  We present a novel approach for the analysis of passively mode-locked
semiconductor lasers that allows for efficient parameter sweeps and time jitter
analysis. It permits accessing the ultra-low 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 magnitudes 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.
