Control of the rings of exceptional points in photonic crystal slabs

Accidental Dirac cones of linear dispersion can occur in photonic crystal (PhC) structures [1]. These configurations can be easily manufactured providing an accessible platform for studying topological properties of Dirac cones and their influence on light-matter interactions. Recently, it has been shown that when the system becomes non-Hermitian, e.g. it is an open system exhibiting radiation losses, Dirac cones can be deformed spawning rings of exceptional points [2]. Within the ring, the dispersion follows the two-dimensional flat band which provides a high density of states and therefore high Purcell factors. Moreover, strong dispersion of loss in the center of the Brillouin zone allows to significantly improve the performance of large-area single mode PhC lasers [3]. These lasers exploit bound states in the continuum [4], and we discuss their relation to Dirac cones.