Replica symmetry breaking in random lasers: A Monte Carlo study with mean-field interacting photonic random walkers

Abstract

We investigate the replica symmetry breaking (RSB) phenomenon in random lasers (RLs) through Monte Carlo simulations employing photonic random walkers that diffuse and get randomly scattered in the active medium. The walkers interact not only with the population of excited atoms, but also among themselves, in a mean-field-type approach based on the Langevin equation for the stochastic dynamics of RL modes. We obtain the proper profile of the distribution $P(q)$ of the Parisi overlap parameter in the RSB glassy phase, with two pronounced side maxima at $q=\ifmmode\pm\else\textpm\fi{}1$ above the RL threshold, in contrast with some recent numerical studies. Remarkably, when the interactions among photonic walkers are not included, a replica-symmetric profile with a single maximum of $P(q)$ at $q=0$ is found for any excitation energy. We further study the Gaussian and L\'evy emission regimes and statistical correlations of intensity fluctuations in distinct modes of the same spectrum, using a Pearson correlation coefficient recently applied to RLs. Our findings are consistent with experimental results for the intensity statistics and $P(q)$ distributions in RL materials.