Principal Component Analysis for Low-dimensional Modeling of Mode-locked Lasers

摘要

The ubiquitous onset of multi-pulsing in a laser cavity is considered in two representative laser models. 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 (Hopf) solutions and a period doubling and Neimark-Sacker (torus) bifurcation route to chaos. 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 proceeding the multi-pulsing transition.