Merging and separation of polarization singularities in complex lattices

The evolution in momentum space of bound states in the continuum (BICs) and circularly polarized states (CPSs) — as far-field polarization singularities — can be observed by controlling the geometric parameters of photonic crystals. This offers significant potential in optics and photonics. Here, we reveal that in complex lattices far-field polarization singularities can be flexibly manipulated while preserving structural symmetry. A change in topological charge for the at-Γ BIC can generate new BICs or CPSs. At an off-Γ point, a BIC can spawn from the collision of two CPSs. As the thickness of the structure increases, this BIC will meet the at-Γ BIC. The merging of BICs can induce topological charge transition and yield a large wavevector space around the Γ point with ultra-high quality (Q) factors. Our findings provide a novel degree of freedom for manipulating polarization singularities, which holds great promise in radiation modulation and singular optics.