Stability and collisions of traveling solitons in Bragg-grating superstructures

We investigate stability of moving solitons in a nonlinear optical fiber with short segments of a relatively strong Bragg grating (BG) periodically inserted into it. The model is related to a class of composite and artificial optical media that have recently attracted much interest. The analysis is focused on moving solitons, as this is relevant to the experiment. By means of systematic simulations, we find that, in accordance with a qualitative consideration, the stability region for moving solitons first increases with velocity c but then decreases (in contrast to the uniform fiber BG, where the stability of the solitons depends very weakly on c). As well as in the uniform system, solitons do not exist for c exceeding the group velocity of light in the fiber, nor may they be stable with negative intrinsic frequencies. Collisions between solitons moving in opposite directions are also studied in a systematic way. A difference from the situation in the uniform fiber BG is strong shrinkage and eventual disappearance of a region where the collision results in a merger of the two solitons into a single one, which is explained too. Fiber waveguides with BG superstructures being currently available, moving solitons can be created in them by means of experimental techniques similar to those that have helped to generate solitons in uniform fiber gratings.