Multiple Light Scattering in Nematic Liquid Crystals

Optical anisotropy measurement in normal and cancerous tissues: backscattering technique

Investigating the deformation of tissue architecture is one of the most important clinical methods for cancer diagnosis. Optical methods are now widely developed for rapid, precise, and real-time assessment of these alterations at the microscopic scale. One of the proposed methods is enhanced backscattering (EBS) technique that allows in-vivo measurement of the optical scattering characteristics. Here, EBS technique is employed to evaluate the optical anisotropy of human epithelial tissues as a measure to distinguish between normal and cancerous one. Orientation dependence of the mean scattering length is assessed in healthy and cancerous tissues of five different human organs i. e. uterus, bladder, colon, kidney, and liver. Helicity preserving channel and rotating ground glass diffuser are utilized to eliminate the polarization induced anisotropy and the background speckle noises respectively. Analysis of the backscattering cones recorded by a high-resolution CCD camera reveals the modification of the strength and degree of optical anisotropy in different tissues during cancer progression. Pathology data affirm the correlation between the experimental results and the morphological alteration of the epithelial cells in each carcinoma type. In general, tissues with fibrous constructional cells are subject to a decrease in anisotropy due to cancer, whereas those with cuboidal cells experience an increase in anisotropy. This complementary information enhances the potency of the EBS technique as a fast, non-destructive, and easily accessible tool for real-time tissue diagnosis.

Correlation between intensity fluctuations of electromagnetic waves scattered from a spatially quasi-homogeneous, anisotropic medium

Within the validity of the first-order Born approximation, expressions are derived for the correlation between intensity fluctuations (CIF) of an electromagnetic plane wave scattered from a spatially quasi-homogeneous (QH), anisotropic medium. Upon establishing the correlation matrix of the scattering potential of the medium, we show that the CIF is the summation of Fourier transforms of the strengths and normalized correlation coefficients (NCCs) of the scattering potential matrix. Numerical results reveal that the CIF is susceptible to the effective width and correlation length of the medium, and degree of polarization of the incident electromagnetic wave. Our study not only extends the current knowledge of the CIF of a scattered field but also provides an important reference to the study of high-order intensity correlations of light scattered from a spatially anisotropic medium.

Anisotropic diffusive transport: connecting microscopic scattering and macroscopic transport properties

This work concerns the modeling of radiative transfer in anisotropic turbid media using diffusion theory. A theory for the relationship between microscopic scattering properties (i.e., an arbitrary differential scattering cross-section) and the macroscopic diffusion tensor, in the limit of independent scatterers, is presented. The theory is accompanied by a numerical method capable of performing the calculations. In addition, a boundary condition appropriate for modeling systems with anisotropic radiance is derived. It is shown that anisotropic diffusion theory, when based on these developments, indeed can describe radiative transfer in anisotropic turbid media. More specifically, it is reported that solutions to the anisotropic diffusion equation are in excellent agreement with Monte Carlo simulations, both in steady-state and time-domain. This stands in contrast to previous work on the topic, where inadequate boundary conditions and/or incorrect relations between microscopic scattering properties and the diffusion tensor have caused disagreement between simulations and diffusion theory. The present work thus falsify previous claims that anisotropic diffusion theory cannot describe anisotropic radiative transfer, and instead open for accurate quantitative diffusion-based modeling of anisotropic turbid materials.

Time-resolved measurements of the optical properties of fibrous media using the anisotropic diffusion equation

Transmittance and reflectance from spruce wood and bovine ligamentum nuchae as two different fibrous media are examined by time-of-flight spectroscopy for varying source detector separations and several orientations of the fibers in the sample. The anisotropic diffusion theory is used to obtain the absorption coefficient and the diffusion coefficients parallel and perpendicular to the fibers. The results are compared to those obtained with the isotropic diffusion theory. It is shown that for increasing source detector separations, the retrieved optical properties change as expected from Monte Carlo simulations performed in a previous study. This confirms that the anisotropic diffusion theory yields useful results for certain experimental conditions.

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.

Equi-intensity distribution of optical reflectance in a fibrous turbid medium

Light propagation in a fibrous anisotropic scattering medium is quite different from that in an isotropic medium. Both the anisotropic diffuse equation (ADE) and the continuous time random walk (CTRW) theory predict that the equi-intensity profiles of the surface reflectance have an elliptical shape in a fibrous turbid medium. In this study, we simulated the spatially resolved surface reflectance in a fibrous sample using a Monte Carlo model. A parametric equation was used to quantitatively characterize the geometric profiles of the reflectance patterns. The results indicated that the equi-intensity profiles of surface reflectance had elliptical shapes only when evaluated at distances far away from the incident point. The length ratio of the two orthogonal axes of the ellipse was not affected by the sample optical properties when the ratio of reduced scattering coefficients along the two axes is the same. But the relationship between the aforementioned two ratios was different from the predication of ADE theory. Only for fibers of small sizes did the fitted axes ratios approach the values predicted from the ADE theory.

Optical anisotropic diffusion: new model systems and theoretical modeling

We have developed several new experimental model systems that demonstrate anisotropic diffusion of light. These systems, consisting of aligned fibers, stretched plastic foam, and stretched plastic frit, have relatively simple microstructures and are easily sliced, making them ideal for testing theoretical models of diffusion. We demonstrate that the solution to the diffusion equation for arbitrary orientation of the diffusion tensor is consistent with experimental measurements. We also show that simple models of microstructure, based on cylindrical and planar scatterers, are consistent with the experimental results. These models provide simple analytical expressions for predicting the degree of alignment of the scatterers from diffuse transmission measurements. The combination of experimental results and theoretical support demonstrates both the power and the limitations of the diffusion model for providing information about microstructure via simple experiments and modeling.

Thermo-recurrent nematic random laser

This experimental work is aimed to investigate the thermal behavior of random laser action in dye doped nematic liquid crystals. The study evidenced an important temperature dependence of the random lasing characteristics in the nematic phase and in close proximity of the nematicisotropic (N-I) phase transition. A lowering of the laser emission intensity as the temperature increases is strictly related to the shift of the lasing threshold as function of the temperature even though the pump energy is kept fixed. The optical losses increasing owing to the thermal fluctuation enhanced scattering drive the input-output smoother behavior until the system stops to lase, because below threshold. The unexpected reoccurrence of random lasing at higher temperature, in proximity of N-I transition is found to be related to a different scattering mechanism, the micro-droplets nucleation and critical opalescence.

Diffusive transport of light in a two-dimensional disordered packing of disks: analytical approach to transport mean free path

We study photon diffusion in a two-dimensional random packing of monodisperse disks as a simple model of granular media and wet foams. We assume that the intensity reflectance of disks is a constant r . We present an analytic expression for the transport mean free path l;{*} in terms of the velocity of light in the disks and host medium, radius R and packing fraction of the disks, and the intensity reflectance. For glass beads immersed in air or water, we estimate transport mean free paths about half the experimental ones. For air bubbles immersed in water, l;{*}R is a linear function of 1epsilon , where epsilon is the liquid volume fraction of the model wet foam. This throws light on the empirical law of Vera [Appl. Opt. 40, 4210 (2001)] and promotes more realistic models.

Full characterization of anisotropic diffuse light

We demonstrate a method for fully characterizing diffuse transport of light in a statistically anisotropic opaque material. Our technique provides a simple means of determining all parameters governing anisotropic diffusion. Anisotropy in the diffusion constant, the mean free path, and the extrapolation length are, for the first time, determined independently. These results show that the anisotropic diffusion model is effective for modeling transport in anisotropic samples, providing that the light is allowed to travel several times the transport mean free path from the source.

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.

Anisotropic light diffusion: an oxymoron?

Light propagation in anisotropic random media is studied in the steady-state and time domains. Solutions of the anisotropic diffusion equation are compared to results obtained by the Monte Carlo method. Contrary to what has been reported so far, we find that even in the "diffusive regime" the anisotropic diffusion equation does not describe correctly the light propagation in anisotropic random media.

Anisotropic diffusion of light in polymer dispersed liquid crystals

Anisotropic diffusion of light was experimentally first observed in bulk nematic liquid crystals. The origin of anisotropy in such a system is due to the optical anisotropy of nematic liquid crystal and to anisotropic scattering of light from nematic orientational fluctuations. In polymer dispersed liquid crystals (PDLCs) anisotropic scatterers-i.e., nematic droplets-are embedded in an optically isotropic polymer. The anisotropy of diffusion of light in this system therefore depends only on the anisotropic scattering from a single nematic droplet and on the average orientation of the droplets in PDLCs. In the absence of an external field droplets in PDLCs are randomly oriented and diffusion of light is isotropic. In an external field the droplets are on average oriented in the direction of the external field and the diffusion of light becomes anisotropic. We calculated the diffusion tensor and expected anisotropy of the diffusion of light as a function of an external field, kR , and volume fraction using the theory developed for bulk nematic liquid crystals. Our calculations show that the anisotropy of diffusion tensor can have both the signs and that the magnitude of diffusion constants increase with increasing external field.

Diffusive transport of light in a Kelvin foam

Although diffusing-wave spectroscopy has already been successfully applied to study dynamic properties of foams, we still lack a clear understanding of the diffusive transport of photons in foams. In this paper, we present a thorough study of photon diffusion in the Kelvin structure as an example for a three-dimensional model foam. We consider the photons' random walk as they are reflected or transmitted by the liquid films according to the rules of ray optics. For constant reflectance and special one- and two-dimensional photon paths, we are able to calculate diffusion constants analytically. Extensive numerical simulations reveal a remarkable similarity with our previous two-dimensional investigations. To implement a more realistic model, we use thin-film reflectances. The simulated diffusion constants exhibit oscillations for varying film thickness d which vanish when disorder is introduced in d. Absolute values and the behavior at small d agree with measurements in very dry foams providing a strong argument for the importance of liquid films in the diffusive photon transport. An analytical theory with a minimum of input parameters reproduces the numerical results.

Quasi-two-dimensional diffusive random laser action

We report on random lasing in a disordered system in which the multiple scattering feedback mechanism can be switched from a three-dimensional random walk to a quasi-two-dimensional type of transport. The emission from this system is anisotropic, extraordinary polarized, and is controlled via an external electric field. The phenomenon is observed in dye-doped polymer dispersed liquid crystals and makes use of the strong scattering anisotropies in these materials.

Anisotropic weak localization of light

We have observed angular anisotropy in weak localization of light from highly scattering, orientationally ordered, nematic liquid crystals. This demonstration of angular anisotropy in a multiple-scattering interference phenomenon was facilitated by a light scattering instrument with extraordinary angular resolution. The measured anisotropies were consistent with a simple model of coherent backscattering generalized for propagation-direction dependent mean free paths.

Electromagnetic scattering by spherical negative-refractive-index particles: Low-frequency resonance and localization parameters

The Mie scattering of electromagnetic waves of wave vector k by spherical negative-refractive-index particles of radius a exhibits an unusual resonance at ka-->0. The scattering enhancement from the ka-->0 resonance is insensitive to the size of scatterers, distinct from the Mie scattering resonances from positive-refractive-index particles. For media consisting of a collection of the negative-refractive-index particles, the unusual resonance results in a significant reduction of the localization parameter, providing a possibility to reach the light localization transition by reducing the wave vector k, in analogy to electronic systems.

Polymer domain growth in ordered liquid crystalline matrices

The growth of polymer domains in the isotropic, nematic, and smectic matrices is studied by the light scattering. In the smectic and isotropic matrices the growth is diffusive, and in the nematic matrix it is influenced by the elastic forces. The scaling is obeyed. A crossover to the wetting fast-mode hydrodynamic regime is also observed at long times. In order to perform these measurements we had to eliminate the multiple scattering of light.

Light transport in chiral and magnetochiral random media

We present a microscopic approach to study electromagnetic wave propagation in media with broken mirror symmetry. We introduce and calculate the transport mean free path l*C associated with the residual polarization of diffuse light in chiral systems. In chiral media subject to an external magnetic field B, all symmetry requirements exist to create a macroscopic "super" light current in the direction of B that persists even in the absence of a spatial photon density gradient. However, we show that such a current is identically zero in our model. We finally show the existence of a linear magnetotransmission in magnetochiral media.

Anisotropic diffusion of light in a strongly scattering material

Light transport in a strongly scattering, strongly anisotropic material is studied experimentally using both static and time-resolved techniques. Both the static and the dynamic results are well characterized by a diffusion equation with an anisotropic diffusion tensor and a scalar absorption term. Light diffuses 4.0 times faster along the uniaxial axis of the material compared with diffusion in the orthogonal directions.

Temporal fluctuations of waves in weakly nonlinear disordered media

We consider the multiple scattering of a scalar wave in a disordered medium with a weak nonlinearity of Kerr type. The perturbation theory, developed to calculate the temporal autocorrelation function of scattered wave, fails at short correlation times. A self-consistent calculation shows that for nonlinearities exceeding a certain threshold value, the multiple-scattering speckle pattern becomes unstable and exhibits spontaneous fluctuations even in the absence of scatterer motion. The instability is due to a distributed feedback in the system "coherent wave + nonlinear disordered medium." The feedback is provided by the multiple scattering. The development of instability is independent of the sign of nonlinearity.

Observation of equipartition of seismic waves

Equipartition is a first principle in wave transport, based on the tendency of multiple scattering to homogenize phase space. We report observations of this principle for seismic waves created by earthquakes in Mexico. We find qualitative agreement with an equipartition model that accounts for mode conversions at the Earth's surface.

Vanishing of energy transport velocity and diffusion constant of electromagnetic waves in disordered magnetic media

The energy transport velocity v(E) and the diffusion constant D of electromagnetic waves in the presence of randomly distributed ferromagnetic scatterers are studied. v(E) presents a strong dependence on the relative magnetic permeability mu and, unlike the nonmagnetic case, exhibits sharp drops in the small-particle limit and never coincides with the phase velocity v(p). Both v(E) and D exhibit an oscillatory dependence on mu and vanish for certain values of mu. Since mu of ferromagnetic scatterers strongly depends on the temperature and applied magnetic field, we suggest that these facts can be explored in technological applications.

Time-resolved experiments on light diffusion in anisotropic random media

Multiple light scattering in isotropic and anisotropic media is studied experimentally with an optical gating technique, as commonly used in fluorescence spectroscopy. The experimental setup permits an accurate analysis of the propagation of a short light pulse through disordered or partially ordered media. The diffusion constant of some isotropic systems is reported, and the anisotropy in the diffusion constant for light diffusion through liquid crystals is observed. For the time-resolved data, good agreement with diffusion theory is found in all cases, including the liquid crystal in the nematic phase.

Spectral changes of light produced by scattering from disordered anisotropic media

We investigate theoretically changes in the spectrum of polychromatic light scattered by a disordered, birefringent medium. We derive an expression for the spectrum of scattered light for ordinary and extraordinary incident waves within the accuracy of the first Born approximation. Using this result, we analyze the changes in the spectrum of light due to the combined action of disorder and anisotropy in the scattering process.

Interference patterns of scattering light induced by orientational fluctuations in an electric-field-biased nematic liquid-crystal film

A new light-scattering phenomenon from a planar aligned nematic liquid-crystal film is observed and studied. This new phenomenon exhibits ring patterns in the orthogonal polarization. A simple model based on optical interference has been developed, and its predictions agree well with experimental observation.