Influence of pulse shape and frequency chirp on stability of optical solitons

We examine conditions under which certain combinations of initial pulse sha pe and chirp. or phase modulation, destabilize solitons in optical fibers, Destabilization occurs when eigenvalues (EVs) of an associated Zakharov-Sha bat system, which move along the positive imaginary axis with increasing ch irp parameter C, either are absorbed into the lower half plane or collide w ith another EV. In either the absorption or collision case the correspondin g soliton, which is a solution of the nonlinear Schrodinger equation with c onstant or periodic amplitude as a function of propagation distance, become s unstable. We have observed for the first time the emergence of an EV from the lower half plane that pursues, and collides with, an existing EV. We i dentify several properties of general EV evolution, as C varies, and give a heuristic criterion under which initial pulses of a certain shape experien ce EV absorptions only, with no collisions. (C) 2001 Elsevier Science B.V. All rights reserved.