标题： 被动锁模半导体激光器在光反馈作用下的时间抖动；一种半解析方法 显示英文标题

标题： Timing jitter of passively mode-locked semiconductor lasers subject to optical feedback; a semi-analytic approach

摘要： 我们提出了一种计算锁模半导体激光器中时间波动的半解析方法，并将其应用于研究延迟相干光反馈对这些激光器脉冲时间抖动的影响。 所提出的方法大大减少了计算时间，因此允许对时间波动在更大参数范围内的依赖性进行研究。 我们表明，共振反馈会导致时间抖动的减少，并且在主要共振附近形成一个频率牵引区域，在该区域内观察到时间抖动的减少。 这些频率牵引区域的宽度随着短反馈延迟时间的增加而线性增加。 我们推导出一个时间抖动的解析表达式，该表达式预测当时间抖动效应与幅度抖动效应完全分离时，随着延迟长度的增加，共振反馈的时间抖动会单调减少。 对于长反馈腔，时间抖动的减少大约随反馈延迟时间$\tau$的增加而按$1/\tau$的比例变化。 显示英文摘要

摘要： We propose a semi-analytical method of calculating the timing fluctuations in mode-locked semiconductor lasers and apply it to study the effect of delayed coherent optical feedback on pulse timing jitter in these lasers. The proposed method greatly reduces computation times and therefore allows for the investigation of the dependence of timing fluctuations over greater parameter domains. We show that resonant feedback leads to a reduction in the timing jitter and that a frequency-pulling region forms about the main resonances, within which a timing jitter reduction is observed. The width of these frequency-pulling regions increases linearly with short feedback delay times. We derive an analytic expression for the timing jitter, which predicts a monotonous decrease in the timing jitter for resonant feedback of increasing delay lengths, when timing jitter effects are fully separated from amplitude jitter effects. For long feedback cavities the decrease in timing jitter scales approximately as $1/\tau$ with the increase of the feedback delay time $\tau$.