Simulation of coherent backscattering of light in nematic liquid crystals

Multiple scattering of light by the fluctuations of the director in a nematic liquid crystal (NLC) aligned by a magnetic field is considered. A peak of coherent backscattering is calculated by numerical simulation. Since the indicatrix of single scattering for a liquid crystal (LC) is known exactly, the calculations are carried out without any simplifying assumptions on the parameters of the liquid crystal. Multiple scattering is simulated as a random walk of photons in the medium. A peak of coherent backscattering in such a medium is very narrow; therefore, the so-called semianalytical method is applied. The parameters of the backscattering peak obtained by numerical simulation are compared with the available experimental data and with the results of analytical approximations. It turns out that the experimental data are in good agreement with the results of simulation. The results of numerical simulation adequately describe the anisotropy and the width of the backscattering peak.     

Coherent backscattering in nematic liquid crystals in an external magnetic field

We consider multiple light scattering in a nematic liquid crystal. Using the Monte Carlo method, we calculate for the first time the effect of a magnetic field on the shape of the peak of coherent backscattering taking into account the long-range action of fluctuations of the orientational order and anisotropy of the scattering length. For a small number of initial and final scattering events, we take into account the ordinary mode of light, which is weakly scattered in a nematic liquid crystal (NLC), whereas a strongly scattered extraordinary mode is taken into account for all scattering events. For simplicity, we use a single-constant approximation of the NLC elastic moduli. We show that the angular shape of the peak of coherent backscattering remains nearly unchanged, whereas the magnetic field and the scattering phase function vary by several orders of magnitude.     

Deducing residual self-interference of inelastic photons in coherent backscattering of intense laser light from two atoms

A coherent backscattering of intense laser light by two isotropic atoms is studied in the helicity preserving polarization channel. It is demonstrated that single scattering has a non-negligible contribution to the background intensity L(θ) at small angles θ with respect to the backwards direction. This contribution can be subtracted from the total signal, and the value of L(0) necessary for evaluating the coherent backscattering enhancement factor – inferred from measurements of the backscattered light intensity beyond the interference peak.     

Effects of nondiffusive wave propagation upon coherent backscattering by turbid media

The nondiffusive contribution to the coherent backscattering intensity is calculated for the media with relatively large particles (size a is greater than wavelength λ). The results are in good agreement with the experimental data at the wings of the angular spectrum of the coherent backscattering. The shape of the backscattering peak is analyzed for strongly absorbing media. The correlation function of the intensity fluctuations is calculated for the scattering by Brownian particles at relatively large time shifts.     

Influence of the nonlocal nature of fluctuations on coherent effects in multiple scattering

We solve the Bethe-Salpeter equation that describes radiation transfer in highly inhomogeneous media with an anisotropic scattering with allowance for the contributions of Legendre polynomials of the zeroth, first, and second degrees. An analytical expression for the radiation-transfer propagator is derived. We show that as the average value of the second-degree Lagrange polynomial increases, the region where the diffusion approximation is valid shifts toward large distances. Within this approach we calculate the coherent backscattering intensity and study the effect of higher-order moments on the angular dependence of this intensity. Finally, we show that it is possible to experimentally detect the coherent backscattering peak in the critical region. Zh. éksp. Teor. Fiz. 113, 2022–2033 (June 1998)     

Weak localization effects in the second-harmonic light scattered by random systems of particles

We report rigorous numerical simulations that show the presence of coherent backscattering effects in the second-harmonic generation and scattering of light by random systems of two-dimensional particles. Since the medium composing the particles is assumed to be homogeneous and isotropic, the second-harmonic field is generated mainly by surface effects. For the fundamental frequency, the results present a clear enhanced backscattering peak. In contrast, the second-harmonic scattering patterns present an intensity dip in the backscattering direction.     

The Milne problem solution for the temporal correlation function of an electromagnetic field

The problem of multiple scattering of light by a medium occupying a half-space is solved in backscattering geometry. The solution obtained in the framework of the Wiener-Hopf method, which is a generalization of the well-known Milne solution for the electromagnetic field, has made it possible for the first time to calculate exactly the initial time dependence of the intensity correlation function as well as the dependence of the backscattering intensity on the scattering angle for different polarizations of the incident and scattered waves.     

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.     

Magnetic field effects on coherent backscattering of light

We have studied the influence of magneto-optical Faraday rotation on coherent backscattering of light experimentally, theoretically and by computer simulations of Monte-Carlo type. The consistency of these three approaches reveals new aspects of the propagation of vector waves in turbid media with and without Faraday rotation. Experimentally, we have demonstrated that the Faraday rotation may almost completely destroy the reciprocity of light paths. However, as shown by the simulations, the cone of coherent backscattering may not only be destroyed but also shifted off the exact backscattering direction, parallel to the magnetic field, as long as the amount of circular polarization is not completely destroyed by the multiple scattering. The relationship between coherent backscattering, depolarization and Faraday rotation are explained by a simple path model of vector waves. This leads to a new characteristic correlation length required to properly describe the influence of Faraday rotation on multiple light scattering. Received 28 January 2000     

Coherent backscattering of light by a layer of discrete random medium

We consider the problem of backscattering of light by a layer of discrete random medium illuminated by an obliquely incident plane electromagnetic wave. The multiply scattered reflected radiation is assumed to consist of incoherent and coherent parts, the coherent part being caused by the interference of multiply scattered waves. Formulas describing the characteristics of the reflected radiation are derived assuming that the scattering particles are spherical. The formula for the incoherent contribution reproduces the standard vector radiative transfer equation. The interference contribution is expressed in terms of a system of Fredholm integral equations with kernels containing Bessel functions. The special case of the backscattering direction is considered in detail. It is shown that the angular width of the backscattering interference peak depends on the polar angle of the incident wave and on the azimuth angle of the reflection direction.     

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.     

Low-coherence enhanced backscattering beyond diffusion

An analytical theory for coherent backscattering (CBS) of low-coherence light is presented. An expression linking the CBS profile to the radial distribution of the incoherent backscattered light is derived when the incident light is partially spatially coherent. The backscattered snake light, which has experienced exactly two large-angle scatterings, is taken into account together with the diffuse light in the analysis. Monte Carlo simulations demonstrate that the model describes well the CBS profile as long as the spatial coherence length, L(c), of the incident beam is larger than the scattering mean free path of light in the medium. The intensity of the enhanced backscattered light in the exact backscattering direction and the width of the CBS cone are found to be proportional to L(c) and L(c)(-1), respectively, in the limit of small L(c).     

非球形烟尘粒子后向散射场的光谱分析

在利用后向散射法测量烟尘浓度和粒径的过程中,对烟尘粒子模型的后向散射光谱特性进了计算,确定影响后向散射光谱强度的主要因素并进行分析。对实际排放的烟尘进行显微观察表明,利用椭球、圆柱和广义切比雪夫3种非球模型可以较好地模拟烟尘粒子,其等效直径约1μm。通过"T矩阵法"对这3种非球形粒子模型后向散射场的光谱特性进行了分析,结果表明:非球形粒子的可见/红外波段后向散射现象较球形粒子明显,特别是广义切比雪夫粒子的后向散射光强最高可达到前向的3.5倍;对于吸收性非球形粒子(复折射率m=1.57-0.56i),后向散射光强远大于非吸收性非球形粒子(复折射率m=1.57-0.001i);随着粒子等效半径的增大,光源波长也应随之增加。这为在实际测量时光源及方位的选择提供了理论依据。     

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.     

Interference effects in backscattering of light by a layer of a discrete random medium

Multiple backscattering of light by a layer of a discrete random medium is considered. A brief derivation of equations for describing the coherent and incoherent components of scattered light is presented. These equations are solved numerically in the approximation of doubled scattering of light by a semi-infinite medium of spherical scatterers having a size comparable with the wavelength in order to study the effect of the properties of particles on the angular dependence of interference effects. Calculations show that the half-width of the interference peak decreases upon an increase in lateral scattering by particles and that the degree of polarization has a complex angular dependence on the properties of the particles. For an optically thin layer of the medium, the relations defining the interference peak half-width and the scattering angle upon extreme linear polarization as functions of the effective refractive index are given.     

Influence of the boundary of a medium on the coherent backscattering of light

The multiple scattering of light from an inhomogeneous medium occupying a half-space is investigated on the basis of the Bethe-Salpeter equation. The latter is integrated over the spatial variables to obtain an identity having the significance of the energy balance of the incident and scattered radiations. This relation is then used to derive a length parameter that plays the role of the Milne interpolation length. The use of this parameter in the method of mirror images for describing the shape of the coherent backscattering peak in isotropic single scattering yields results in almost perfect agreement with the predictions of the Milne theory. The application of the given approach for an anisotropic single-scattering diagram yields quantitative agreement of the theory with experiments on the angular dependence of coherent backscattering. The new approach is generalized to an electromagnetic (vector) field, and backscattering polarization effects are investigated. Zh. éksp. Teor. Fiz. 116, 1912–1928 (December 1999)     

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.     

Backscattering of linearly and circularly polarized light in randomly inhomogeneous media

The scattering of linearly or circularly polarized light from a semibounded randomly inhomogeneous medium is considered. A new technique for simulating the electromagnetic radiation transport using the Monte Carlo method is proposed, which makes it possible to avoid cumbersome calculation of Muller matrices. Expressions are obtained for the co- and cross-polarized components of backscattered light for incident light of arbitrary polarization. The coherent and incoherent backscattering components are calculated for arbitrary combinations of incident and scattered light polarizations. It is shown that the main contribution to coherent backscattering is from the co- and cross-polarized components for linearly and circularly polarized light, respectively. The backscattering from an optically active random medium is calculated.     

Nonlinear coherent transport of waves in disordered media

We present a diagrammatic theory for coherent backscattering from disordered dilute media in the nonlinear regime. We show that the coherent backscattering enhancement factor is strongly affected by the nonlinearity, and we corroborate these results by numerical simulations. Our theory can be applied to several physical scenarios such as scattering of light in a nonlinear Kerr medium or propagation of matter waves in disordered potentials.