Statistical outliers in random laser emission

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

A method to measure the diffusion coefficient of homogeneous and layered media

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Higher order perturbation theory for the diffusion equation in heterogeneous media: application to layered and slab geometries

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Topological complexity of photons' paths in biological tissues

In the present contribution three means of measuring the geometrical and topological complexity of photons' paths in random media are proposed. This is realized by investigating the behavior of the average crossing number, the mean writhe, and the minimal crossing number of photons' paths generated by Monte Carlo (MC) simulations, for different sets of optical parameters. It is observed that the complexity of the photons' paths increases for increasing light source/detector spacing, and that highly "knotted" paths are formed. Due to the particular rules utilized to generate the MC photons' paths, the present results may have an interest not only for the biomedical optics community, but also from a pure mathematical point of view

General perturbative approach to the diffusion equation in the presence of absorbing defects: frequency-domain and time-domain results

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The use of India ink in tissue-simulating phantoms

The optical properties of India ink, an absorber often used in preparation of tissue simulating phantoms, have been investigated at visible and near infrared wavelengths. The extinction coefficient has been obtained from measurements of collimated transmittance and from spectrophotometric measurements, the absorption coefficient from multidistance measurements of fluence rate in a diffusive infinite medium with small concentrations of added ink. Measurements have been carried out on samples of India ink from five different brands, and for some brands also from different batches. As also reported in previously published papers the results we have obtained showed large inter-brand and inter-batch variations for both the absorption and the extinction coefficient. On the contrary, our results showed small variations for the ratio between the absorption and the extinction coefficient. The albedo is therefore similar for all samples: The values averaged over all samples investigated were 0.161, 0.115, and 0.115 at λ = 632.8, 751, and 833 nm respectively, with maximum deviations of 0.044, 0.019, and 0.035. These results indicate that, using the values we have obtained for the albedo, it should be possible to obtain with uncertainty smaller than about 4% the absorption coefficient of a sample of unknown ink from simple measurements of extinction coefficient. A similar accuracy is not easily obtained with the complicated procedures necessary for measurements of absorption coefficient

Invariance property in scattering media and absorption

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

Invariance property in inhomogeneous scattering media with refractive-index mismatch

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