The multi-pulsing transition in mode-locked lasers: a low-dimensional approach using waveguide arrays

The onset of multi-pulsing, a ubiquitous phenomenon in laser cavities, is considered. The multi-pulsing transition is studied in a specific model that uses a waveguide array as the cavity saturable absorber. Using a low-dimensional reduction constructed by the method of proper orthogonal decomposition (principal components), a complete characterization of the multi-pulsing transition is given, including the onset of periodic solution (Hopf bifurcation) and period-doubling bifurcation and Neimark–Sacker (torus) bifurcation as routes to chaos. To the best of our knowledge, this is the first low-dimensional construction of the entire multi-pulsing transition from N to N+1 pulses per round trip. The reduced model qualitatively reproduces the dynamics observed in the multi-pulse transition of the mode-locked laser and confirms recent experimental observations of periodic and chaotic behavior preceding the multi-pulsing transition.