Random laser model for Nd³⁺-doped powders and its application to stimulated emission cross-section calculations

A new theoretical approach for random lasing of Nd³⁺doped powders is presented. The model's singularity lies in the fact that it proposes a probability distribution of the stimulated photon paths lengths in the sample, as well as a population inversion shared by different photon paths. The model's predictions satisfactorily compare with the results of laser threshold and absolute input/output energy slope of a real Random Laser. The main novel issue is that the best fit to the experimental results requires considering a high level of shared population inversion among different paths. The model simulation of local and spatially integrated Random Laser emissions, as well as their time evolution, is in accordance with the experimental behavior. These results also provide a new method of measuring the stimulated emission cross-section in this kind of random laser materials.