Coherent wave backscattering by random medium. Exact solution of the albedo problem (original) (raw)
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Optical coherent backscattering by random media : an experimental study
Journal de Physique, 1988
Requ le 15 juillet 1987, accepté le 22 septembre 1987)' Résumé. 2014 Nous présentons une étude détaillée de la rétrodiffusion cohérente de la lumière par des suspensions aqueuses de microbilles de polystyrène. Nous discutons particulièrement les effets, sur la forme et la hauteur du pic de rétrodiffusion, de la taille des particules, de l'absorption 2014 contrôlée par l'addition d'un colorant 2014 et de la polarisation de la lumière. Lorsque les polarisations incidente et détectée sont parallèles, la théorie de diffusion scalaire, caractérisée par le libre parcours moyen de transport l *, rend compte de la forme du pic jusqu'à des angles de (rétro)diffusion étonnement élevés (ql * ~ 1) et de son arrondissement progressif en présence d'absorption. Nous n'observons aucune déviation à la statistique gaussienne habituelle pour le champ diffusé, et ce jusqu'à des rapports 03BB/l* ~ 0,1. Abstract. 2014 A detailed experimental study of coherent backscattering of light from aqueous suspensions of polystyrene microspheres is presented. Emphasis is on the effects of particle size, of absorption due to added dye and of light polarization on the shape and height of the backscattering cone. For parallel polarization of incident and scattered beams, the scalar diffusion theory, parametrized by the transport mean free path l*, agrees well with our data up to surprizingly large scattering angles (ql * ~ 1) and quantitatively accounts for the rounding of the cones due to absorption. No deviations from the usual Gaussian statistics of scattered fields is observed up to 03BB/l* ~ 0.1.
Numerical simulation of coherent backscattering and temporal intensity correlations in random media
Quantum Electronics, 2006
A review of studies on the numerical simulation of coherent effects in random media performed by using exact analytic results is presented. The simulation procedure is based on a comparison of the Monte-Carlo method and the iteration solution of the Bethe ë Salpeter equation. The results of calculations of the time correlation function and the interference component of coherent backscattering for scalar and electromagnetic éelds are described. The simulation results are compared for the érst time with known generalisations of the Milne solution and are in good agreement with experimental data. The interference component of backscattered low-coherent radiation is calculated for the érst time. The localisation of backscattered low-coherent laser radiation along the penetration depth is described. The theory and numerical simulation predict, in accordance with the experiment, a considerable broadening of the backscattering peak with decreasing the coherence length, which opens up essentially new possibilities for the use of this effect, especially for medical diagnostics.
Coherent Backscattering of Light by Disordered Media: Analysis of the Peak Line Shape
Physical Review Letters, 1986
Recent experiments have confirmed that coherent effects in the multiple scattering of light affect the angular dependence of the intensity reflected by disordered media. By considering the constructive interferences between time-reversed paths of light in a semi-infinite medium,~e analyze the experimental line shape of the albedo within the diffusion approximation and explain the observed effects of polarization.
Theoretical study of the coherent backscattering of light by disordered media
Journal de Physique, 1988
2014 Nous présentons une étude théorique de la rétrodiffusion cohérente de la lumière par un milieu désordonné dans diverses situations incluant les effets dépendant du temps, les milieux absorbants et les effets liés à la modulation d'amplitude de la lumière. Nous discutons tout particulièrement le cas de la diffusion anisotrope et les effets de la polarisation afin d'expliquer quantitativement les résultats expérimentaux. Nous donnons un calcul microscopique de l'albedo cohérent afin de justifier la relation heuristique précédemment établie. Nous prédisons aussi la forme de l'albedo cohérent d'un milieu fractal. Enfin, la validité des différentes approximations utilisées est discutée et quelques développements ultérieurs sont évoqués. Abstract. 2014 A theoretical study of the coherent backscattering effect of light from disordered semi-infinite media is presented for various situations including time-dependent effects as well as absorption and amplitude modulation. Particular attention is devoted to the case of anisotropic scattering and to polarization in order to explain quantitatively experimental results. A microscopic derivation of the coherent albedo is given which strongly supports the heuristic formula previously established. In addition the coherent albedo of a fractal system is predicted. The validity of the different approximations used are discussed and some further theoretical developments are presented.
Applied Optics, 2007
Phase curves of intensity are calculated for light scattering in media randomly packed with large nontransparent spheres (x=125), the surfaces of which reflect according to the Fresnel equations. We consider three values of refractive index: m = 0.73 + i5.93 (metal Al), 1.6 + i1.72 (metal Fe), and 1.5 + i0.1 (black glass). We use a Monte Carlo ray-tracing approach. Different kinds of electromagnetic phase differences of reciprocal trajectories are investigated for the second and third orders of scattering; the highest orders give comparatively small contributions due to the backward-scattering indicatrix of large nontransparent spheres. We find that the main electromagnetic phase difference between the direct and time-reversal (reciprocal) trajectories is the outer phase difference that depends only on the relative positions of the first and last points of the ray reflections and the phase angle. The inner phase difference is connected with the changing path length of the ray inside the medium. This depends on the particle size and the phase angle that is the angle between the source and receiver from the scatterer, i.e., 180 degrees minus the scattering angle. The inner phase difference can give oscillations in the phase curve consisting of second-order components if the medium consists of strictly monodisperse spheres. Usually the coherent backscattering enhancement is calculated ignoring the shadow-hiding effect. We show that accounting for the shadowing of the reciprocal trajectory is important for the formation of the backscattering effect. The third-order scattering surge is a superposition of wide and narrow opposition spikes that correspond to two different types of scattering trajectories, closed and opened ones. The first type is due to scattering by two particles; the second one corresponds to scattering by three particles.
Random Backscattering in the Parabolic Scaling
Journal of Statistical Physics, 2008
In this paper we revisit the parabolic approximation for wave propagation in random media by taking into account backscattering. We obtain a system of transport equations for the moments of the components of reflection and transmission operators. In the regime in which forward scattering is strong and backward scattering is weak, we obtain closed form expressions for physically relevant quantities related to the reflected wave, such as the beam width, the spectral width and the mean spatial power profile. In particular, we analyze the enhanced backscattering phenomenon, that is, we show that the mean power reflected from an incident quasi-plane wave has a maximum in the backscattered direction. This enhancement can be observed in a small cone around the backscattered direction and we compute the enhancement factor as well as the shape of the enhanced backscattering cone.
Reflection and transmission by a slab with randomly distributed isotropic point scatterers
Journal of Computational and Applied Mathematics, 2010
The problem of how a wave propagates in an infinite medium filled with scatterers has revealed the notion of an effective medium: the mean wave propagates as in an homogeneous medium with complex index. Is this notion of an effective medium still valid when the scatterers are bounded in space? The problem is treated here for isotropic point scatterers. It is shown that (i) the waves propagate inside the slab with an effective wavenumber K being the same as that in an infinite medium, (ii) the reflection and transmission coefficients of the slab mainly behave as R (1−e iKL )(k−K )/2k and T e iKL at leading order, (iii) the reflection and transmission coefficients of a single interface are related to R and T with the usual law of optics and (iv) the boundary conditions to be applied at the interface are the continuity of the field and its first derivative for isotropic scatterers. Finally, numerical experiments in one dimension show satisfactory agreement with the presented theory.
Modeling low-coherence enhanced backscattering using Monte Carlo simulation
Applied Optics, 2006
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 to the transport meanfree-path length l s * of a random medium. In biological media a large l s * ϳ 0.5-2 mm Ͼ Ͼ results in an extremely small ͑ϳ0.001°͒ 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 L sc Ͻ Ͻ 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.
Multiple light scattering in random systems: Analysis of the backscattering spot image
The European Physical Journal Applied Physics, 1999
This study concerns the multiple scattering of light in random granular systems and the analysis of the image formed by the light scattered by a random medium. We developed an imagery method with high grey level resolution for visualization and analysis of the intensity profile in the backscattering spot image. We further present statistical models for the radiative transfer in granular media only involving the photon mean path length, the asymmetry factor and the absorption probability of photons. A renormalization of the photon trajectory in the medium gives a photon transport equation for anisotropic scattering and leads to an analytical expression for the intensity profile in the backscattering spot. We finally compare the results from imagery experiments with the predictions from numerical simulations and statistical models. Résumé. Ce travail concerne la diffusion multiple de la lumière dans les systèmes dispersés aléatoires et la caractérisation du milieu par analyse de la tache de rétrodiffusion. Nous avons mis au point une technique d'imagerieà haute résolution en niveaux de gris pour la visualisation et l'analyse du profil de luminosité dans la tache de rétrodiffusion. Nous présentons par ailleurs des modèles statistiques du transfert radiatif dans les milieux granulaires où interviennent seulement le libre parcours moyen, le facteur d'asymétrie et la probabilité d'absorption des photons. Dans le cas de la diffusion anisotrope, nous effectuons une renormalisation de la trajectoire des photons dans le milieu pour aboutirà uneéquation de transport des photons età une expression analytique du flux lumineux dans la tache de rétrodiffusion. Nous comparons enfin les résultats des expériences d'imagerie avec les prévisions des simulations numériques et des modèles statistiques.
Coherent backscattering of circularly polarized light from a disperse random medium
To describe propagation of polarized electromagnetic wave within a disperse random medium a new Monte Carlo based technique with an adopted vector formalism has been developed. The technique has been applied for simulation of coherent backscattering of circularly polarized optical radiation from a random scattering medium. It has been found that the sign of helicity of circular polarized light does not change for a medium of point-like scatterers and can change significantly for the scatterers with the higher anisotropy. We conclude that the helicity flip of the circular polarized light can be observed in the tissue-like media. We find that this phenomenon manifests itself in case of limited number of scattering events and, apparently, can be attributed to the pulse character of incident radiation rather than to the specific form of scattering particles.