Martínez, Alejandro J.Molina, Mario I.Turitsyn, Sergei K.Kivshar, Yuri2015-03-182015-03-181050-2947http://hdl.handle.net/1885/12986We 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 ƤƬ -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 ƤƬ -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.This work was supported in part by Fondo Nacional de Ciencia y Tecnología (Grant 1120123), Programa Iniciativa Científica Milenio (Grant P10-030-F), Programa de Financiamiento Basal (Grant FB0824) and the Australian Research Council. In addition, A.J.M. acknowledges support from Comisión Nacional de Investigación Científica y Tecnológica (Fellowship BCH72130485/2013).© 2015 American Physical Society. http://www.sherpa.ac.uk/romeo/issn/1050-2947/..."On author's personal website, employer's website or institutional repository. Publisher's version/PDF may be used. Link to publisher version required. " SHERPA/RoMEO site (as at 18/03/15)Keywords: Light propagation; Asymmetric coupling; Non-linear response; Periodic modulation; Propagation constant; Propagation direction; Radially symmetric; Stabilization mechanisms; Waveguiding structures; Waveguides2015-02-1710.1103/PhysRevA.91.0238222024-03-03