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.

中文翻译：

---

被动锁模半导体激光器的功能映射

我们提出了一种现代方法来分析无源锁模半导体激光器，该方法可进行有效的参数扫描和时间抖动分析。它允许访问超低重复率模式，其中脉冲变为局部状态。包括慢速（例如热）过程或横向动力学在内的分析变得可行。我们的方法弥合了现象学但高效的脉冲迭代模型（即Haus主方程）与依赖于时间延迟方程的更为复杂的第一性原理描述之间的鸿沟。我们的迭代功能映射利用锁相模态在快速和慢速阶段之间的基本划分，并允许仅在脉冲附近计算动力学。演示了将仿真时间和内存占用量减少多达两个数量级的方法。最后，该映射还提供了用于基于延迟微分方程式从第一原理模型推导Haus主方程式的通用框架。