We study existence, stability, and dynamics of linear and nonlinear stationary modes propagating in radially symmetric multicore waveguides with balanced gain and loss. We demonstrate that, in general, the system can be reduced to an effective $\mathcal{PT}-\text{symmetric}$ dimer with asymmetric coupling. In the linear case, we find that there exist two modes with real propagation constants before an onset of the $\mathcal{PT}-\text{symmetry}$ breaking while other modes have always the propagation constants with nonzero imaginary parts. This leads to a stable (unstable) propagation of the modes when gain is localized in the core (ring) of the waveguiding structure. In the case of nonlinear response, we show that an interplay between nonlinearity, gain, and loss induces a high degree of instability, with only small windows in the parameter space where quasistable propagation is observed. We propose a novel stabilization mechanism based on a periodic modulation of both gain and loss along the propagation direction that allows bounded light propagation in the multicore waveguiding structures.

• Received 15 May 2014
• Revised 18 November 2014

DOI:https://doi.org/10.1103/PhysRevA.91.023822