Abstract

Ring lasers containing a nonlinear dispersive fiber (eventually ion doped) should be described by an infinite dimensional map involving the nonlinear Schroedinger (NLS) equation. This includes, for example, sinchronously pumped modulational instability lasers and erbium doped soliton lasers. We show that, under proper hypotheses, spatial averaging procedures allow us to describe the periodic forcing and damping along the ring by means of a single partial derivative equation, in the form of a driven-damped NLS or forced Ginzburg–Landau equation. The model permits us to study the formation of dissipative temporal patterns from an injected signal (i.e., from modulational instability). The numerical integration of this equation, in agreement with that of the map, reveals the existence of regimes where either the stable emission of pulse trains or the chaotic emission of temporal structures may occur. We are able to determine the role of the different parameters, such as pump power, fiber dispersion, cavity detuning, and gain dispersion (for active fibers), in laser emission. A simple insight is given by means of linear stability analysis, whereas we describe the nonlinear depleted stage of the emission by means of a truncated modal expansion. The reduced description preserves the complexity of the original model and permits us to characterize the existence of Hopf bifurcations, leading to periodic emission of patterns as well as the chaotic regime of operation.

© 1992 Optical Society of America