Breathers in PT-symmetric optical couplers

Abstract

We show that the parity-time (PT) symmetric coupled optical waveguides with gain and loss support localised oscillatory structures similar to the breathers of the classical $\phi^4$ model. The power carried by the PT-breather oscillates periodically, switching back and forth between the waveguides, so that the gain and loss are compensated on the average. The breathers are found to coexist with solitons and be prevalent in the products of the soliton collisions. We demonstrate that the evolution of the small-amplitude breather's envelope is governed by a system of two coupled nonlinear Schr\"odinger equations, and employ this Hamiltonian system to show that the small-amplitude PT-breathers are stable.