An iterative model based on the LambertW function was developed for estimating the fundamental mode parameters of resonators with saturable gain guiding. The process of pulse buildup in passively Q-switched, end-pumped lasers was analyzed. The effective ABCD cavity matrix for consecutive round-trips was calculated, taking into account spatially variable saturated gain in an active medium and absorption bleaching in a saturable absorber. The twofold decrease in beam width, as compared with the fundamental mode of the bare cavity, was demonstrated. The application of such a model for resonators with other nonlinear elements is feasible.
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