Effect of Relative Phase on the Stability of Temporal Bright Solitons in a PT- Symmetric NLDC

In this paper we numerically investigate the effect of relative phase on the stability of temporal bright solitons in a Nano PT- Symmetric nonlinear directional coupler (NLDC) by considering gain in bar and loss in cross. We also study the effect of relative phase on the output perturbed bright solitons energies, in the range of pt 0 to  180 . By using perturbation theory three eigenfunctions and corresponding eigenvalues were derived analytically. These eigenvalues behave like equilibrium points and are not stable in all cases. Stability of these perturbed solitons under the effect of relative phase are examined and show that temporal bright solitons are almost unstable in the range of pt 0 top t 90 , but they keep their solitary shapes in the range of p t 90 to p t 180 . In addition the evolution of normalized energies in these ranges are investigated. Output pulse energy at bar and cross strongly depend on the relative phase. This effect in a PT-Symmetric NLDC can be used for designing all-optical ultrafast self-switches and logic gates and Nano structures