Generalized Haus master equation model for mode-locked class-B lasers

Using an asymptotic technique, we develop a generalized version of the class-B Haus partial differential equation mode-locking model that accounts for both the slow gain response to the averaged value of the field intensity and the fast gain dynamics on the scale comparable to the pulse duration. We show that unlike the conventional class-B Haus mode-locked model, our model is able to describe not only Q-switched instability of the fundamental mode-locked regime but also the leading edge instability leading to harmonic mode-locked regimes with the increase of the pump power.