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We propose a semi-analytical method of calculating the timing fluctuations inmode-locked semiconductor lasers and apply it to study the effect of delayedcoherent optical feedback on pulse timing jitter in these lasers. The proposedmethod greatly reduces computation times and therefore allows for theinvestigation of the dependence of timing fluctuations over greater parameterdomains. We show that resonant feedback leads to a reduction in the timingjitter and that a frequency-pulling region forms about the main resonances,within which a timing jitter reduction is observed. The width of thesefrequency-pulling regions increases linearly with short feedback delay times.We derive an analytic expression for the timing jitter, which predicts amonotonous decrease in the timing jitter for resonant feedback of increasingdelay lengths, when timing jitter effects are fully separated from amplitudejitter effects. For long feedback cavities the decrease in timing jitter scalesapproximately as $1/\tau$ with the increase of the feedback delay time $\tau$.

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