Perturbations of Solitons in Optical Fibers

Abstract

Bright and dark solitons, namely, decaying localized pulses and dips off of a continuous-wave background, were predicted to occur in optical fibers more than 40 years ago. Since then, they have been extensively studied in theory and in experiments as they were proposed for applications in optical fiber communications. In the ideal case, optical fiber solitons are described by the completely integrable nonlinear Schrödinger (NLS) equation. In practice, however, solitons in real optical fibers evolve under the presence of various perturbations, such as linear loss, third-order dispersion, stimulated Raman scattering, and so on. Therefore, the study of solitons under perturbations is a particularly relevant and interesting problem. Here, we review soliton propagation (for both bright and dark solitons) in optical fibers. We provide a general framework, relying on the adiabatic perturbation theory for solitons, and then apply our methodology to a rather general higher-order NLS model. Special emphasis is given to the case of dark solitons, because – especially in the presence of dissipation – perturbation theory should take into account an additional generic feature of the propagation: a “shelf.” This is a linear wave that develops around the dark soliton as a result of the perturbations and accompanies the soliton during its propagation. Effects beyond the adiabatic perturbation theory, namely, the perturbation-induced emission of radiation and its influence on soliton interactions, are also discussed.