Stability of pulses in the master mode-locking equation

The master mode-locking equation is a canonical model for mode locking in solid-state lasers. We consider the dynamics and stability of the localized pulse solutions that this equation admits of. We provide analytic proof of stable mode-locking behavior along with analysis that shows that mode locking can become destabilized as a result of either a radiation-mode or a saddle-node instability. This is to our knowledge the first analytic proof of the stability of the pulse solutions that takes the time-dependent gain saturation mechanism of mode-locked lasers into account.

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