  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.
