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In this work, we present a robust and powerful method for the verification, with arbitrary accuracy, of Monte Carlo codes for simulating random walks in complex media. Such random walks are typical of photon propagation in turbid media, scattering of particles, i.e., neutrons in a nuclear reactor or animal/humans’ migration. Among the numerous applications, Monte Carlo method is also considered a gold standard for numerically “solving” the scalar radiative transport equation even in complex geometries and distributions of the optical properties. In this work, we apply the verification method to a Monte Carlo code which is a forward problem solver extensively used for typical applications in the field of tissue optics. The method is based on the well-known law of average path length invariance when the entrance of the entities/particles in a medium obeys to a simple cosine law, i.e., Lambertian entrance, and annihilation of particles inside the medium is absent. By using this law we achieve two important points: (1) the invariance of the average path length guarantees that the expected value is known regardless of the complexity of the medium; (2) the accuracy of a Monte Carlo code can be assessed by simple statistical tests. We will show that we can reach an arbitrary accuracy of the estimated average pathlength as the number of simulated trajectories increases. The method can be applied in complete generality versus the scattering and geometrical properties of the medium, as well as in presence of refractive index mismatches in the optical case. In particular, this verification method is reliable to detect inaccuracies in the treatment of boundaries of finite media. The results presented in this paper, obtained by a standard computer machine, show a verification of our Monte Carlo code up to the sixth decimal digit. We discuss how this method can provide a fundamental tool for the verification of Monte Carlo codes in the geometry of interest, without resorting to simpler geometries and uniform distribution of the scattering properties.

In this paper we deal with the influence on absorption of the diffusive media characteristics framing the problem in connection with the invariance property (IP) of the mean path length. We show that the IP is an important issue that regulates but not prevent the search of absorption maximization by scattering characteristics. We find that the scattering may increase the absorption or even be detrimental, depending on the geometry of the medium and the conditions of its illumination.

The mean path-length invariance property is a very important property of scattering media illuminated by an isotropic and homogeneous radiation. Here, we investigate the case of inhomogeneous media with refractive-index mismatch between the external environment and also among their subdomains. The invariance property remains valid by the introduction of a correction, dependent on the refractive index, of the mean path-length value. It is a consequence of the stationary solution of the radiative transfer equation in a medium subjected to an isotropic and homogeneous radiance. The theoretical results are in agreement with the reported results for numerical simulations for both the three-dimensional and the two-dimensional media.

In this work, special invariance properties of a class of exact solutions of the radiative transfer equation (RTE) pertaining to a uniform Lambertian illumination of any non-absorbing homogeneous and inhomogeneous volume are presented and discussed. This class of solutions of the RTE traces a reference ground under which light propagation can be studied in a special simplified regime. Despite the difficulties to obtain general solutions of the radiative transfer equation, the condition of Lambertian illumination determines a unique regime of photon transport where quite easy and simple invariant solutions can be obtained in all generality for homogeneous and inhomogeneous geometries. These solutions are invariant both with respect to the geometry (size and shape of the volume) and with respect to the scattering properties, i.e. scattering coefficient, scattering function and homogeneity of the considered domain. Another evident advantage of these solutions is that they are exact solutions known with arbitrary precision and can thus be used as reference standard for photon migration studies.

The peculiar characteristics of random laser emission have been studied in many different media, leading to a classification of the working regimes based on the statistics of spectral fluctuations. Alongside such studies, the possibility to constrain light propagation by L\'evy walks, i.e., with a ``heavy-tailed'' distribution of steps, has opened the opportunity to investigate the behavior of a superdiffusive optical gain medium that can lead to a ``superdiffusive random laser.'' Here, we present a theoretical investigation, based on Monte Carlo simulations, on such a kind of medium, focusing on the widespread presence of fluctuation regimes, that, in contrast to a diffusive random laser, appears very hard to switch off by changing the gain and scattering strength. Hence, the superdiffusion appears as a condition that increases the value of the threshold energy and promotes the presence of fluctuations in the emission spectrum.

A random laser is an optical system where the light is amplified by stimulated emission along random paths in a disordered medium. In recent years, a new kind of non-invasive sensor based on random lasing has been proposed. The striking point is that a sensor based on random lasing has an emission "fed" by the feedback due to the scattering properties of the medium, making such a system a natural candidate for studying materials with strong disorder. Here, we report the recent advances in the sensor structure and performances.

We provide theoretical and experimental evidence of statistical outliers in random laser emission that are not accounted for by the, now established, power-law tailed (L\'evy) distribution. Such outliers manifest themselves as single, large isolated spikes over an otherwise smooth background. A statistical test convincingly shows that their probability is larger than the one extrapolated from lower-intensity events. To compare with experimental data, we introduced the anomaly parameter that allows for an identification of such rare events from experimental spectral measurements and that agrees as well with the simulations of our Monte Carlo model. A possible interpretation in terms of Black Swans or Dragon Kings, large events having a different generation mechanism from their peers, is discussed.

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.

We show how the velocity of an optical pulse propagating through a dispersive medium depends on the pulse duration. A transition from the group velocity for long pulses to the in-vacuum velocity for short pulses is shown both in experimental results and in theoretical predictions. The temporal duration of the experimental pulses are 150 ps and 3.5 ns. A description of the pulse propagation in terms of the time “center of mass” of the energy flow allows an intuitive overview of the results.

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 L\'evy statistical regime. A model based on a phase-insensitive feedback mechanism has been used in order to explain the experimental data and two different L\'evy subregimes have been identified.

We present an experimental realization of slow and fast light schemes for a few ns long optical pulses that makes use of incoherent interactions in an atomic medium. The combination of such different schemes allows us to demonstrate that the propagation delay acquired in the slow light stage, can be completely recovered in a fast light one. The use of an incoherent interactions scheme makes the control of the propagation dynamics of light pulses easer to realize. Delays up to 13 ns, in slow light regime, and advances up to 500 ps, in fast light regime, are reported when the stages work individually for a 3 ns long pulse. When both stages are switched-on the fast light stage is able to recover a previously induced delay and even to produce an extra advance, with an overall advance up to 1 ns. Since every optical transmission line needs an amplification system to overcome the unavoidable losses, the results suggest the opportunity and perspective of a proper tailoring of the amplification stage for data timing purposes.

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 L\'evy 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 L\'evy 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.

We present an experimental study of temporal retardation combined with temporal compression of weak laser pulses. The effect is optically controlled by the presence of another light pulse, although no coherent control is required. Probe pulse delays up to 13 ns and maximum compression factor of 3 were observed using few-ns-long laser pulses. We also present a theoretical model of pulse propagation that is able to reproduce the experimental results with fairly good accuracy.

We present recent theoretical and experimental results concerning both retardation and acceleration of light pulses in schemes involving a second ‘control’ laser field but that do not involve any coherent preparation of the atomic medium.

Causality and special relativity pose an upper limit to the amount of advance that an optical pulse can acquire during a superluminal propagation. Such a limit can be circumvented if the pulse, before entering the superluminal medium, is retarded by letting it propagate under normal dispersion. We present an experimental evidence of this fact by showing that a laser pulse propagating in an atomic vapor, quasi resonant with an inverted transition and in conditions of anomalous dispersion, moves faster if it is previously retarded in a cell containing the same medium with no population inversion. Optical transmission lines often need an amplification stage to overcome the signal attenuation and the unavoidable delay respect to propagation at c; in this paper we tailor such stage to provide also an optical controlled recover of such delay. We believe that our results can open exciting prospects for real-life optical data processing and communication.