Collisions of dark solitons in optical fibers

Abstract

We have used numerical simulations to study dark soliton collisions in optical fibers. The starting field consists of two gray solitons either on an infinite background or on a finite duration background pulse. The phase profiles of the input gray solitons are chosen so that they have equal and opposite velocities with respect to the background. According to simulations that use the conventional nonlinear Schrodinger equation, the dark solitons pass through each other and emerge unchanged except for a temporal shift, in confirmation of the soliton nature of the input pulses. As the blackness1 (i.e., the soliton depth) is increased toward 1.0, the relative velocity of the solitons decreases toward zero and the temporal shift resulting from the collision increases. The blackness dependence of the shift is determined. When the blackness is less than about (3/4)0.5 (minimum intensity greater than one-quarter of the maximum), there is a single minimum in the resultant intensity at the time of intersection. For blacker pulses, there is always a double minimum in the intensity. When the Raman contribution to the nonlinear index is included,2 the slower soliton becomes blacker and more shifted than the faster one. These calculations lay the groundwork for possible experiments aimed at observation of dark soliton collisions.