We study the operation of a synchronously pumped mode-locked dye laser when the pump pulse is taken as a Dirac delta function, a limit that is sometimes experimentally reasonable. We find that in this limit the model simplifies considerably and that with further assumptions the physical interpretation of synchronously pumped mode-locked operation becomes apparent. Specifically, our nonlinear dynamical model reduces to the same set of equations that govern a prepumped Q-switched laser, and from

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... his simple picture we are able to derive approximate analytic formulas for the synchronously pumped mode-locked laser pulse width and peak intensity. Additionally, we present a closed-form solution for the output pulse in the limit of zero-cavity-length mismatch between the pump laser and the dye laser.