# Spectral singularities of a potential created by two coupled microring resonators

## TL;DR

This paper explores how a system of two coupled microring resonators with gain and loss can exhibit spectral singularities, enabling diverse optical phenomena like lasing, perfect absorption, and unidirectional transparency at specific wavelengths.

## Contribution

It demonstrates the realization of spectral singularities in coupled microring resonators and their role in phase transitions between real and complex spectra, enabling various optical functionalities.

## Key findings

- Spectral singularities mark phase transitions in the system.
- The system can act as a laser or perfect absorber depending on parameters.
- Multiple optical effects occur at specific incident wavelengths.

## Abstract

Two microring resonators, one with gain and one with loss, coupled to each other and to a bus waveguide, create an effective non-Hermitian potential for light propagating in the waveguide. Due to geometry, coupling for each microring resonator yields two counter-propagating modes with equal frequencies. We show that such a system enables implementation of many types of scattering peculiarities, which are either the second or fourth order. The spectral singularities separate parameter regions where the spectrum is either pure real or else comprises complex eigenvalues; hence, they represent the points of the phase transition. By modifying the gain-loss relation for the resonators such an optical scatterer can act as a laser, as a coherent perfect absorber, be unidirectionally reflectionless or transparent, and support bound states either growing or decaying in time. These characteristics are observed for a discrete series of the incident-radiation wavelengths.