Pulse energy equalization in harmonically FM mode-locked lasers with slow gain

Harmonic mode locking in lasers with slow gain relaxation times requires fast intensity-dependent loss (fast loss) to equalize the pulse energies. A practical method to obtain fast loss is to use self-phase modulation and spectral filtering (SPM+F). We show that in a frequency modulation mode-locked laser SPM+F produces a fast loss only when the cavity dispersion is anomalous. In the absence of SPM the dispersion creates a gain imbalance between the pulsing modes in the upchirped and downchirped modulation cycles, which causes one mode to dominate over the other.