Figure-9 mode-locked fiber laser using liquid crystal variable retarders

We propose a scheme for a Figure-9 mode-locked fiber laser that utilizes liquid crystal variable retarders (LCs) with tunable splitting ratios and non-reciprocal phase shifts. Simulation results demonstrate that the parameter space can be effectively explored through full-wave scanning of the two LCs, while fast axes of both LCs are oriented at an angle of -1/4π to the horizontal plane. Under quasi-symmetric conditions, experimental results confirm the scheme's capability to control the mode-locking state. By varying the retardance of the LCs, we map the distribution of mode-locking states in the parameter space. Our findings reveal that, due to the difference in nonlinear transmission from the conventional scheme, this scheme has a similar distribution of mode-locking states but is more conservative. This innovative scheme offers a fast-response laser platform without moving parts, making it suitable for research in laser technology, intelligent mode locking, and ultrafast dynamics.