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

TL;DR

This paper explores the existence of quadruplets of exceptional points and bound states in the continuum within dielectric rings, revealing their analytical and numerical properties and characteristic field distributions.

Contribution

It introduces the concept of paired exceptional points adjacent to bound states in the continuum in dielectric resonators, forming quadruples of singular photonic states.

Findings

Exceptional points in the resonator exist in pairs.

Each exceptional point is adjacent to a bound state in the continuum.

Characteristic field distributions identify these states.

Abstract

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.