Multisoliton perturbation theory for the Manakov equations and its applications to nonlinear optics

Abstract

The effect of small perturbations on the collision of vector solitons in the Manakov equations is studied in this paper. The evolution equations for the soliton parameters (amplitude, velocity, polarization, position, and phases) throughout collision are derived. The method is based on the completeness of the bounded eigenstates of the associated linear operator in ${L}_{2}$ space and a multiple-scale perturbation technique. These results are applied to the coupled nonlinear Schr\"odinger equations, which govern the pulse propagation in birefringent nonlinear optical fibers. Both transmission and repulsion scenarios are predicted. More interestingly, it is found that, near the transition from transmission to repulsion, the collision outcome is very sensitive to the cross-phase modulational coefficient and initial soliton parameters. Rapid and considerably large oscillations in the parameters of the final vector solitons are observed. All these predictions are confirmed by direct numerical simulations. Applications of these results to ultrafast soliton switching devices are also discussed.