Effective gain spectra vary the pulses spectrum in a mode-locked cavity

Filters typically play a crucial role in generating solitons by strictly confirming the working wavelength in a mode-locked laser. However, we have found that the broad smoothing filter with saturable gain also helps to regulate the pulses' operating wavelength. The effective gain, formed by the original gain spectrum and filters, shifts its center based on pulse energy, thereby affecting the pulse spectrum. A virtual mode-locked cavity is established to verify this approach in simulation. The results indicate that the spectrum changes with pulse energy, leading to a wider spectrum output. Our method paves the way for further investigations of the pulse spectrum and provides a practical approach to generating pulses at specific wavelengths.