Incoherent and coherent backscattering of light by a layer of densely packed random medium

The problem of light scattering by a layer of densely packed discrete random medium is considered. The theory of light scattering by systems of nonspherical particles is applied to derive equations corresponding to incoherent (diffuse) and interference parts of radiation reflected from the medium. A solution of the system of linear equations describing light scattering by a system of particles is represented by iteration. It is shown that the symmetry properties of the T-matrices and of the translation coefficients for the vector Helmholtz harmonics lead to the reciprocity relation for an arbitrary iteration. This relation is applied to consider the backscattering enhancement phenomenon. Equations expressing the incoherent and interference parts of reflected light from statistically homogeneous and isotropic plane-parallel layer of medium are given. In the exact backscattering direction the relation between incoherent and interference parts is identical to that of sparse media.     

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.     

Optical properties of aggregate particles comparable in size to the wavelength

The angular dependence of brightness and linear polarization of randomly oriented aggregates has been investigated in order to find rules connecting their scattering properties with their structure, packing density, complex refractive index, and number and size of the spheres forming the aggregate. Our study is based on an interpretation in terms of successive orders of scattering, in particular on the analysis of the contribution of the interference and near-field effects. Such an approach allowed us to explain and interrelate the main peculiarities of the angular dependence of the intensity and polarization displayed by aggregates. Of special interest are the aggregates showing a so-called negative branch of linear polarization of light scattered into angles close to the backscattering direction. It has been shown that the enhancement of intensity and the negative polarization in this angular range are mainly caused by the interference of multiply scattered waves as well as by near-field effects. If the number of particles in the aggregate is large enough and its size is comparable to the wavelength, the backscattering enhancement is caused by the particles in the surface layers of the aggregate, where the radiation field is mostly homogeneous, while the negative branch is mainly generated by the deeper layers of particles, where the radiation field is inhomogeneous with chaotic changes of amplitudes and phases. This results in a rather weak dependence of the negative polarization on particle location in the deeper layers of the aggregate and on particle number but not on packing density.     

Polarization of light backscattered by small particles

We study scattering of light by wavelength-scale spherical, cubic, and spheroidal particles as well as clusters of spherical particles for equal-volume-sphere size parameters 4≤x≤10 and refractive indices 1.1≤m≤2.0. Such particles exhibit three specific features in the regime of backscattering: first, the intensity shows a backscattering peak; second, the degree of linear polarization for unpolarized incident light is negative; and, third, the depolarization ratio is double-lobed. We find that the overall characteristics of the scattering-matrix elements can be explained by an internal field composed of waves propagating in opposite directions near the particle perimeter and forming standing waves, as well as a wave propagating forward with the wavelength of the internal medium. When moving from the central axis of the particle toward its perimeter, the internal field changes from a forward-propagating wave with a wavelength dictated by the particle refractive index toward a standing wave with an apparent wavelength of the surrounding medium. The mapping of the internal field to the scattered far field is like an interference dial where rotation of the dial by a quarter of a wavelength on the particle perimeter results in a change from a destructive to constructive interference feature in the angular patterns (or vice versa). The dial is a manifestation of a well-known rule of thumb: the number of maxima or minima in the scattering-matrix elements is given by the size parameter. We explain the backscattering peak as deriving from the backward-propagating internal wave near the particle perimeter. Negative polarization follows from the spatial asymmetry of the internal fields: inside the particle, the fields are amplified near the central plane perpendicular to the polarization state of incident light, resulting in more pronounced interference effects for the perpendicular polarization than for the parallel polarization. The double-lobe feature in the depolarization results from the same internal-field structure with leading cross-polarized fields located slightly different from the copolarized fields. We discuss practical implications of these findings for the retrieval of particle sizes, shapes, and refractive indices from observations and laboratory experiments.     

Effect of electric field on light scattering by aqueous colloids of diamond and graphite

We present the results of our experimental investigation of light scattering by polydisperse colloids of diamond and graphite. The scattering is studied at a random orientation of particles and in an external radiofrequency electric field, which orients particles along the strength. The average dimensions of particles in both colloids are close to each other and comparable with the wavelength of the incident light. The shape of particles and the optical and electrooptical properties of diamond and graphite colloids are significantly different. We analyze the polarization components of scattered light energy when the light incident on the colloids is linearly polarized. We show that the quadrupole light scattering by isotropic diamond particles has the main effect on angular dependences of depolarization of scattered light. For light scattering by anisotropic graphite particles, the depolarization of scattered light is mainly determined by a particular feature of the dipole scattering of particles. It is shown that, in both colloids, the orientational order of particles considerably reduces the depolarization of light scattered by particles. We show that relative changes in the intensity and depolarization of scattered light, which depend on the scattering angle and polarization direction of light, as well as on the parameters of particles, can be used as a measure of electrooptical effects observed in colloids.     

Scattering by a plane-parallel layer with high concentration of optically soft particles

A method describing light propagation in a plane-parallel light-scattering layer with large concentration of homogeneous particles is developed. It is based on the radiative transfer equation and the doubling method. The interference approximation is used to take into account collective scattering effects. Spectral dependence of transmitted light for a layer of nonabsorbing optically soft particles with subwavelength-sized particles is investigated. At small volume concentration of the particles the weak spectral dependences of wave exponents for coherently transmitted and diffuse light are observed. It is shown that in a layer with large volume concentration of the subwavelength-sized particles the wave exponent can exceed considerably the value of four, which takes place for the Rayleigh particles. The dependence of wave exponents for coherently transmitted and diffuse light on the refractive index and concentration of particles is investigated in detail. Multiple scattering of light results in the reduction of the exponent. The quantitative results are presented and discussed. It is shown that there is a range of wavelengths where the negative values of the wave exponent at the regime of multiple scattering are implemented.     

X-ray radiation toward relativistic electrons incident on a flat target

Features of X-ray radiation emitted toward the velocity vector of relativistic electrons incident on a flat target are discussed. The contribution of polarization bremsstrahlung (PB) considered as scattering of the intrinsic field of a fast charge by electrons of the medium is estimated taking into account its dispersion properties. Spectral-angular characteristics of coherent and incoherent PB are analyzed for unstructured and structured targets. Such PB feature not only different intensities, but also different angular dependences reaching a maximum near the velocity direction of a fast charge. It is shown that coherent PB emitted from the target surface layer is characterized by an extraordinary, i.e., inversely proportional to the squared frequency, intensity dependence.     

Electromagnetic radiation from a polarization sheet located at an interface between two media

We derive concise expressions for the intensity of radiation emitted by an oscillating polarization sheet located at an interface between two media. The expressions find application in a number of experimental situations involving scattering or secondharmonic generation at an interface. As an application we discuss the angular dependence of p-polarized second-harmonic light emitted by a layer of adsorbed molecules stimulated by s-polarized incident radiation.     

Coherent opposition effects for semi-infinite discrete random medium in the double-scattering approximation

The rigorous equations of the theory of multiple scattering of light by a layer of disordered medium have been used in the double-scattering approximation for semi-infinite medium to determine the influence of the particle properties on the coherent opposition effects. The effects were found to be strongly dependent on the concentration of scatterers in the medium. The polarization opposition effect is more sensitive to the properties of the scatterers than the photometric opposition effect. The interference of waves could result in the negative polarization at the backscattering direction as well as in the positive polarization.     

Theory of stimulated concentration scattering of light in a liquid suspension of transparent microspheres

A theory of stimulated light scattering in a nonlinear liquid suspension of transparent microspheres—an artificially created medium whose nonlinearity is caused by modulation of the concentration of microspheres by gradient forces in a field of spatially inhomogeneous laser radiation—is constructed. The threshold, angular, and spectral characteristics of the scattering are studied in the diffusion-limit approximation based on the solution of the system of wave equations in combination with the Planck-Nernst two-dimensional equation for the concentration of microspheres. The transient regime of scattering in the field of a specified step-like pump pulse is considered. A sharp angular dependence of the scattering efficiency on the microsphere radius is predicted and proposed for use in optical diagnostics of liquid suspensions of dielectric microspheres—highly efficient wideband nonlinear media.     

Imaging and multiple scattering through media containing optically active particles

This paper examines the behaviour of polarized light scattered by a medium containing small chiral spheroidal particles. We show that for single scattering the observed phenomena of optical activity may be interpreted in terms of an averaged Mueller matrix and describe how the degree of polarization is affected by such a medium. The polarization properties of multiply scattered light by chiral particles are considered through the use of Monte Carlo simulations. It is shown that the effects of chirality under multiple scattering can be interpreted as an order-preserving influence in a disordered system and that this influence can, in principle, be exploited for the purposes of imaging.     

Coherent backscattering of polarized light from a turbid medium

Approximate analytical expressions for the intensities of the polarized components of light reflected from a disordered medium with large discrete particles (larger than the wavelength) have been derived with the use of the method of decoupling of the vector transfer equation that is based on separate treatment of basic and additional polarization modes. The results obtained provide the relation between the peak shape in the angular distribution of the backscattered radiation with a given polarization and the optical characteristics of the medium and are in good agreement with experimental data and numerical calculations.     

Light scattering in disperse layers with a high concentration of optically soft particles

A model describing the propagation of radiation in disperse close-packed layers of optically soft particles is proposed. The model is based on the radiative transfer equation used for describing a light field in the multiple scattering regime and on the interference approximation for describing collective scattering effects; it also takes into account the Fresnel reflection at the layer boundaries. To describe the single-scattering characteristics, the Mie formulas are used. The model allows one to consider scattering in layers of any optical thickness. Calculations of the angular structure of the radiation leaving the layer and estimates of the errors of the calculations were performed. The possibility of forming a maximum at small scattering angles in media with correlated particles is shown. The theoretical results are in good agreement with the available experimental data.     

Anomalous polarization effects during light scattering in random media

The dependence of the intensity of light backscattered from a layer of a randomly inhomogeneous medium on the polarization of incident light and the size of scatterers has been investigated. The results of numerical simulation have demonstrated that the direction of rotation of the plane of polarization is different in systems with small- and large-scale inhomogeneities. It is shown for the first time that the dependence of the sign of the residual circular polarization on the size of scatterers can be observed in systems described by the Henyey-Greenstein phase function used in simulating biological tissues. A similar anomalous polarization effect, which consists in changing the direction of rotation of the plane of polarization of backscattered light with an increase in the scattering angle, is revealed in studying the coherent backscattering component. These polarization effects are observed in light backscattering from optically active media.     

基片与多形态缺陷粒子的复合光散射

为了给基片无损检测工程提供强有力的理论基础,提出三种形态的缺陷粒子散射模型。针对基片与缺陷粒子的半空间问题,吸收边界使用了广义完全匹配吸收层,结合三波技术引入激励源给出相应的连接边界条件并将互易性定理应用到近远场外推中使过程简化。数值计算给出了镶嵌于基片中的多种几何体Cu和SiO2缺陷粒子的散射场的角分布及p偏振和s偏振下镶嵌Cu球体粒子的电场分布。结果显示:角分布和场分布跟粒子形态关系密切。椭球体散射场的震荡明显比柱体场震荡激烈。在s偏振下电场强度分布差值极小,不利于通过分析场值分布特点反演缺陷特征值。因此建议工程上使用p偏振光对基片进行无损检测。     

Imaging and multiple scattering through media containing optically active particles

Abstract

This paper examines the behaviour of polarized light scattered by a medium containing small chiral spheroidal particles. We show that for single scattering the observed phenomena of optical activity may be interpreted in terms of an averaged Mueller matrix and describe how the degree of polarization is affected by such a medium. The polarization properties of multiply scattered light by chiral particles are considered through the use of Monte Carlo simulations. It is shown that the effects of chirality under multiple scattering can be interpreted as an order-preserving influence in a disordered system and that this influence can, in principle, be exploited for the purposes of imaging.     

沙尘气溶胶粒子群的散射和偏振特性

根据Mie散射理论,以对数正态分布函数描述沙尘气溶胶粒子群的粒径尺度分布,计算了沙尘气溶胶粒子群在0.2～40μm波段间对太阳短波辐射和地球大气长波辐射的单次散射反照率、散射相矩阵函数,揭示了不同相对湿度时,沙尘粒子群对入射辐射的散射和偏振的特征。结果表明,沙尘粒子群的单次散射反照率随着入射波长的增加有较大起伏,不同相对湿度条件下,变化趋势基本一致;在可见光、近红外波段单次散射反照率随湿度增加而变大,湿度95%时非常接近于1;大于10μm的热红外波段单次散射反照率随相对湿度增加而减小,具有较强的吸收辐射能力。散射辐射强度受湿度影响较小,随散射角的增加呈现先减小后增大的趋势,且增大的趋势随着波长的增加而减弱;不同波段上,线偏振和圆偏振随散射角和相对湿度变化存在差异;在前向和后向仅对入射辐射为圆偏振辐射产生圆偏振散射;散射光的偏振特性及其湿度差异主要表现在后向散射区,多以拱形形式体现。拱顶峰值散射角位置存在差异,且峰值散射角随相对湿度的降低向后向漂移。     

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)