We present a theoretical and experimental study aimed at characterizing statistical regimes in a random laser. Both the theoretical simulations and the experimental results show the possibility of three region of fluctuations increasing the pumping energy. An initial Gaussian regime is followed by a Lévy statistics and Gaussian statistic is recovered again for high pump pulse energy. These different statistical regimes are possible in a weakly diffusive active medium, while the region of Lévy statistics disappears when the medium is strongly diffusive presenting always a Gaussian regime with smooth emission spectrum. Experiments and theory agree in identification of the key parameters determining the statistical regimes of the random laser.

In a random laser the optical feedback is provided by scattering rather than by an optical cavity. Then, since its emission characteristics are very susceptible to the scattering details, it is a natural candidate for making active sensors to use as a diagnostic tool for disordered media like biological samples. However, the methods reported up to now, requiring the injection of toxic substances in the sample, have the drawback of altering the physical-chemical composition of the medium and are not suitable for in-vivo measurements. Here we present a random laser based sensor that overcomes these problems by keeping gain and diffusion separated. We provide an experimental characterisation of the sensor by using a reference diffusive liquid phantom and we show that, compared to a passive method, this sensor takes advantage of the gain and spectral properties of the random laser principle.

Random lasers are optical sources where light is amplified by stimulated emission along random paths through an amplifying scattering medium. Connections between their physics and the one of quenched disordered nonlinear systems, notably spin glasses, have been recently suggested. Here we report a first experimental study of correlations of spectral fluctuations intensity in a random laser medium where the scatterers displacement significantly changes among consecutive shots. Remarkably, our results reveal that the replica symmetry breaking (RSB) phenomenology is robust with respect to an averaging over different realizations of the disorder. Moreover, besides opening new intriguing questions about the understanding of such a phenomenon, this work aims to clarify the connection between the RSB with the onset of the Lévy regime, i.e. the fluctuations regime that is a peculiar feature of the random lasing under critical conditions. Our results suggest that the former occurs independently of the latter and then the RSB phenomenology is a generic feature linked to the random laser threshold.

Unlike a conventional optical cavity laser, a random laser system is generally characterized by a nondirectional output emission. In this work we report an experimental and theoretical study on the angular properties of the random laser emission and its dependence on the diffusive properties of the sample and the spatial gain profile, showing the possibility of controlling it by the total amount of available energy. We show that the directional characteristics are associated with the statistical regime of fluctuations in the emission spectrum and, in particular, with a Levy statistical regime. A model based on a phase-insensitive feedback mechanism has been used in order to explain the experimental data and two different Levy subregimes have been identified.

Optical sensing is a very important method for investigating different kinds of samples. Recently, we proposed a new kind of optical sensor based on random lasing [Sci. Rep. 6, 35225 (2016)], that couples the advantages of stimulated emission in detecting small variations on scattering properties of a sensed material, to the needs of no alteration of the sample under investigation. Here, we present a method to achieve a quantitative measurement of the scattering properties of a material. The results on samples of calibrated microspheres show a dependence of the peak intensity of the emission spectrum on the transport mean free path of the light within the sample, whatever the dimension (down to ≈100 nm of particle diameter) and the concentration of scatterers dispersed in the sensed material. A direct and fast measurement of the scattering properties is obtained by calibration with a well-known and inexpensive reference medium.