Geometrical description of the onset of multi-pulsing in mode-locked laser cavities

A simple iterative model is introduced quantifying the interaction of saturable gain and nonlinear loss in a mode-locked laser cavity. The resulting geometrical description of the laser dynamics completely characterizes the generic multi-pulsing instability observed in experiments. The model further shows that the onset of multi-pulsing can be preceded by periodic and chaotic transitions as recently confirmed in theory and experiment. The results suggest ways to engineer the nonlinear losses in the cavity in order to achieve an enhanced performance.