Generalization of exceptional point conditions in perturbed coupled resonators

Abstract

The phase singularity in open systems, known as the exceptional point (EP), has revealed exotic functionalities, especially in optics---as an illustration, ultrasensitive sensors and laser beam unidirectionality. The strong sensitivity to perturbations around the EP has been suggested for sensing applications. Nevertheless, the characteristics of such highly sensitive systems can be affected by unwanted perturbations during the fabrication process. However, if one can control perturbation, it can be considered as an additional degree of freedom to create and tune EPs, enabling fascinating phenomena. In this paper, we propose an analytical method to investigate such systems. We analytically derive the general conditions of EPs in the perturbed pair of coupled ring resonators, where both resonators can be perturbed by different scatterers. Several numerical examples are employed to verify the proposed analytical method. We propose a simple experimental scheme where the predicted effects can be confirmed. It is also shown that by changing the relative position of the scatterers with respect to each other, quite interesting states such as a chiral EP in one resonator or simultaneous chiral EPs in both resonators could be observed, making such a system a highly functional tunable device which can have several applications such as quantized reflection/transmission and $q$-bits.