Title: Topological polarization singularities induced by the non-Hermitian Dirac points

Abstract: A Dirac point in the Hermitian photonic system will split into a pair of exceptional points (EPs) or even spawn a ring of EPs if non-Hermiticity is involved. Here, we present a new type of non-Hermitian Dirac point which is situated in the complex plane of eigenfrequency. When there is differential loss, the Dirac point exhibits a dual behavior: it not only splits into a pair of EPs with opposite chirality in the band structure but also induces a pair of circularly polarized states (C points) with opposite handedness in the far-field radiation. Furthermore, breaking the corresponding mirror symmetries enables independent control of these Dirac-point induced C points, facilitating the merging of two C points and generation of unidirectional guided resonances. Our results demonstrate an explicit relation between the band singularities and polarization singularities, and provide a new mechanism to generate unidirectional emission, which can be useful in the band engineering and polarization manipulation.