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

We study the effect of delayed coherent optical feedback on the pulse timing jitter in passively-mode-locked semiconductor lasers with the help of a semi-analytical method which we develop to calculate the timing fluctuations in these lasers. Through the proposed method physical insights into the feedback dependence of the timing jitter are gained and the greatly reduced computation times allow 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 monotonic 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 increasing feedback delay time tau. This behavior is not related to the stability of the system but is instead due to the influence of the noise, on the timing jitter, being reduced since the solution space is larger for increasing tau.