Integrability and trajectory confinement in -symmetric waveguide arrays

Abstract

Abstract We consider -symmetric ring-like arrays of optical waveguides with purely nonlinear gain and loss. Regardless of the value of the gain–loss coefficient, these systems are protected from spontaneous -symmetry breaking. If the nonhermitian part of the array matrix has cross-compensating structure, the total power in such a system remains bounded—or even constant—at all times. We identify two-, three-, and four-waveguide arrays with cross-compensatory nonlinear gain and loss that constitute completely integrable Hamiltonian systems.