Inverse saturable absorption mechanism and design optimization of mode-locked fiber lasers with a nonlinear amplifying loop mirror

From the point of view of the differential phase delay experienced by the two counterpropagating optical fields, the self-starting of the mode-locked fiber laser with a nonlinear 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 nonlinear phase shifts (NPSs) in these two cases, resulting in inverse saturable absorption (ISA) during 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. In addition, we analyze the influences of gain-fiber position, splitting ratio, and optical attenuator in the fiber loop, on the differential NPS and self-starting process. 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.