Photon channelling in foams

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.

Pathlength determination for gas in scattering media absorption spectroscopy

Gas in scattering media absorption spectroscopy (GASMAS) has been extensively studied and applied during recent years in, e.g., food packaging, human sinus monitoring, gas diffusion studies, and pharmaceutical tablet characterization. The focus has been on the evaluation of the gas absorption pathlength in porous media, which a priori is unknown due to heavy light scattering. In this paper, three different approaches are summarized. One possibility is to simultaneously monitor another gas with known concentration (e.g., water vapor), the pathlength of which can then be obtained and used for the target gas (e.g., oxygen) to retrieve its concentration. The second approach is to measure the mean optical pathlength or physical pathlength with other methods, including time-of-flight spectroscopy, frequency-modulated light scattering interferometry and the frequency domain photon migration method. By utilizing these methods, an average concentration can be obtained and the porosities of the material are studied. The last method retrieves the gas concentration without knowing its pathlength by analyzing the gas absorption line shape, which depends upon the concentration of buffer gases due to intermolecular collisions. The pathlength enhancement effect due to multiple scattering enables also the use of porous media as multipass gas cells for trace gas monitoring. All these efforts open up a multitude of different applications for the GASMAS technique.

Diffusive transport of light in two-dimensional granular materials

We study photon diffusion in a two-dimensional random packing of monodisperse disks as a simple model of granular material. We apply ray optics approximation to set up a persistent random walk for the photons. We employ Fresnel's intensity reflectance with its rich dependence on the incidence angle and polarization state of the light. We present an analytic expression for the transport-mean-free path l* in terms of the refractive indices of grains and host medium, grain radius, and packing fraction. We perform numerical simulations to examine our analytical result.

Optical analog of Matthiessen's rule in a one-dimensional model for diffusive light transport in foams

We study photon diffusion in a one-dimensional model foam composed of thin films and Plateau borders. Each thin film or Plateau border is characterized by its own intensity transmittance. We relate l(Foam)*, the transport-mean-free path of photons diffusing in the foam, to the foam microstructure. Denoting by l(Film)* (l(PB)*) the transport-mean-free path of photons in a medium composed only of thin films (Plateau borders), we find 1/l(Foam)*=φ(F)/l(Film)*+φ(P)/l(PB)*. Here φ(F) and φ(P)=1-φ(F) are the fraction of films and Plateau borders, respectively.

Optical porosimetry and investigations of the porosity experienced by light interacting with porous media

We investigate how light samples disordered porous materials such as ceramics and pharmaceutical materials. By combining photon time-of-flight spectroscopy and sensitive laser-based gas sensing, we obtain information on the extent to which light interacts with solid and pore volumes, respectively. Comparison with mercury intrusion porosimetry shows that light predominantly interacts with the solid. Analysis based on a two-state model does not fully explain observations, revealing a need for refined modeling. Nonetheless, excellent correlation between actual porosity and the porosity experienced by photons demonstrates the potential of nondestructive optical porosimetry based on gas absorption.

Persistent random walk on a one-dimensional lattice with random asymmetric transmittances

We study the persistent random walk of photons on a one-dimensional lattice of random asymmetric transmittances. Each site is characterized by its intensity transmittance t (t;{'} not equalt) for photons moving to the right (left) direction. Transmittances at different sites are assumed independent, distributed according to a given probability density F(t,t;{'}) . We use the effective medium approximation and identify two classes of F(t,t;{'}) which lead to the normal diffusion of photons. Monte Carlo simulations confirm our predictions. We mention that the metamaterial introduced by Fedetov [Nano Lett. 7, 1996 (2007)] can be used to realize a lattice of random asymmetric transmittances.

Diffusive transport of light in three-dimensional disordered Voronoi structures

The origin of diffusive transport of light in dry foams is still under debate. In this paper, we consider the random walks of photons as they are reflected or transmitted by liquid films according to the rules of ray optics. The foams are approximately modeled by three-dimensional Voronoi tessellations with varying degree of disorder. We study two cases: A constant intensity reflectance and the reflectance of thin films. Especially in the second case, we find that in the experimentally important regime for the film thicknesses, the transport-mean-free path l;{ *} does not significantly depend on the topological and geometrical disorder of the Voronoi foams including the periodic Kelvin foam. This may indicate that the detailed structure of foams is not crucial for understanding the diffusive transport of light. Furthermore, our theoretical values for l;{ *} fall in the same range as the experimental values observed in dry foams. One can therefore argue that liquid films contribute substantially to the diffusive transport of light in dry foams.

Diffusive wave spectroscopy of a random close packing of spheres

We are interested in the propagation of light in a random packing of dielectric spheres within the geometrical optics approximation. Numerical simulations are performed using a ray tracing algorithm. The effective refractive indexes and the transport mean free path are computed for different refractive indexes of spheres and intersticial media. The variations of the optical path length under small deformations of the spheres assembly are also computed and compared to the results of Diffusive Wave Spectroscopy experiments. Finally, we propose a measure of the transport mean free path and a Diffusive Wave Spectroscopy experiment on a packing of glass spheres. The results of those experiments agree with the predictions of this ray tracing approach.

Superdiffusion in a honeycomb billiard

We investigate particle transport in the honeycomb billiard which consists of connected channels placed on the edges of a honeycomb structure. The spreading of particles is superdiffusive due to the existence of ballistic trajectories which we term perfect paths. Simulations give a time exponent of 1.72 for the mean-square displacement and a starlike, i.e., anisotropic, particle distribution. We present an analytical treatment based on the formalism of continuous-time random walks and explain the anisotropic distribution under the assumption that the perfect paths follow the directions of the six lattice axes. Furthermore, we derive a relation between the time exponent and the exponent of the distribution function for trajectories close to a perfect path. In billiards with randomly distributed channels, conventional diffusion is always observed in the long-time limit, although for small disorder transient superdiffusional behavior exists. Our simulation results are again supported by an analytical analysis.

Persistent random walk on a site-disordered one-dimensional lattice: photon subdiffusion

We study the persistent random walk of photons on a one-dimensional lattice of random transmittances. Transmittances at different sites are assumed independent, distributed according to a given probability density f(t). Depending on the behavior of f(t) near t=0, diffusive and subdiffusive transports are predicted by the disorder expansion of the mean square-displacement and the effective medium approximation. Monte Carlo simulations confirm the anomalous diffusion of photons. To observe photon subdiffusion experimentally, we suggest a dielectric film stack for realization of a distribution f(t).