Slip Rates and Slip Modes in an Actively Mode-Locked Laser

Pulses in an actively mode-locked laser can occasionally slip relative to the timing signal, leading to fluctuations in the pulse repetition rate. Such events happen rarely, however, making it infeasible to use traditional methods to determine the slip rate. Here, in a model of a soliton-based mode-locked laser, quantification of the error rate is obtained using importance-sampled Monte Carlo simulations guided by soliton perturbation theory. Position slips are studied in two distinct cases: an overdamped regime where they are primarily direct and an underdamped regime where they typically involve oscillations. Quantification of the slip rate is shown to be more straightforward in the overdamped regime, but dynamic importance sampling is found to be necessary to accurately and efficiently capture error rates. Dynamic importance sampling is shown to be more difficult to implement in the underdamped regime due to the existence of multiple routes by which errors can occur.