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.
© 2002 Optical Society of America
Todd Kapitula, J. Nathan Kutz, and Björn Sandstede, "Stability of pulses in the master mode-locking equation," J. Opt. Soc. Am. B 19, 740-746 (2002)