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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.

An active disordered medium, i.e., a diffusive material where a population inversion is established by a pumping system, can emits a optical radiation known as random laser. Since such a optical source is very sensitive to the scattering, a sensor based on random lasing can be developed to investigate diffusive samples. Here we report a design of a sensor with non-invasive characteristics achieved by means of separation between the active medium and the investigated sample.

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.

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.

Optical sensing has been subject to a great interest for the moderate intrusiveness of its operation. The introduction of random lasers in ’90s has opened the door for developing a new kind of optical sensors. In such a source, disorder is introduced within an inverted medium, increasing the lifetime of the radiation without the presence of an optical cavity. The striking point is that the spectral characteristics of the output emission are strongly dependent on the scattering properties of the medium, suggesting new methods to investigate disordered materials. Recently, a novel concept for optical sensing based on the physics of random laser has been reported,1 overcoming the limits due to the alteration of the investigated sample by injecting an active material. Here we present a characterization of such a kind of sensor, suggesting non-invasive and also in-vivo applications.

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.

Optical sensors have been extensively studied in order to develop new methods of investigation for different materials. In particular, light scattering and absorption in biological tissues have been investigated for diagnostic and therapeutic applications. Here we present an experimental work devoted to develop a new kind of optical sensor based on the random laser emission. Such an optical phenomenon finds its origin in the combination of scattering and gain in a mirror-less disordered active medium.

The random laser has represented an important topic in photonics and an opportunity to develop new potential practical applications. Our work, both experimental and theoretical, has been devoted to characterize, understand and control the emission in random laser systems in weakly scattering media. Three statistical regimes of the emission spectrum have been detected, besides modifications in the output directionality. Moreover, here we report our preliminary results in the field of sensing, that can open new promising perspectives.