Random laser thresholds in cw and pulsed regimes

We analyze the system of rate equations that, according to our previous studies, adequately describes the behavior of neodymium random lasers. We show that random lasers, in which a noticeable fraction of spontaneous emission goes to lasing modes, have different threshold behavior than regular lasers. We also demonstrate that although the dynamics of stimulated emission in random lasers is strongly dissimilar in different pumping regimes, the threshold energy remains constant, equal to the product of the cw threshold power and the spontaneous emission lifetime $\tau$, if the pumping pulse is much shorter than $\tau$. The results of the study suggest that one can compare the performance of random lasers in different operation regimes and use a cw approximation (with some restrictions) in an analysis of thresholds of pulsed random lasers.