A Functional Mapping for Passively Mode-Locked Semiconductor Lasers

TL;DR

This paper introduces a new functional mapping approach for passively mode-locked semiconductor lasers, enabling efficient analysis of parameter spaces, time jitter, and ultra-low repetition rates by bridging phenomenological and first-principle models.

Contribution

The novel iterative functional mapping method significantly reduces simulation time and memory usage while connecting the Haus master equation with detailed delay differential equation models.

Findings

Reduces simulation time and memory by up to two orders of magnitude.

Enables analysis of ultra-low repetition rate regimes.

Provides a framework to derive the Haus master equation from first principles.

Abstract

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.