Spectral singularities of a potential created by two coupled microring resonators

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, the 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. The spectral singularities, which are either the second or fourth order, separate parameter regions where the spectrum is either purely real or composed of 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.