Dependence of the Gaussian-Lévy transition on the disorder strength in random lasers

Abstract

We examine the dependence of the Gaussian-L\'evy transition in random lasers on the disorder strength, through experimental and theoretical studies. Experiments are performed on samples whose disorder strength varied over almost an order of magnitude. It is found that the L\'evy regime is easily accessed under low excitation when the disorder is weak, compared to the energetically expensive transition in strong disorder. Besides, under conditions of weak disorder, the transition energy is mildly dependent on the disorder strength. The Gaussian-L\'evy transition also progresses rapidly in weakly scattering samples. In the theoretical investigation, we employ an analytical-numerical method to estimate the parameters of intensity statistics in random lasers. A Monte Carlo simulation is implemented to accurately calculate the excitation region of the random laser, yielding the ${\ensuremath{\ell}}_{g}$ and the geometric features of this region. The aspect ratio of this pumped region allows us to further analytically calculate the scale parameter $\ensuremath{\langle}L\ensuremath{\rangle}$ of a photon diffusing out of the amplifying region, thereby providing the power-law exponent $\ensuremath{\mu}$, which allows us to trace the Gaussian-L\'evy transition. We find an excellent agreement between the experimental and the theoretical results on the Gaussian-L\'evy transition with regard to the location and the rate of transition as a function of the disorder strength.