Probing the mode-locking pattern in the parameter space of a Figure-9 laser

Due to the many available cavity configurations, a generalized approach for identifying the optimal operating state of a Figure-9 mode-locked laser has proved a challenge. In this Letter, we probe the output pulsation states of an exemplar Figure-9 laser by meticulously scanning its parameter space. Regions corresponding to mode-locked operations are identified periodically in the map of the output states. We correlate these regions to a set of band-like cavity transmission functions that fundamentally allow ultra-short pulse formation. Interestingly, a clear correlation between the mode-locking pattern and the cavity configuration is observed. For example, with the decrease of the fiber loop symmetry in the cavity, half of the solutions in the mode-locking pattern are found to transit to forbidden states. Numerical calculations based on the Jones matrix are used to explain the experimental observations. In addition, the dynamic change of the map of output states is illustrated by using a setup with an automatic algorithm. Our results provide a visually-rich yet simple way for evaluating and optimizing a Figure-9 laser.