Holey random walks: optics of heterogeneous turbid composites

Probability density functions for photon propagation in a binary (isotropic-Poisson) statistical mixture with unmatched positive and negative refractive indexes

The exact homogenized probability density function, for a photon making a step of length s has been analytically derived for a binary (isotropic-Poisson) statistical mixture with unmatched refractive indexes. The companions, exact, homogenized probability density functions for a photon to change direction ("scatter"), with polar ϑ and azimuthal φ angles, and the homogenized albedo, have also been obtained analytically. These functions also apply to negative refractive indexes and can reduce the number of Monte Carlo simulations needed for photon propagation in complex binary (isotropic-Poisson) statistical mixtures from hundreds to just one, for an equivalent homogeneous medium. Note, that this is not an approximate approach, but a mathematically equivalent and exact result. Additionally, some tutorial examples of homogenized Monte Carlo simulations are also given.

Sample size effects for Lévy flight of photons in atomic vapors

Lévy flight superdiffusion consists of random walks characterized by very long jumps that dominate the transport. However, the finite size of real samples introduces truncation of long jumps and modifies the transport properties. We measure typical Levy flight parameters for photon diffusion in atomic vapor characterized by a Voigt absorption profile. We observe the change of Lévy parameter as a function of truncation length. We associate this variation with size-dependent contributions from different spectral regions of the emission profile with the Doppler core dominating the transport for thin samples and Lorentz wings for thick samples. Monte Carlo simulations are implemented to support the interpretation of results.

Lévy flights of photons with infinite mean free path

Multiple scattering of light by resonant vapor is characterized by Lévy-type superdiffusion with a single-step size distribution p(x)∝1/x^{1+α}. We investigate Lévy flight of light in a hot rubidium vapor collisional-broadened by 50 torr of He gas. The frequent collisions produce Lorentzian absorptive and emissive profiles with α<1 and a corresponding divergent mean step size. We extract the Lévy parameter α≈0.5 in a multiple-scattering regime from radial profile of the transmission and from violation of the Ohm's law. The measured radial transmission profile and the total diffusive transmission curves are well reproduced by numerical simulations for Lorentzian line shapes.

Spatially Resolved Spectral Powder Analysis: Experiments and Modeling

Understanding the behavior of light in granular media is necessary for determining the sample size, shape, and weight when probing using fiber optic setups. This is required for a correct estimate of the active pharmaceutical ingredient content in a pharmaceutical blend via near-infrared spectroscopy. Several strategies to describe the behavior of light in granular and turbid media exist. A common approach is the Monte-Carlo simulation of individual photons and their description using mean free path lengths for scattering and absorption. In this work, we chose a complementary method by approximating these parameters via real physical counterparts, i.e., the particle size, shape, and density and the resulting chord lengths. Additionally, the wavelength dependence of refractive indices is incorporated. The obtained results were compared with those obtained in an experimental setup that included the SAM-Spec Felin probe head by Indatech for detecting spatially resolved spectra of samples. Our method facilitates the interpretation of the acquired experimental results by contrasting the optical response, the physical particle attributes, and the simulation results.

Finite-size effects and percolation properties of Poisson geometries

Random tessellations of the space represent a class of prototype models of heterogeneous media, which are central in several applications in physics, engineering, and life sciences. In this work, we investigate the statistical properties of d-dimensional isotropic Poisson geometries by resorting to Monte Carlo simulation, with special emphasis on the case d=3. We first analyze the behavior of the key features of these stochastic geometries as a function of the dimension d and the linear size L of the domain. Then, we consider the case of Poisson binary mixtures, where the polyhedra are assigned two labels with complementary probabilities. For this latter class of random geometries, we numerically characterize the percolation threshold, the strength of the percolating cluster, and the average cluster size.

Strongly enhanced light trapping in a two-dimensional silicon nanowire random fractal array

We report on the unconventional optical properties exhibited by a two-dimensional array of thin Si nanowires arranged in a random fractal geometry and fabricated using an inexpensive, fast and maskless process compatible with Si technology. The structure allows for a high light-trapping efficiency across the entire visible range, attaining total reflectance values as low as 0.1% when the wavelength in the medium matches the length scale of maximum heterogeneity in the system. We show that the random fractal structure of our nanowire array is responsible for a strong in-plane multiple scattering, which is related to the material refractive index fluctuations and leads to a greatly enhanced Raman scattering and a bright photoluminescence. These strong emissions are correlated on all length scales according to the refractive index fluctuations. The relevance and the perspectives of the reported results are discussed as promising for Si-based photovoltaic and photonic applications.

Signatures of Lévy flights with annealed disorder

We present theoretical and experimental results of Lévy flights of light originating from a random walk of photons in a hot atomic vapor. In contrast to systems with quenched disorder, this system does not present any correlations between the position and the step length of the random walk. In an analytical model based on microscopic first principles including Doppler broadening we find anomalous Lévy-type superdiffusion corresponding to a single-step size distribution P(x)∝x^{-(1+α)}, with α≈1. We show that this step size distribution leads to a violation of Ohm's law [T_{diff}∝L^{-α/2}≠L^{-1}], as expected for a Lévy walk of independent steps. Furthermore, the spatial profile of the transmitted light develops power-law tails [T_{diff}(r)∝r^{-3-α}]. In an experiment using a slab geometry with hot Rb vapor, we measured the total diffuse transmission T_{diff} and the spatial profile of the transmitted light T_{diff}(r). We obtained the microscopic Lévy parameter α under macroscopic multiple scattering conditions paving the way to investigation of Lévy flights in different atomic physics and astrophysics systems.

Photon transport in cylindrically-shaped disordered meso-macroporous materials

We theoretically and experimentally investigate light diffusion in disordered meso-macroporous materials with a cylindrical shape. High Internal Phase Emulsion (HIPE)-based silica foam samples, exhibiting a polydisperse pore-size distribution centered around 19 μm to resemble certain biological tissues, are realized. To quantify the effect of a finite lateral size on measurable quantities, an analytical model for diffusion in finite cylinders is developed and validated by Monte Carlo random walk simulations. Steady-state and time-resolved transmission experiments are performed and the transport parameters (transport mean free path and material absorption length) are successfully retrieved from fits of the experimental curves with the proposed model. This study reveals that scattering losses on the lateral sides of the samples are responsible for a lowering of the transmission signal and a shortening of the photon lifetime, similar in experimental observables to the effect of material absorption. The recognition of this geometrical effect is essential since its wrong attribution to material absorption could be detrimental in various applications, such as biological tissue diagnosis or conversion efficiency in dye-sensitized solar cells.

Laser absorption spectroscopy of oxygen confined in highly porous hollow sphere xerogel

An Al2O3 xerogel with a distinctive microstructure is studied for the application of laser absorption spectroscopy of oxygen. The xerogel has an exceptionally high porosity (up to 88%) and a large pore size (up to 3.6 µm). Using the method of gas-in-scattering media absorption spectroscopy (GASMAS), a long optical path length (about 3.5m) and high enhancement factor (over 300 times) are achieved as the result of extremely strong multiple-scattering when the light is transmitted through the air-filled, hollow-sphere alumina xerogel. We investigate how the micro-physical feature influences the optical property. As part of the optical sensing system, the material's gas exchange dynamics are also experimentally studied.

Light diffusion in quenched disorder: role of step correlations

We present a theoretical and experimental study of light transport in disordered media with strongly heterogeneous distribution of scatterers formed via nonscattering regions. Step correlations induced by quenched disorder are found to prevent diffusivity from diverging with increasing heterogeneity scale, contrary to expectations from annealed models. Spectral diffusivity is measured for a porous ceramic where nanopores act as scatterers and macropores render their distribution heterogeneous. Results agree well with Monte Carlo simulations and a proposed analytical model.

Superdiffusion and transport in two-dimensional systems with Lévy-like quenched disorder

We present an extensive analysis of transport properties in superdiffusive twodimensional quenched random media, obtained by packing disks with radii distributed according to a Lévy law. We consider transport and scaling properties in samples packed with two different procedures, at fixed filling fraction and at self-similar packing, and we clarify the role of the two procedures in the superdiffusive effects. Using the behavior of the filling fraction in finite size systems as the main geometrical parameter, we define an effective Lévy exponent that correctly estimates the finite size effects. The effective Lévy exponent rules the dynamical scaling of the main transport properties and identifies the region where superdiffusive effects can be detected.

Sensing the dynamics of oxidative stress using enhanced absorption in protein-loaded random media

Reactive oxygen species play a key role in cell signalling and oxidative stress mechanisms, therefore, sensing their production by living organisms is of fundamental interest. Here we describe a novel biosensing method for extracellular detection of endogenous hydrogen peroxide (H2O2). The method is based on the enhancement of the optical absorption spectrum of the hemoprotein cytochrome c when loaded into a highly scattering random medium. Such a configuration enables, in contrast to existing techniques, non-invasive and dynamic detection of the oxidation of cyt c in the presence of H2O2 with unprecedented sensitivity. Dynamic information on the modification of the cell oxidative status of Chlamydomonas reinhardtii, an aquatic green algae, was obtained under oxidative stress conditions induced by the presence of trace concentrations of Cd(II). Furthermore, the dynamics of H2O2 production was investigated under different lighting conditions confirming the impact of Cd(II) on the photosynthetic activity of those phytoplanktonic cells.