Vortex-frequency-comb generation assisted by PT-symmetric ring resonators

We study propagation of optical vortices (OVs) in coupled parity-time (PT) symmetric multimode fibers with equal gain and loss. We show that this system has two second-order exceptional points (EPs) of spectral branches confluence where the degenerate modes are odd and even Laguerre-Gaussian (LG) modes. We study the evolution of an arbitrary incoming superposition of LG modes with the same orbital index in such a coupler. We prove that if the loss parameter exceeds its value in the lowest-lying EP, in the limit of the large coupler's length the outcoming field tends to the same attractor state depicted on the orbital Poincare sphere (PS) by the orbital "black hole." We show that localization of such a "black hole" on the PS does not change with variations of loss parameter beyond its value at the lowest EP, which can be called the pinning of the orbital "black hole." We also demonstrate that the fiber ring resonator based on such a coupler can generate an optical vortex frequency comb (FC) far from the EP. The mechanism of such generation is not connected with any nonlinearity in the system. We determine the coupler's parameters under which such generation is feasible. This property can be useful for optimizing fiber-based orbital angular momentum communications.