Anisotropic weak localization of light

Emergence of coherent backscattering from sparse and finite disordered media

Coherent backscattering (CBS) arises from complex interactions of a coherent beam with randomly positioned particles, which has been typically studied in media with large numbers of scatterers and high opacity. We develop a first-principles scattering model for scalar waves to study the CBS cone formation in finite-sized and sparse random media with specific geometries. The current study provides insights into the effects of density, volume size, and other relevant parameters on the angular characteristics of the CBS cone emerging from sparse and bounded random media for various types of illumination, with results consistent with well-known CBS studies which are typically based on samples with much larger number of scatterers and higher opacity. The enhancements are observed in scattering medium with dimensions between 10× and 40× wavelength and the number of particles as few as 370. This work also highlights some of the potentials and limitations of employing the CBS phenomenon to characterize disordered configurations. The method developed here provides a foundation for studies of complex electromagnetic fields beyond simple incident classical beams in randomized geometries, including structured wavefronts in illumination and quantized fields for investigating the effects of the quantum nature of light in multiple scattering, with no further numerical complications.

Electrically tunable polarization of random lasing from dye-doped nematic liquid crystals

Tunable polarizing direction of random lasing emission by an applied electric field which radiated from the lateral end face of homogeneously aligned, dye-doped nematic liquid crystal (NLC) cell was demonstrated for the first time, to the best of our knowledge. The lasing emission was partially polarized in the direction along the director of the NLC without the applied electric field. By tuning the applied electric field, the NLC director could be rotated to arbitrary direction from homogeneous to homeotropic alignment, resulting in the polarizing direction of lasing emission to any direction from parallel to perpendicular to the substrate surface in the end face.

An electronic approach for the automation of angle-resolved spectroscopic measurements

Angle-resolved light scattering techniques are powerful tools to obtain structural and spectroscopic information on the investigated sample by means of the study of the pattern of the angular distribution of scattered light. In this paper, we show the details of a new electronic system conceived to automate a Raman coherent backscattering setup, in which it is crucial to acquire several spectra at different angles in a wide spectral acquisition range. In this frame, we used this electrical circuit to trigger the signal edges between the charged-coupled device and the motorized nanorotator stage in our setup, carrying out a considerable quantity of measurements only with an initial input given by the operator and minimizing the supervision of the experiment and, therefore, the time invested by the user in it. By means of this system that can be easily integrated in the setup, we can perform distinct type of measurements by using different configurations of the components that make up the experimental setup.

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.

Coherent backscattering of light by an anisotropic biological network

The scattering strength of a random medium relies on the geometry and spatial distribution of its components as well as on their refractive index. Anisotropy can, therefore, play a major role in the optimization of the scattering efficiency in both biological and synthetic materials. In this study, we show that, by exploiting the coherent backscattering phenomenon, it is possible to characterize the optical anisotropy in Cyphochilus beetle scales without the need to change their orientation or their thickness. For this reason, such a static and easily accessible experimental approach is particularly suitable for the study of biological specimens. Moreover, estimation of the anisotropy in Cyphochilus beetle scales might provide inspiration for improving the scattering strength of artificial white materials.

Double anisotropic coherent backscattering of light

A double anisotropic coherent backscattering cone was found. In contrast to the (single) anisotropic coherent backscattering, which was observed in liquid crystals, here, the long axis of the elongated structures changes its orientation with angular distance. We compared our results with the two-dimensional Fourier transform of spatially resolved reflectance measurements and found good agreement, which is predicted by the reciprocity thesis. Furthermore, a Monte Carlo model was applied to reproduce successfully the results of the experiment, whereas the double anisotropy is not predicted by diffusion models.

Backward optical gain originating from weak localization strengthened three-photon process in Er/Yb co-doped (Pb,La)(Zr,Ti)O3 ceramics

The enhancement of green upconverted emission from the Er³⁺/Yb³⁺ co-doped (Pb,La)(Zr,Ti)O₃ ceramic powder under a pumping light with a wavelength of 1480 nm was observed to be greater than 30 times that from the bulk of the same sample. Weak localization of light supported by the spatial profile of scattered light facilitated the three-photon process contributing to stronger green upconverted emission. Significant backward light amplification was also observed and studied in detail. Additionally, the distribution of the localization zones in the sample was investigated using a probing laser beam with a wavelength of 532 nm. The findings in this work could be used in improving the solar cell efficiency, modulating color, and designing smart devices.

Dynamic coherent backscattering mirror

The phase of multiply scattered light has recently attracted considerable interest. Coherent backscattering is a striking phenomenon of multiple scattered light in which the coherence of light survives multiple scattering in a random medium and is observable in the direction space as an enhancement of the intensity of backscattered light within a cone around the retroreflection direction. Reciprocity also leads to enhancement of backscattering light in the spatial space. The random medium behaves as a reciprocity mirror which robustly converts a diverging incident beam into a converging backscattering one focusing at a conjugate spot in space. Here we first analyze theoretically this coherent backscattering mirror (CBM) phenomenon and then demonstrate the capability of CBM compensating and correcting both static and dynamic phase distortions occurring along the optical path. CBM may offer novel approaches for high speed dynamic phase corrections in optical systems and find applications in sensing and navigation.

Observation of weak localization of light in gold nanofluids synthesized using the marine derived fungus Aspergillus niger

Decreasing particle size with increasing pH in gold nanofluids.

Simulation of radiation transfer and coherent backscattering in nematic liquid crystals

We consider the multiple scattering of light by fluctuations of the director in a nematic liquid crystal. Using methods of numerical simulation the peak of the coherent backscattering and the coefficients of anisotropic diffusion are calculated. The calculations were carried out without simplifying assumptions on the properties of the liquid crystal. The process of multiple scattering was simulated as a random walk of photons in the medium. We investigated in detail the transition to the diffusion regime. The dependence of the diffusion coefficients on the applied magnetic field and the wavelength of light were studied. The results of simulation showed a nonmonotonic dependence of the diffusion coefficients on the external magnetic field. For calculation of the peak of the coherent backscattering we used the semianalytical approach as long as in nematic liquid crystals this peak is extremely narrow. The parameters of the backscattering peak and of diffusion coefficients which were found in numerical simulations were compared with the experimental data and the results of analytical calculation.

Open source software for electric field Monte Carlo simulation of coherent backscattering in biological media containing birefringence

ABSTRACT. We present an open source electric field tracking Monte Carlo program to model backscattering in biological media containing birefringence, with computation of the coherent backscattering phenomenon as an example. These simulations enable the modeling of tissue scattering as a statistically homogeneous continuous random media under the Whittle-Matérn model, which includes the Henyey-Greenstein phase function as a special case, or as a composition of discrete spherical scatterers under Mie theory. The calculation of the amplitude scattering matrix for the above two cases as well as the implementation of birefringence using the Jones N-matrix formalism is presented. For ease of operator use and data processing, our simulation incorporates a graphical user interface written in MATLAB to interact with the underlying C code. Additionally, an increase in computational speed is achieved through implementation of message passing interface and the semi-analytical approach. Finally, we provide demonstrations of the results of our simulation for purely scattering media and scattering media containing linear birefringence.

Coherent backscattering cone shape depends on the beam size

Coherent backscattering (CBS) is a beautiful physical phenomenon that takes place in a highly scattering medium, which has potential application in noninvasive optical property measurement. The current model that explains the CBS cone shape, however, assumes the incoming beam diameter is infinitely large compared to the transport length. In this paper, we evaluate the effect of a finite scalar light illumination area on the CBS cone, both theoretically and experimentally. The quantitative relationship between laser beam size and the CBS cone shape is established by using two different finite beam models (uniform top hat and Gaussian distribution). A series of experimental data with varying beam diameters is obtained for comparison with the theory. Our study shows the CBS cone shape begins to show distortion when beam size becomes submillimeter, and this effect should not be ignored in general. In biological tissue where a normal large beam CBS cone is too narrow for detection, this small beam CBS may be more advantageous for more accurate and higher resolution tissue characterization.

Weak localization of light in superdiffusive random systems

Lévy flights constitute a broad class of random walks that occur in many fields of research, from biology to economy and geophysics. The recent advent of Lévy glasses allows us to study Lévy flights-and the resultant superdiffusion-using light waves. This raises several questions about the influence of interference on superdiffusive transport. Superdiffusive structures have the extraordinary property that all points are connected via direct jumps, which is expected to have a strong impact on interference effects such as weak and strong localization. Here we report on the experimental observation of weak localization in Lévy glasses and compare our results with a recently developed theory for multiple scattering in superdiffusive media. Experimental results are in good agreement with theory and allow us to unveil the light propagation inside a finite-size superdiffusive system.

Low-coherence enhanced backscattering from highly forward scattering media

We present a theoretical basis for calculation of the angular profile of the coherent backscattering intensity under low spatial coherence illumination. We take into account two contributions to the intensity, namely, the diffusion contribution and the contribution from the waves that experience the small-angle multiple scattering before and after single deflection in the backward direction. The latter contribution describes transport of light at subdiffusion length scales and is responsible for the wings of the backscattering angular profile. Our results are in good agreement with data of Monte-Carlo simulations and experiment.

Effect of external field on coherent backscattering in nematics

For a one-elastic-constant model of nematic liquid crystal the optical theorem is shown to produce an explicit relationship between the scattering length of extraordinary wave mode and magnetic coherence length. The Monte Carlo simulation of coherent backscattering is performed accounting for the long-range orientational fluctuations and scattering length anisotropy; the coherent backscattering peak is shown to change quite weakly while the magnetic field varies several orders.

Wings of coherent backscattering from a disordered medium with large inhomogeneities

We calculate the nondiffusive contribution to the intensity of coherent backscattering from a disordered medium composed of large-scale scatterers. The wings of the coherent backscattering cone are shown to be governed by short-path waves that experience small-angle multiple scattering before and after single scattering in the backward direction. For relatively large angles θ of deviation from the backward direction, θ > λ/l(tr) (λ is the wavelength of light, l(tr) is the transport mean free path), the intensity falls off slower than θ(-1) and is directly related to a law of single scattering through small angles. Our calculations are in good agreement with experimental data for large Mie spheres.

Measurement of optical scattering properties with low-coherence enhanced backscattering spectroscopy

Low-coherence enhanced backscattering (LEBS) is a depth selective technique that allows noninvasive characterization of turbid media such as biological tissue. LEBS provides a spectral measurement of the tissue reflectance distribution as a function of distance between incident and reflected ray pairs through the use of partial spatial coherence broadband illumination. We present LEBS as a new depth-selective technique to measure optical properties of tissue in situ. Because LEBS enables measurements of reflectance due to initial scattering events, LEBS is sensitive to the shape of the phase function in addition to the reduced scattering coefficient (μ(s) (*)). We introduce a simulation of LEBS that implements a two parameter phase function based on the Whittle-Matérn refractive index correlation function model. We show that the LEBS enhancement factor (E) primarily depends on μ(s) (*), the normalized spectral dependence of E (S(n)) depends on one of the two parameters of the phase function that also defines the functional type of the refractive index correlation function (m), and the LEBS peak width depends on both the anisotropy factor (g) and m. Three inverse models for calculating these optical properties are described and the calculations are validated with an experimental measurement from a tissue phantom.

Self-assembled photonic structures

Photonic crystals have proven their potential and are nowadays a familiar concept. They have been approached from many scientific and technological flanks. Among the many techniques devised to implement this technology self-assembly has always been one of great popularity surely due to its ease of access and the richness of results offered. Self-assembly is also probably the approach entailing more materials aspects owing to the fact that they lend themselves to be fabricated by a great many, very different methods on a vast variety of materials and to multiple purposes. To these well-known material systems a new sibling has been born (photonic glass) expanding the paradigm of optical materials inspired by solid state physics crystal concept. It is expected that they may become an important player in the near future not only because they complement the properties of photonic crystals but because they entice the researchers' curiosity. In this review a panorama is presented of the state of the art in this field with the view to serve a broad community concerned with materials aspects of photonic structures and more so those interested in self-assembly.

Light-controllable coherent backscattering from water suspension of lithium niobate microcrystalline particles

We experimentally study coherent backscattering of light for a water suspension of lithium niobate microcrystalline particles. Light-controllable weak localization of photons in a suspension is demonstrated for the first time to our knowledge. The effect is attributed to the reorientation of microcrystalline particles in the field of a linearly polarized pump beam. Thus the isotropic suspension becomes partially anisotropic.

Light scattering in a magnetically polarizable nanoparticle suspension

We investigate magnetic-field-induced changes on transmitted light intensity in a magnetic disordered phase of iron oxide nanoparticle suspension. We observe a dramatic decrease in the transmitted light intensity at a critical magnetic field. The critical magnetic field follows power-law dependence with the volume fraction of the nanoparticles suggesting a disorder-order structural transition. The light intensity recovers fully when the magnetic field is switched off. We discuss the possible reasons for the reduction in the light intensity under the influence of magnetic field. Among the various mechanisms such as Kerker's condition for zero forward scattering, Faraday effect, Christiansen effect, photoinduced refractive index mismatch between the two components of the dispersion, etc., the resonances within the magnetic scatterers appear to be the plausible cause for the extinction of light. The circular pattern observed on a screen placed perpendicular to the incident beam confirms the formation of rodlike structures along the direction of propagation of the light.

Statistical analysis of random lasing emission properties in nematic liquid crystals

A statistical analysis of random lasing events observed in dye-doped nematic-liquid-crystal films is reported. The occurrence of random laser action in such complex fluids is due to residual resonances in the multiple scattering of spontaneously emitted photons. The Shannon entropy and a local-Poisson test are used here in order to quantitatively characterize the chaotic behavior of laser spikes and gain further understanding of the mechanisms underlying the lasing effect in strongly scattering organized fluids arising by an unexpected interplay of localization and amplification.

Anisotropy and interference in wave transport: an analytic theory

A theory is presented which incorporates the effect of dielectric anisotropy in random multiple scattering media. It predicts anisotropic diffusion, and a deflection of the diffuse energy flow in anisotropic slabs in the direction parallel to the slab. The transmittance integrated over all incoming and outgoing directions scales with the transport mean free path along the surface normal. The escape function in anisotropic dielectrics is no longer bell shaped. In this model anisotropy facilitates Anderson localization.

Light propagation in strongly scattering, random colloidal films: the role of the packing geometry

We study the propagation of light through randomly packed films of micron-sized spheres. Dried films consist of strongly scattering core-shell particles mixed with polymer spheres, which are then dissolved to tune the number of contacts, Z, among the remaining scatterers. The transport mean free path l* is measured from the width of the coherent backscattering cone; l*=2.1 microm when Z ~ 4-5, but increases twofold (scattering weakens) in a film with Z ~ 9-10. The results contradict the standard diffusive transport model, but are explained by accounting for optical coupling of contacting spheres.

Incoherent light transport in an anisotropic random medium: a probe of human erythrocyte aggregation and deformation

This paper investigates the flow induced disaggregation, deformation and orientation of several modified human red blood cells suspended in concentrated, physiological like conditions (volume fraction in erythrocytes of 0.4). The aim is to determine simultaneously, and under flow, the aggregate sizes as well as the deformation and orientation of the cells. The measurement method uses steady, incoherent, unpolarized light transport while the sample is sheared in a flow cell controlled by a rheometer. Several blood samples were prepared to alter the erythrocyte's aggregating, deformability and shape properties. The measurements using these samples show a clear relationship between the intrinsic properties of the cells and the evolution of aggregate sizes, average cell orientation and anisotropy as a function of the applied shear, which may lead to clinical applications. In other words, the careful analysis of the incoherent light transport in concentrated media provides quantitative insight into their microscopic details. In particular, the topological properties (average anisotropy and orientation) and size of the suspended objects can be determined.

Coherence loss in light backscattering by random media with nanoscale nonuniformities

An experimental technique for measuring time-resolved coherence loss and destruction of backscattered wave packets in random media is described. The results of such measurements, performed with a modified Michelson interferometer, contain rich information about the characteristics of media nonuniformities. Experimental data for model nanosuspensions are compared with theoretical expressions developed in the paper which include the effects of Mie-type resonant scattering. We attribute one such observed effect to enhanced ineleastic optical transitions near the surface of nonmetallic nanoparticles. The inverse problem of characterization of multiscattering random media by backscattering is also considered.

Penetration depth of low-coherence enhanced backscattered light in subdiffusion regime

The mechanisms of photon propagation in random media in the diffusive multiple scattering regime have been previously studied using diffusion approximation. However, similar understanding in the low-order (subdiffusion) scattering regime is not complete due to difficulties in tracking photons that undergo very few scatterings events. Recent developments in low-coherence enhanced backscattering (LEBS) overcome these difficulties and enable probing photons that travel very short distances and undergo only a few scattering events. In LEBS, enhanced backscattering is observed under illumination with spatial coherence length L{sc} less than the scattering mean free path l{s}. In order to understand the mechanisms of photon propagation in LEBS in the subdiffusion regime, it is imperative to develop analytical and numerical models that describe the statistical properties of photon trajectories. Here we derive the probability distribution of penetration depth of LEBS photons and report Monte Carlo numerical simulations to support our analytical results. Our results demonstrate that, surprisingly, the transport of photons that undergo low-order scattering events has only weak dependence on the optical properties of the medium (l{s} and anisotropy factor g) and strong dependence on the spatial coherence length of illumination, L{sc} relative to those in the diffusion regime. More importantly, these low-order scattering photons typically penetrate less than l{s} into the medium due to the low spatial coherence length of illumination and their penetration depth is proportional to the one-third power of the coherence volume (i.e., [l{s}piL{s}{2}]1/3) .

Delocalization of classical waves in highly anisotropic random media

We discuss localization phenomena in multilayer films doped with scattering particles. If the films exhibit a particular type of transmission resonance then above a critical frequency waves in the sample can decay as a power law rather than exponentially. This phenomenon is independent of the scattering strength of the particles, in stark contrast to previous work. We find that this phenomenon has many similarities to a second order phase transition. This work points to interesting avenues in the study of waves in anisotropic disordered media.

Modeling low-coherence enhanced backscattering using Monte Carlo simulation

Constructive interference between coherent waves traveling time-reversed paths in a random medium gives rise to the enhancement of light scattering observed in directions close to backscattering. This phenomenon is known as enhanced backscattering (EBS). According to diffusion theory, the angular width of an EBS cone is proportional to the ratio of the wavelength of light lambda to the transport mean-free-path length l(s)* of a random medium. In biological media a large l(s)* approximately 0.5-2 mm >> lambda results in an extremely small (approximately 0.001 degrees ) angular width of the EBS cone, making the experimental observation of such narrow peaks difficult. Recently, the feasibility of observing EBS under low spatial coherence illumination (spatial coherence length Lsc << l(s)*) was demonstrated. Low spatial coherence behaves as a spatial filter rejecting longer path lengths and thus resulting in an increase of more than 100 times in the angular width of low coherence EBS (LEBS) cones. However, a conventional diffusion approximation-based model of EBS has not been able to explain such a dramatic increase in LEBS width. We present a photon random walk model of LEBS by using Monte Carlo simulation to elucidate the mechanism accounting for the unprecedented broadening of the LEBS peaks. Typically, the exit angles of the scattered photons are not considered in modeling EBS in the diffusion regime. We show that small exit angles are highly sensitive to low-order scattering, which is crucial for accurate modeling of LEBS. Our results show that the predictions of the model are in excellent agreement with the experimental data.

Low-coherence enhanced backscattering: review of principles and applications for colon cancer screening

The phenomenon of enhanced backscattering (EBS) of light, also known as coherent backscattering (CBS) of light, has been the object of intensive investigation in nonbiological media over the last two decades. However, there have been only a few attempts to explore EBS for tissue characterization and diagnosis. We have recently made progress in the EBS measurements in tissue by taking advantage of low spatial coherence illumination, which has led us to the development of low-coherence enhanced backscattering (LEBS) spectroscopy. In this work, we review the current state of research on LEBS. After a brief discussion of the basic principle of EBS and LEBS, we present an overview of the unique features of LEBS for tissue characterization, and show that LEBS enables depth-selective spectroscopic assessment of mucosal tissue. Then, we demonstrate the potential of LEBS spectroscopy for predicting the risk of colon carcinogenesis and colonoscopy-free screening for colorectal cancer (CRC).

Experimental evidence of zero forward scattering by magnetic spheres

Magnetically induced diffraction patterns by micron sized magnetic spheres dispersed in a ferrofluid disappear at a certain critical magnetic field. This critical field is found to depend on the concentration of the ferrofluid and on the volume of the magnetic spheres. We attribute this effect to the zero forward scattering by magnetic spheres as predicted by Kerker, Wang, and Giles [J. Opt. Soc. Am. 73, 765 (1983)]. We suggest that such a dispersion can be used to study the optical analogues of localization of electrons in condensed matter, the Hall effect, and the anisotropic diffusion, etc. The combination of the micron sized magnetic spheres and the ferrofluid will also be useful to design magnetically tunable photonic devices.

Manifestation of weak localization and long-range correlation in disordered wave functions from conical second harmonic generation

We experimentally demonstrate that the near-field patterns of conical second harmonic generation of a laser in random domain structures can be used to explore the spatial structure of two-dimensional disordered wave functions with weak localization. The statistics of the experimental near-field patterns agree very well with the theoretical distributions. In addition to the short-range correlation, the localization effects are found to contribute a nearly constant value to the long-range correlation. The result of this Letter also confirms the possibility of using conical second harmonic generation as a diagnostic tool for topographical characterization of crystals.

Weak localization of light in a disordered microcavity

We report the observation of weak localization of light in a semiconductor microcavity. The intrinsic disorder in a microcavity leads to multiple scattering and hence to static speckle. We show that averaging over realizations of the disorder reveals a coherent backscattering cone that has a coherent enhancement factor > or =2, as required by reciprocity. The coherent backscattering cone is observed along a ring-shaped pattern due to confinement by the microcavity.

Depth-resolved low-coherence enhanced backscattering

The phenomenon of enhanced backscattering (also known as coherent backscattering), an object of substantial scientific interest, has awaited application to tissue optics for the past two decades. Here we demonstrate, for the first time to our knowledge, depth-resolved spectroscopic elastic light scattering measurements in tissue by use of low-coherence enhanced backscattering (LEBS). We achieve the depth resolution by exploiting the nature of the LEBS peak that contains information about a wide range of tissue depths. We further demonstrate that depth-resolved LEBS spectroscopy has the potential to identify the origin of precancerous transformations in the colon at an early, previously undetectable stage.

Low-coherent backscattering spectroscopy for tissue characterization

Although the phenomenon of coherent backscattering (CBS) in nonbiological media has generated substantial research interest, observing CBS in biological tissue has been extremely difficult. Here we show that the combination of low-spatial-coherence, broadband illumination, and low-temporal-coherence, spectrally resolved detection significantly facilitates CBS observation in biological tissue and other random media with long-transport mean-free path lengths, which have been previously beyond the reach of conventional CBS investigations. Furthermore, we demonstrate that depth-selective, speckle-free, low-coherent backscattering spectroscopy has the potential to diagnose the earliest, previously undetectable, precancerous alterations in the colon by means of probing short light paths.

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.

Localization of classical waves in weakly scattering two-dimensional media with anisotropic disorder

We study the localization of classical waves in weakly scattering two-dimensional systems with anisotropic disorder. The analysis is based on a perturbative path-integral technique combined with a spectral filtering that accounts for the first-order Bragg scattering only. It is shown that in the long-wavelength limit the radiation is always localized, and the localization length is independent of the direction of propagation, the latter in contrast to the predictions based on an anisotropic tight-binding model. For shorter wavelengths that are comparable to the correlation scales of the disorder, the transport properties of disordered media are essentially different in the directions along and across the correlation ellipse. There exists a frequency-dependent critical value of the anisotropy parameter, below which waves are localized at all angles of propagation. Above this critical value, the radiation is localized only within some angular sectors centered at the short axis of the correlation ellipse and is extended in other directions.

Anisotropic enhanced backscattering induced by anisotropic diffusion

The enhanced backscattering cone displaying a strong anisotropy from a material with anisotropic diffusion is reported. The constructive interference of the wave is preserved in the helicity preserving polarization channel and completely lost in the nonpreserving one. The internal reflectivity at the interface modifies the width of the backscatter cone. The reflectivity coefficient is measured by angular-resolved transmission. This interface property is found to be isotropic, simplifying the backscatter cone analysis. The material used is a macroporous semiconductor, gallium phosphide, in which pores are etched in a disordered position but with a preferential direction.