Superposition- and interference-induced optical spectrum distortion in the figure-9 fiber laser

The output pulse spectra of the figure-8 and figure-9 lasers typically exhibit more pronounced distortion than those from mode-locked lasers based on other saturable absorbers, as well as the spectra of their own intracavity pulses. Here, we demonstrate two figure-9 lasers with repetition rates of 190.6 MHz and 92.4 MHz and introduce a self-designed beam splitter that exhibits minimal spectral filtering into the fiber loop to output two interference-free pulses. By applying superposition and interference calculations to the experimental spectra of these two pulses, we obtained calculated spectra and found that their characteristics agree with the distortion features observed in the experimental spectra from the other two ports where superposition and interference occur. Therefore, we conclude that the severe spectral distortion is caused by spectral superposition and interference, rather than the commonly believed nonlinear effects. Furthermore, analysis based on the interference theory of the figure-9 laser reveals that the $p$-components of the two intracavity light beams usually interfere with non-equal intensity at the beam splitter where interference occurs, while the $s$-components always interferes with almost equal intensity. This mechanism results in a significant yet stable spectral difference between the intracavity and output pulses. Moreover, a change in the pump power can amplify the difference between the two $s$-components, thereby leading to the emergence of a minor peak at the optical spectrum center. These findings provide new perspectives for simulating spectra that closely resemble experimental results and deepen our understanding of spectral evolution and pulse dynamics of the figure-9 lasers.