Split-step solitons in long fiber links

We consider a long fiber-optical link consisting of alternating dispersive and nonlinear segments, i.e., a split-step model (SSM), in which the disper sion and nonlinearity are completely separated. Passage of a soliton (local ized pulse) through one cell of the link is described by an analytically de rived 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 dispersi on length z(D), SSM supports stable propagation of pulses which almost exac tly coincide with fundamental solitons of the corresponding averaged nonlin ear Schrodinger (NLS) equation. However, in contrast with the NLS equation, the SSM soliton is a strong attractor, i.e., a perturbed soliton rapidly r elaxes to it, emitting some radiation. A pulse whose initial amplitude is t oo large splits into two solitons; however, splitting can be suppressed by appropriately chirping the initial pulse. On the other hand, if the initial amplitude is too small, the pulse turns into a breather, and, below a cert ain threshold, it quickly decays into radiation. If L is essentially larger than z(D), the input soliton rapidly rearranges itself into another solito n, with nearly the same area but smaller energy. At L still larger, the pul se becomes unstable, with a complex system of stability windows found insid e the unstable region. Moving solitons are generated by lending them a freq uency shift, which makes it possible to consider collisions between soliton s. Except for a case when the phase difference between colliding solitons i s less than or similar to 0.05 pi, the interaction between them is repulsiv e. We also simulate collisions between solitons in two-channel SSM, conclud ing that the collisions are strongly inelastic: even if the solitons pass t hrough each other, they suffer a large reduction of the amplitude. (C) 2000 Elsevier Science B.V. All rights reserved.