Statistical mechanics models for multimode lasers and random lasers

Referring to recent approaches to multimode laser theory, including Monte Carlo simulations of effective models and statistical mechanical analytic computations, the status for a complete nonperturbative theory in open and disordered cavities is discussed and the derivation of the general statistical models in this framework is presented. When light is propagating in a disordered medium, the relevant models can be analysed via the replica method. For high degrees of disordered-induced frustration and nonlinearity, a glassy behaviour is expected beyond the lasing threshold, providing a suggestive link between glasses and photonics. We describe in detail the results for the general Hamiltonian model in the mean field approximation and we analytically justify an available test for replica symmetry breaking from intensity spectra measurements. Finally, we draw perspectives for such approaches.