  Planar microcavities allow the control and manipulation of spin-polarization,
manifested in phenomena like the optical spin Hall effect due to the intrinsic
polarization mode splitting. Here, we study a transparent microcavity with
broken rotational symmetry, realized by aligning the optical axis of a uniaxial
cavity material in the cavity plane. We demonstrate that the in-plane optical
anisotropy gives rise to exceptional points in the dispersion relation, which
occur pair-wise, are circularly polarized, and are cores of polarization
vortices. These exceptional points are a result of the non-Hermitian character
of the system, and are in close relationship to singular optical axes in
absorptive biaxial systems.
