Split-step solitons in single-and multichannel fiber links

Abstract

We consider a long fiber-optic link consisting of alternating dispersive and nonlinear segments, i.e., a split-step model (SSM). Passage of a soliton through one cell of the link is described by an analytically derived map. Multiple numerical iterations of the map reveal that, at values of the system's stepsize (cell's size) L comparable to the pulse's dispersion length ZD, SSM supports stable propagation of pulses which almost exactly coincide with fundamental solitons of the corresponding averaged NLS equation. However, in contrast with the NLS equation, the SSM soliton is a strong attractor, i.e., a perturbed soliton rapidly relaxes to it, emitting some radiation. If the initial amplitude of the pulse is too small, it turns into a breather, and, below a certain threshold, it quickly decays into radiation. If L is essentially larger than ZD, the pulse rapidly rearranges itself into another one, with nearly the same area but essentially smaller energy. At L still larger, the pulse becomes unstable, with a complex system of stability windows found inside the unstable region. Moving solitons are generated by "pushing" them with a frequency shift, which makes it possible to consider collisions between solitons in a two-channel model emulating the WDM regime of data transmission in a communication line. We conclude that the collisions are strongly inelastic if they take place inside the nonlinear section of the system, and the solitons pass through each other without interaction if they collide inside the linear section.