From the perspective of the differential phase delay experienced by the two counterpropagating optical fields, the self-starting of the mode-locked fiber laser with a non-linear amplifying loop mirror (NALM) is theoretically studied. Although it is generally believed that NALM shows a saturable absorption effect on both continuous wave (CW) light and pulses, we find a counter-intuitive fact that cross-phase modulation (XPM) leads to opposite signs of differential non-linear phase shifts (NPSs) in these two cases, resulting in inverse saturable absorption (ISA) during the pulse formation process. The ISA is not helpful for the self-starting of laser mode-locking and can be alleviated by introducing a non-reciprocal phase shifter into the fiber loop. These results are helpful for optimizing the design of NALM and lowering the self-starting threshold of the high-repetition-rate mode-locked fiber laser.
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