Integrability and trajectory confinement in-symmetric waveguide arrays

Abstract

We consider $\mathcal{PT}$-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 $\mathcal{PT}$-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.

Publication
Journal of Physics A: Mathematical and Theoretical