Stability of Temporal Dark Soliton in PT-Symmetric Nonlinear FiberCouplers in Normal Dispersion Regime

In this paper, we present analytical soliton solutions in a nonlinear PT-symmetric coupler with gain in one fiber and loss in the other one in the normal dispersion regime. As usual, we derive a temporal dark soliton solution for the coupler in the normal dispersion regime. We study the stability of the soliton solution by imposing a perturbation in the system by using the eigenvalue method. The results show that there exist two forms of perturbed soliton solutions, bright and dark. The numerical calculations show that the perturbed solutions in the bright form are stable and the dark form are unstable. Previous works in bright solitons show that there exists only one perturbed bright soliton solution which is stable only in particular regions.