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

Abstract

We examine conditions under which certain combinations of initial pulse shape and chirp, or phase modulation, destabilize solitons in optical fibers. Destabilization occurs when eigenvalues (EVs) of an associated Zakharov–Shabat system, which move along the positive imaginary axis with increasing chirp parameter C, either are absorbed into the lower half plane or collide with another EV. In either the absorption or collision case the corresponding soliton, which is a solution of the nonlinear Schrödinger equation with constant or periodic amplitude as a function of propagation distance, becomes 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 identify several properties of general EV evolution, as C varies, and give a heuristic criterion under which initial pulses of a certain shape experience EV absorptions only, with no collisions.