Dependence of NdSc_3(BO_3)_4 random laser parameters on particle size

We have studied the threshold, slope efficiency, and emission kinetics in the ${\mathrm{NdSc}}_3({\mathrm{BO}}_3{)}_4$ random laser as a function of powder particle size. The experimental results are compared with the predictions of diffusion theory. It is shown that under a certain set of assumptions, the diffusion model can qualitatively explain major features in random laser behavior, such as the minimum of the threshold pumping energy at intermediate particle sizes. However, we could not describe with this model functional relationships between various system parameters measured in the experiment.