Functional mapping for passively mode-locked semiconductor lasers.

We present a modern approach for the analysis of passively mode-locked semiconductor lasers that allows for efficient parameter sweeps and time jitter analysis. It permits accessing the ultralow repetition rate regime where pulses become localized states. The analysis including slow (e.g., thermal) processes or transverse dynamics becomes feasible. Our method bridges the divide between the phenomenological, yet highly efficient, pulse iterative model that is the Haus master equation, and the more involved first principle descriptions relying on time-delayed equations. Our iterative functional mapping exploits the fundamental division of the mode-locking regime between fast and slow stages and allows computing the dynamics only in the pulse vicinity. Reductions of the simulation times and of the memory footprint up to two orders of magnitude are demonstrated. Finally, the mapping also provides a general framework for deducing the Haus master equation from first principle models based upon delayed differential equations.