Blow-up regimes in thePT-symmetric coupler and the actively coupled dimer

Abstract

In the actively coupled (AC) pair of waveguides, the growth of small perturbations is saturated by the focusing nonlinearity that couples the linearly growing mode to the linearly damped mode. On the other hand, in the $\mathcal{PT}$-symmetric coupler, the focusing nonlinearity promotes the blow-up of stationary light beams. The purpose of this study is to compare the nonlinear dynamics and explain the opposite effect of the same nonlinearity in the two systems. We show that, while the blow-up regimes are stable in the $\mathcal{PT}$-symmetric pair of waveguides, they are unstable and hence cannot be observed in the AC dimer.