Applicability of the diffusion model to random lasers with non-resonant feedback

Abstract

We demonstrate, theoretically and numerically, that the classical diffusion model does not correctly describe the propagation of photons in a scattering medium with non-uniformly distributed gain or loss. Correspondingly, the diffusion model fails to predict a number of interesting features in the behaviour of random lasers, in which the spatial distribution of gain, as a rule, is not uniform. We show that in the first approximation, although not exactly, the dynamics of photon propagation in a scattering medium with non-uniformly distributed gain (loss) can be described in terms of a diffusion equation with a gain-dependent (loss-dependent) diffusion coefficient. We have modelled the stimulated emission threshold and the stimulated emission dynamics in the surface-pumped laser with non-uniformly distributed gain. The model predictions include the dependence of the effective photon residence time on gain and the existence of the 'diffusion' and 'skin-layer' regimes of random laser operation.