Evolution of Topological Polarization Singularity in a Photonic Crystal Slab

The polarization singularity in momentum space, known as a new type of topological defect, has garnered tremendous attention across the nanophotonic community. Bound states in the continuum (BICs) and unidirectional guided resonances (UGRs) in a photonic crystal slab are two typical examples of polarization singularities. In this work, the fundamental connections among merging BICs, accidental BICs, and UGRs are established in a 1D dielectric photonic crystal slab. It is shows that UGRs in a slanted grating are rooted in merging BICs with a topological charge q = 0. By deviating the thickness from the critical value that forms merging BICs, two pairs of accidental BICs with opposite topological charges q = +1 and q = −1 are created along k_x-axis and k_y-axis in the first Brillouin zone, respectively. Moreover, such accidental BICs along k_x-axis can be evolved into UGRs if the tilted angles of two side walls are properly chosen. Also, it is shows that the sum of two tilted angles remains almost constant for UGRs, indicating an easy way of finding UGRs. Additionally, UGRs can be converted into accidental BICs by tuning the grating's thickness when the slanted grating has an inversion symmetry despite the broken mirror symmetry. Finally, it is shows that such BICs-UGRs transition is quite general, and works for high-order modes. Following the same designing strategy, more examples are found in both 1D metagratings (TE and TM cases) and 3D metasurfaces. The results deepen the understanding of the relationship between BICs and UGRs.