Superimposition of topological charges between vortex beams and singular points of photonic crystal slabs

The bound state in the continuum (BIC) is a singular point of polarization in the momentum space of a periodic structure. It has been demonstrated that vortex beams can be generated by utilizing the polarization vortex around BIC based on the geometric phase in momentum space. In this letter, we propose a reflective photonic crystal (PhC) to generate a vortex beam and demonstrate the superimposition of topological charges in the momentum space between PhC and the vortex beams. In addition to BICs, we demonstrate that other singularities like degenerate points can also be used to generate vortex beams.