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.
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