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.     

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.     

Scattering from a layer of discrete random medium over a random interface: application to microwave backscattering from forests

Abstract

The distorted Born approximation is used to calculate the bistatic scattering coefficients from a layer of sparsely distributed discrete dielectric scatterers over a random interface. After specializing to the backscatter case, the scattering coefficient is determined as a sum of direct, direct reflected and interface scatter contributions. The direct reflected term contains contributions from the average interface and the interface fluctuations. These direct reflected terms include both incoherent and coherent or enhancement terms. The results are applied to backscattering from a mature hemlock forest over a roughened ground. The model results show that the direct reflected surface fluctuation terms give the dominant contribution to backscatter at P band and are equal in magnitude to the volume scatter at L band. Use of these new results brings the model predictions and experimental results into agreement.     

Numerical simulation of coherent effects under conditions of multiple scattering

The time correlation function and the interference component of the coherent backscattering from a multiple-scattering medium are calculated in the framework of the Monte Carlo technique. By comparing the stochastic Monte Carlo technique with the iteration procedure of solving the Bethe-Salpeter equation, it is shown that the simulation of the optical path of photon packets that have experienced n scattering events is exactly equivalent to calculating the nth-order ladder diagram. Using this equivalence, the Monte Carlo technique is generalized for simulation of the time correlation functions and coherent backscattering.     

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.     

Scattering from a layer of discrete random medium over a random interface: application to microwave backscattering from forests

The distorted Born approximation is used to calculate the bistatic scattering coefficients from a layer of sparsely distributed discrete dielectric scatterers over a random interface. After specializing to the backscatter case, the scattering coefficient is determined as a sum of direct, direct reflected and interface scatter contributions. The direct reflected term contains contributions from the average interface and the interface fluctuations. These direct reflected terms include both incoherent and coherent or enhancement terms. The results are applied to backscattering from a mature hemlock forest over a roughened ground. The model results show that the direct reflected surface fluctuation terms give the dominant contribution to backscatter at P band and are equal in magnitude to the volume scatter at L band. Use of these new results brings the model predictions and experimental results into agreement.     

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.     

Anomalous diffusion of light in TiO<Subscript>2</Subscript>-powder layers near the absorption edge

The transfer of visible and near-IR radiation in layers of polydisperse TiO₂ (rutile) particles has been studied by measuring diffusion transmission and coherent backscattering in order to determine the optical parameters of the samples under investigation. An approach based on the coherent potential approximation is applied. It has been shown that, in the short-wavelength region of the visible range, anomalous diffusion of light occurs due to the effect of interference at mesoscopic scales on the transport characteristics of the scattering medium.     

Coherent effects in multiple scattering of linearly polarized light

Comparing the stochastic Monte Carlo technique with the iteration procedure for solving the Bethe-Salpeter equation in the framework of numerical simulation, the time correlation function and the interference component of the coherent backscattering of a linearly polarized light wave in a multiply scattering medium are calculated. The results of the simulation agree well with theoretical results obtained by generalizing the Milne solution, as well as with experimental data.     

Ultimate degree of residual polarization of incoherently backscattered light for multiple scattering of linearly polarized light

By invoking ideas about the distribution of the optical paths of partial components of the scattered field, we obtain an expression for estimating the degree of residual polarization of light that is incoherently backscattered from a disordered multiply scattering semi-infinite medium illuminated by linearly polarized light. In the backscattering regime, the depolarization length of the linearly polarized light in the disordered medium becomes smaller with the passage from the isotropic to anisotropic scattering. Experiments with model media featuring substantially anisotropic scattering (the anisotropy parameter of 0.90 ≤ g ≤ 0.95) demonstrated that for backscattering of linearly polarized light, the depolarization length is close to the transport length of the scattering medium.     

Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films

Abstract

The enhanced backscattering of light from a random surface is manifested by a well defined peak in the retro-reflection direction in the angular distribution of the intensity of the incoherent component of the light scattered from such a surface. In this paper we present several new theoretical and experimental results bearing on the conditions under which enhanced backscattering occurs, and the way in which this phenomenon depends on the nature of the random surface roughness, both in the case that the random surface bounds a semi-infinite scattering medium and in the case that it bounds a film, either free-standing or on a reflecting substrate. In addition, we present new results on the transmission of light through thin metallic films bounded by random surfaces, which display the phenomenon of enhanced transmission, namely a well defined peak in the antispecular direction in the angular distribution of the intensity of the incoherent component of the light transmitted through such films.     

Enhanced backscattering and transmission of light from random surfaces on semi-infinite substrates and thin films

The enhanced backscattering of light from a random surface is manifested by a well defined peak in the retro-reflection direction in the angular distribution of the intensity of the incoherent component of the light scattered from such a surface. In this paper we present several new theoretical and experimental results bearing on the conditions under which enhanced backscattering occurs, and the way in which this phenomenon depends on the nature of the random surface roughness, both in the case that the random surface bounds a semi-infinite scattering medium and in the case that it bounds a film, either free-standing or on a reflecting substrate. In addition, we present new results on the transmission of light through thin metallic films bounded by random surfaces, which display the phenomenon of enhanced transmission, namely a well defined peak in the antispecular direction in the angular distribution of the intensity of the incoherent component of the light transmitted through such films.     

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.     

Multiple scattering of light by a layer of discrete random medium: backscattering

The problem of multiple scattering of light by a layer of discrete random medium is considered. The medium is supposed to be rarefied with scatterers randomly positioned in the layer. Backscattering of light incident normal to the plane of the layer is considered. The scattering matrix is presented as a sum of three matrices, one of them corresponding to incoherent scattering of light and difference of the other two matrices describing coherent scattering. Equations for the calculation of these matrices are given.     

Light scattering in a layer of correlatively arranged optically soft particles

The light scattering by an ensemble of monodisperse spatially correlated optically soft spherical particles is studied in the interference approximation. A model of the interaction of particles is proposed in which the spatial correlation between particles is determined by a radius R _c exceeding the particle radius R _p. The radial distribution function is calculated in the Percus-Yevick approximation for hard spheres of the radius R _c. To simulate the radiation scattering from an individual particle of the radius R _p, the Mie equations are used. It is shown that, in a medium of correlated small nonabsorbing particles of the radius R _c > R _p, an abnormal wavelength dependence of the refractive index is possible at a low volume concentration of particles. The results obtained explain some experimentally observed features of the scattering in sodium borosilicate glasses with a small concentration of scattering centers.     

双层散射介质的单次后向散射光谱分析

从上皮组织的结构特点出发,基于米氏(Mie)散射理论,建立了双层散射介质的单次后向散射光谱的理论模型,该模型通过偏振门屏蔽来自下层的噪声背景,只保留来自上层的单次散射光。计算分析了粒子的形态学参量如平均尺寸及其分布、相对折射率变化时,单次散射光谱的特征。并用傅里叶波形分析法研究了这些参量对单次后向散射光谱曲线形状及其谐波幅值的影响。结果表明,这些只经历了表层粒子单次散射的光谱信号对表层粒子的平均尺寸及其分布、相对折射率具有灵敏性。对光谱曲线波纹结构的幅值、频率,散射强度,光谱谐波的幅值有直接的影响。研究结果对早期癌症的散射光谱特征识别及其特征提取有重要的实用价值。     

Incoherent properties of induced radiation

The evolution of a quantized electromagnetic field in a thermally excited dispersion medium is determined by two scattering channels. The coherent channel is formed exclusively by the elastic scattering of quanta. The incoherent channel, along with elastic scattering processes, necessarily contains inelastic scattering processes, including induced radiation. Interference between the channels is absent because of the orthogonality of the wave functions of the medium in its final states, which correspond to different scattering channels. Therefore, in an excited medium, interference processes that are not described by its refractive index may arise. An interference pattern of this kind can be formed, in particular, as a result of the superposition of the resonance radiation incident on an excited medium and the radiation reflected from this medium. In this case, the conventional perturbation theory proves to be inadequate.     

Coherent multiple scattering effects and Monte Carlo method

Based on the comparison of the iteration procedure of solving the Bethe-Salpeter equation and the Monte Carlo method, we developed a method for simulating coherent multiple-scattering effects within the framework of a unified stochastic approach. The time correlation function and the interference component were calculated for the coherent backscattering from a multiply scattering medium.     

Boson peak, flickering noise, backscattering processes and radiative transfer in random media

The method of matrix Green’s functions in the classical theory of electromagnetic waves is stated. This method allows to obtain a closed equation system in the presence of the random media for the calculation both coherent, and incoherent (fluctuating) components of radiation. The density and heterogeneity of scattering media can be arbitrary. The coherent channel is calculated independently. The fluctuating radiation distribution in the medium is developed initially by an interference pattern generated by the coherent channel. The limitations of the processes speed are absent. The theory embraces such phenomena as the boson peak, flickering noise, memory effect, backscattering processes and also conventional radiative transfer equation and Fresnel’s formulae.     

用遗传算法反演类上皮组织模型的偏振散射光谱

基于生物组织的粒状模型以及光谱对米氏(Mie)散射体形态的灵敏性,构建了类上皮组织模型的偏振后向散射光谱反演模型。针对反演模型的多参量、多极值、非线性,涉及到非常复杂的三角函数计算,模型空间极小的特点,采用每代保留最优个体的浮点遗传算法对类上皮组织模型的偏振后向散射光谱反演。对编码策略、适值调整策略及选择策略进行了讨论。研究结果表明:经过70代反演迭代,每个参量的相对误差趋于稳定,最小的达到0.02%左右,最大的不超过3%。采用基于实数编码的遗传算法能从偏振散射光谱中同时反演获得表层粒子的形态参量,具有全局收敛性和良好的反演精度与抗噪声能力。