The effect of relative phase on the stability of temporal dark soliton in $${{\mathcal {PT}}}$$ PT -symmetric nonlinear directional fiber coupler

Abstract

In this paper, we numerically investigate the effect of relative phase on the stability of dark solitons in $${\mathcal {PT}}$$ -Symmetric nonlinear directional coupler (NLDC), by considering gain in the bar and loss in the cross in the range of $$\theta =0^\circ$$ to $$180^\circ$$ . The $${\mathcal {PT}}$$ -Symmetric perturbed eigenfunctions are used to study the soliton stability. The results of simulations are shown that in the first half region of the relative phase the soliton is unstable while in the second one, is stable. In the stable region gain and loss cancel each other and also the perturbed eigenfunctions have no effect on solitons while in the unstable region solitons are amplified in the bar and attenuated in the cross except for some small intervals which the roles are changed. The behavior of such perturbation can be interpreted as self all-optical phase soliton switching and optical logic gates.