Polarization singularities and optical chirality in dielectric metasurfaces

We theoretically study the relation between polarization singularities and optical properties in dielectric metasurfaces, or photonic crystal slabs. We focus on nondegenerate photonic bands leading to symmetry-protected Bound States in a Continuum (BICs). First, we discuss how BICs lead to polarization singularities in the far field, whose winding numbers – or topological charges – follows from the symmetry of the lattice. Then, we determine the polarization properties via the Stokes parameters, focusing on the conditions for the occurrence of a nonvanishing circular polarization. Finally, we calculate the optical response in reflection and the degree of circular dichroism. The results shed light on the role of polarization singularities and symmetry in determining the optical chirality.