Soliton dynamics in optical fibers

This thesis examines the behavior of solitons in optical fiber communications and mode-locked fiber laser cavities. The techniques employed are mathematical and numerical analysis. The background material presented covers the derivation of the governing equation for soliton pulse propagation in optical fibers and outlines the perturbation methods used in analyzing optical systems which include the effects of linear loss, optical amplification, phase-modulation, and bandwidth filtering. Original research is then presented in two areas. First, the dynamics of a soliton pulse inside an erbium-doped fiber laser cavity are examined. Under the influence of a periodic phase-modulation the fiber laser can be mode-locked and produces a periodic stream of soliton pulses. Such a laser can be used as a clock-recovery circuit in an all-optical regeneration device which has been shown to reduce the timing jitter present in a transmitted data stream. The laser consists of an erbium-doped fiber amplifier enclosed in a cavity with a length of single-mode fiber and a frequency filter. The 'noisy' data stream and the laser radiation interact inside the single-mode fiber through cross-phase modulation. If the cavity period is equal to (or an integer multiple of) the bit period of the transmitted data then mode-locking occurs. We examine the behavior of the mode-locked laser in the limit where the group-velocity dispersion and self-phase modulation are sufficiently strong so that all other effects can be treated as small perturbations. Soliton perturbation theory is used to derive equations of motion for the soliton parameters under the influence of these perturbations. Secondly, a long-distance communication line is analyzed where the loss in the fiber is compensated by phase-sensitive amplification. Stable pulse evolution in such a system has been demonstrated in previous studies. Here we extend the model to include a phase-locking mechanism which provides phase-matching between the amplifier's pump waves and the in-phase field amplitude of the propagating signal pulse.