One of the interesting features of open quantum and wave systems is the non-Hermitian degeneracy called an exceptional point, where not only energy levels but also the corresponding eigenstates coalesce. We demonstrate that such a degeneracy can appear in optical microdisk cavities by deforming the boundary extremely weakly. This surprising finding is explained by a semiclassical theory of dynamical tunneling. It is shown that the exceptional points come in nearly degenerated pairs, originating from the different symmetry classes of modes. A spatially local chirality of modes at the exceptional point is related to vortex structures of the Poynting vector.
