamental limitation by capturing the full set of winding numbers of (S_{1}, S_{2}, S_{3}) axes on the Poincaré sphere. Using bilayer photonic crystal slabs as a model system, we reveal that nontrivial VTCs can be manifested through pseudopolarization singularity generated by BICs within the perturbation parameter space. Intriguingly, such a VTC further links BICs to counterrotating phase singularities in the upward and downward radiation channels-an effect invisible in scalar frameworks. Moreover, the multicomponent nature of VTCs drives a BIC to split into multiple pairs of half-integer pseudopolarization singularities under symmetry breaking, rather than merely forming a pair of circular pseudopolarization states, thereby defying the conventional rules of topological charge evolution. Our findings reveal a richer vectorial topology that enables control of BICs beyond scalar descriptions.