Numerical investigation of the fractional-soliton mode-locked fiber laser.

We propose and numerically investigate a fractional-soliton mode-locked fiber laser by utilizing an intracavity spectral pulse shaper (SPS). The fiber laser can generate stable fractional-soliton pulses for three different Lévy index α (1 < α < 2), whose profiles are all close to the sech shape. We find that the positions of Kelly sidebands, pulse energy, and peak power of the emitted fractional pulses conform to three theoretical expressions, respectively. The numerical results are in good agreement with the theoretical analyses. In addition, the intracavity dynamics of the fractional pulses have been discussed. Our findings not only deepen the fundamental understanding of temporal fractional soliton but also provide a novel, to the best of our knowledge, approach to generating stable ultrashort fractional pulses.