Polarization dynamics in harmonic mode-locked vector soliton laser

Recently, harmonic mode locking (HML) has emerged as a practical pathway to high-repetition-rate pulse generation in fiber lasers. One intriguing characteristic of HML, the stepwise continuous harmonic order increase with pump power, has yet to be thoroughly examined for its detailed polarization and pulse characteristics. Here, we systematically investigate the polarization dynamics in the stepwise continued increase of harmonic order in a HML fiber laser. With the combined detections of a polarization-resolved measurement and a polarimeter, it is found, for the first time, that the stepwise growth in harmonic order induced by increasing pump power is accompanied by periodic switching between polarization-locked and polarization-rotation states. We experimentally unveiled that the boundary between polarization-locked and polarization-rotation regions is soliton energy dependent. Uniquely, the critical soliton energy (CSE) where a transition occurs between polarization-locked and polarization-rotation vector soliton remains almost invariant across all harmonic orders. During the stepwise continued increasing of harmonic order process, the polarization rotation dynamics leave the side-mode suppression ratio (SMSR) unaffected but degrade the signal-to-noise ratio (SNR) of HML operation due to the emerging polarization evolution frequency (PEF). We also discovered that the abrupt jumps of phase difference between orthogonal polarization components during the polarization-rotation process will cause SMSR degradation and consequent HML destabilization. Our findings provide profound insights into vector solitons in ultrafast fiber lasers and offer essential guidance for developing stable high-repetition-rate lasers with controllable polarization states.