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A theoretical model is developed for characterizing mode-locking behavior using the variational method. The variational method is applied to three laser-cavity models, and a reduced master mode-locking model is obtained. Characterizing the mode-locking dynamics is the existence of a stable node, stable spiral, or limit cycle in the reduced equations highlighting the regions of a stable mode-locked operation. Fundamental in driving the laser dynamics is the nontrivial phase profiles generated during the mode-locking process. The variational method provides an excellent theoretical framework for optimizing laser performance for a wide range of mode-locking models.
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Bale et al. (2008) studied this question.
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