Quadruplets of exceptional points and bound states in the continuum in dielectric rings

In photonics, most systems are non-Hermitian due to radiation into open space and material losses. At the same time, non-Hermitianity defines a new physics, in particular, it gives rise to a new class of degenerations called exceptional points, where two or more resonances coalesce in both eigenvalues and eigenfunctions. The point of coalescence is a square root singularity of the energy spectrum as a function of interaction parameter. We investigated analytically and numerically the photonic properties of a narrow dielectric resonator with a rectangular cross section. It is shown that the exceptional points in such a resonator exist in pairs, and each of the points is adjacent in the parametric space to a bound state in the continuum, as a result of which quadruples of singular photonic states are formed. We also showed that the field distribution in the cross section of the ring is a characteristic fingerprint of both the bound state in the continuum and the exceptional point.