Light scattering by multilayer nonconfocal ellipsoids in the Rayleigh approximation

The Rayleigh approximation of light scattering by multilayer nonconfocal coaxial ellipsoids is constructed. The ellipsoids that form a multilayer particle have coincident centers, and their principal axes are parallel. A particle in a constant electric field is considered, and the corresponding system of Laplace equations and boundary conditions is solved. Since the ellipsoidal surfaces of the interlayer interfaces are not confocal, the layers are divided into many sublayers, in each of which the potential is written in the proper ellipsoidal systems of coordinates. The potentials are sewn together at the sublayer interfaces by approximate matching conditions (the continuity of potentials and their normal derivatives). The polarizability of a multilayer particle is expressed as a 2×2 matrix in terms of the parameters of the core and the subsequent layers.     

随机取向群聚椭球粒子光散射特性研究

利用离散偶极子近似方法,考虑单元粒子之间的电磁相互作用,数值计算了随机取向的不同尺度参数、不同纵横比的群聚椭球粒子的缪勒矩阵元素,给出了各个缪勒矩阵元素的角分布曲线,探讨了随机取向的群聚椭球粒子的尺度参数、纵横比、基本粒子相对位置对其缪勒矩阵元素的影响。并将随机取向群聚椭球粒子的光散射特性与单个等效球形粒子的数值结果进行了比较。结果表明,随机取向群聚椭球粒子的光散射特性与等效球形粒子的光散射特性存在很大差别,基本粒子的形状越偏离球形,这种差别就越大; 随机取向群聚椭球粒子中椭球粒子的纵横比和相对位置对整个群聚粒子的缪勒矩阵元素存在不同程度的影响,并且此影响随着粒子尺度参数的增大而变得更加显著。     

随机取向群聚椭球粒子光散射特性研究

利用离散偶极子近似方法,考虑单元粒子之间的电磁相互作用,数值计算了随机取向的不同尺度参数、不同纵横比的群聚椭球粒子的缪勒矩阵元素,给出了各个缪勒矩阵元素的角分布曲线,探讨了随机取向的群聚椭球粒子的尺度参数、纵横比、基本粒子相对位置对其缪勒矩阵元素的影响。并将随机取向群聚椭球粒子的光散射特性与单个等效球形粒子的数值结果进行了比较。结果表明,随机取向群聚椭球粒子的光散射特性与等效球形粒子的光散射特性存在很大差别,基本粒子的形状越偏离球形,这种差别就越大; 随机取向群聚椭球粒子中椭球粒子的纵横比和相对位置对整个群聚粒子的缪勒矩阵元素存在不同程度的影响,并且此影响随着粒子尺度参数的增大而变得更加显著。     

Optical equivalence of isotropic ensembles of ellipsoidal particles in the Rayleigh-Gans-Debye and anomalous diffraction approximations and its consequences

Light scattering by isotropic ensembles of ellipsoidal particles is considered in the Rayleigh-Gans-Debye approximation. It is proved that randomly oriented ellipsoidal particles are optically equivalent to polydisperse randomly oriented spheroidal particles and polydisperse spherical particles. Density functions of the shape and size distributions for equivalent ensembles of spheroidal and spherical particles are presented. In the anomalous diffraction approximation, equivalent ensembles of particles are shown to also have equal extinction, scattering, and absorption coefficients. Consequences of optical equivalence are considered. The results are illustrated by numerical calculations of the angular dependence of the scattering phase function using the T-matrix method and the Mie theory.     

An Ellipsoidal Model for Small Multilayer Particles

This paper presents an ellipsoidal model that is constructed for small layered nonspherical particles and methods for constructing “effective” multilayer ellipsoids, the light-scattering properties of which would be close to the corresponding properties of original particles. In the case of axisymmetric particles, prolate or oblate spheroids (ellipsoids of revolution) are implied. Numerical calculations of the polarizability and scattering cross sections of small layered nonspherical particles, including nonconfocal (similar) spheroids, Chebyshev particles, and pseudospheroids, are performed by different approximate and rigorous methods. Approximate approaches involve the use of an ellipsoidal model, in which the polarizability of a layered particle is determined in two ways. In the first case, the polarizability is calculated in the approximation of confocal spheroids, while, in the second case, it is sought as a linear combination of the polarizabilities of embedded spheroids proportionally to the volumes of layers. Among rigorous methods, the extended boundary conditions method and the generalized separation of variables method are applied. On the basis of a comparison of the results obtained with rigorous and approximate approaches, their drawbacks and advantages are discussed.     

取向比对椭球气溶胶粒子散射特性的影响

利用T矩阵和离散坐标法研究了取向比对椭球粒子散射特性的影响, 计算了小尺度范围内椭球粒子的散射特征参量, 包括消光效率因子、不对称因子、单次散射反照率、散射相矩阵及双向反射函数(BRDF). 结果表明, 椭球粒子的散射特性与取向比密切相关, 粒子取向比会影响散射参量的振荡频率和振幅, 与球形粒子散射参量的相对差异也呈周期振荡趋势. 研究还发现, 某些特殊粒子尺寸的散射参量与粒子取向比基本无关. 在多次散射条件下, 分析不同取向比粒子群的BRDF随反射角和光学厚度的变化特性. 结果显示: 不同取向比粒子群的BRDF随反射角的变化趋势基本一致, 球形粒子群比非球形粒子群的BRDF曲线波动振幅更大; 球形-非球形粒子的BRDF相对差异随光学厚度和取向比的增大而减小, 随入射角的增大而增大.     

Applicability of quasi-static and Rayleigh approximations for spheroidal particles

Expressions are obtained for the efficiency of absorption and scattering of radiation by uniform spheroids in the quasi-static approximation and the region of their applicability is studied. The prolate and oblate nonabsorbing particles with refractive indices 1.1≤n≤10 and axial ratios 1.1≤a/b≤100 were studied. The approximation expressions are found for the particle size at which the efficiency factors are calculated in the quasi-static approximation with an accuracy of 1%.     

An ellipsoidal model for small nonspherical particles

We have proposed an ellipsoidal model (ElM) for small nonspherical particles, i.e., we have proposed a method to construct “effective” ellipsoids the light scattering properties of which are similar to those of original particles. It has been shown that the semiaxes of a model ellipsoid should be determined from the requirement of equality of the volumes of particles, as well as of the equality of the ratios of their maximal longitudinal and transverse dimensions. Along with the ElM, the uniform internal field approximation (UFA) has also been considered, which is the first approximation in terms of the rigorous ЕВСМ solution of the electrostatic problem. In order to analyze the applicability of the ElM and UFA approximate approaches, rigorous methods for solving the problem of light scattering have been used, such as the discrete dipole approximation (DDA) and the SVM. The comparison of results of numerical calculations for parallelepipeds, finite circular cylinders and cones, Chebyshev particles and pseudospheroids has shown that the relative errors of calculations of the particle polarizability using ElM approximate formulas do not exceed 1–5%, while, for the absorption and scattering cross sections, they are roughly twice as large, since they depend on the squared polarizability module. As a rule, the ElM is preferable to the uniform field approximation, which is advantageous only in the case of a circular cylinder with close longitudinal and transverse dimensions.     

Light Scattering by Small Particles: an Ellipsoidal Model That Uses a Quasistatic Approach

Optics and Spectroscopy - To describe light scattering by small nonspherical particles, we have constructed an ellipsoidal model using a quasistatic approximation. The semiaxes of the model...     

烟尘簇团粒子光学截面和散射矩阵的数值计算

用离散偶极子近似方法，计算了单个烟尘簇团粒子的光学特性，得到了簇团粒子的散射截面、吸收截面及不对称因子随入射角的变化关系，为研究波在烟尘粒子中的传输特性提供了有效的计算方法；给出了不同入射角情况下烟尘簇团粒子散射矩阵元素的角分布，为研究散射体的散射特性、极化特性以及散射体结构特性提供了一种理论方法. 关键词： 烟尘簇团粒子 散射矩阵 光学截面 DDA     

Study of the sensitivity of size-averaged scattering matrix elements of nonspherical particles to changes in shape, porosity and refractive index

Studies of the physical parameters that influence the single scattering properties of a size distribution of small particles in random orientation are fundamental in understanding the origin of the observed dependence of the scattering matrix elements on the scattering angle. We present results of extensive calculations of the single scattering matrices of small nonspherical particles performed by a computational model based on the Discrete-Dipole Approximation. We have particularly studied the sensitivity of the size-averaged scattering properties at visible wavelengths of nonspherical, randomly oriented absorbing particles considering changes in shape, porosity and refractive index. These studies have importance regarding the inversion of physical properties of small particles as measured in the laboratory and the dust properties in various astrophysical and atmospherical environments. We have found that size distributions of randomly oriented irregular particles of different shape, including large aspect ratio particles, show similar scattering matrix elements as a function of the scattering angle, in contrast with the pattern found for regularly shaped particles of varying axis ratios, for which the scattering matrix elements as a function of the scattering angle show much larger differences among them. Regarding porosity, we have found a very different pattern in the scattering matrix elements for an ensemble of compact and porous particles. In particular, the linear polarization for incident unpolarized light produced by compact and absorbing particles of large size parameter tend to mimic the pattern found for large absorbing spheres. For porous particles, however, the linear polarization for incident unpolarized light tends to decrease as the size of the particle grows, with the maximum being displaced towards smaller and smaller scattering angles.     

Coherent Transmission and Reflection by a monolayer of discrete scatterers

Coherent transmission and reflection of a plane wave through a monolayer of discrete particles are considered on the basis of simple and physically transparent formulae for the single scattering approximation (SSA) corrected by introducing a multiple scattering permittivity factor. This factor allows for multiple scattering of Waves between monolayer particles, opposite to the SSA. The multiple scattering permittivity factor is considered on the basis of the quasi-crystalline approximation (QCA) via ? matrix formalism. The multiple scattering permittivity factor and parameters for obtaining coherent transmission and reflection coefficients (the effective extinction coefficient and the transmission and reflection coefficients due to rescattering) are calculated within the scope of QCA and plotted for comparison with SSA results. The expressions for these values are simplified for small Rayleigh particles to simple analytical formulae.     

Light scattering by multilayer ellipsoids in the Rayleigh approximation

A problem of light scattering by multilayer confocal ellipsoids is solved in the Rayleigh approximation. The electric field of a light wave is assumed constant and a set of Laplace equations with the corresponding boundary conditions is considered. The final expression for the polarizability of a particle is represented in the matrix form (2×2 matrices) in terms of parameters of a nucleus and subsequent layers. Numerical calculations of the scattering and absorption efficiencies of small multilayer spheres obtained using the exact (the generalization of the Mie theory) and approximate solutions well agree with each other.     

The scattering matrix of transparent particles of random shape in the geometrical optics approximation

A numerical model that allows one to calculate elements of the scattering matrix for transparent particles of random shape in the geometrical optics approximation is presented. It is shown that a deviation from sphericity, which, in particular, is modeled by a reduction of the number of triangular facets approximating a sphere, essentially affects the magnitude, position, and width of peaks of the photometric and polarimetric indicatrices. Thus, when 1500 facets were used for the approximation, the amplitude of the polarimetric peak associated with the first rainbow, which is located close to the scattering angle 160°, decreases by a factor of two. Calculations showed that, in the region of backscattering, for particles of an arbitrary shape, the linear polarization ?F ₁₂/F ₁₁ has no negative branch, which is well observed for spherical particles. In going from spherical to nonspherical particles, the backscattering peak also disappears. The indicatrices for particles of irregular shape that were calculated for small distances from the center of a particle noticeably differ from the indicatrices at infinity. Thus, when simulating multiple scattering in dense powderlike media, the use of particle scattering indicatrices that were calculated for infinite distances is incorrect even in the geometrical optics approximation.     

Anisotropic local-field effects of nanoparticles in plasmonic optics and magneto-optics

A theory of anisotropic optical local-field effects caused by resonantly polarizable small particles in multilayer polarizable media is developed. Considered is the model of a rectangular lattice of ellipsoidal nanoparticles with taking account of “image forces” at an interface in a layered medium. The lattice sums for anisotropic dipolar interactions are found using the Green’s function method in the quasi-point dipole approximation, and the effective polarizabilities of particles in a layer located near an interface are calculated self-consistently. The manifestation of an anisotropic local field of nanoparticles in optical radiation and propagation of evanescent waves responsible for optical near-field effects is investigated. Applications of the obtained results in the polar magneto-optical Kerr effect and reflectance anisotropy spectroscopy in propagating the polarized light along the normal to layers are considered. The resonant features in the spectra due to enhancement of the optical effects under excitation of surface (local) plasmons in nanoparticles of a noble metal are studied.     

基片与不同方位多形态缺陷粒子的复合光散射特性分析

结合光学表面无损检测工艺实际情况,给出基片与镶嵌及掩埋的球体/回转椭球体缺陷粒子的散射特性分析。针对基片与缺陷粒子的半空间问题,结合时域有限差分方法使用广义完全匹配吸收层(GPML),结合三波技术引入激励源,给出了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及掩埋的球体/回转椭球体缺陷粒子的散射场的角分布。结果显示:镶嵌比掩埋的缺陷粒子受粒子尺寸的影响更明显。在大散射角下,缺陷粒子的位置因素带来的贡献较大。粒子分别掩埋或镶嵌于基片时,在-10°、30°、70°附近的球体粒子和回转椭球体粒子的微分散射截面(DSCS)差别较大。在基片无损检测工程中可以通过对特定角度散射场的测量定标诊断出缺陷的方位和形态。     

Laboratory measurements of single light scattering by ensembles of randomly oriented small irregular particles in air. A review

In this paper we present an overview of light scattering experiments devoted to measure one or more elements of the scattering matrix as functions of the scattering angle of ensembles of randomly oriented small irregular particles in air. A summary of the most important findings in light scattering experiments on ensembles of randomly oriented particles in air is given. The particles of interest are relevant for studies of atmospheres of planets and satellites and also for other astronomical bodies and environments. Some applications of light scattering experiments are also presented.     

Scattering matrices and reflectance spectra of forsterite particles with different size distributions

We present measurements of the complete scattering matrix as a function of the scattering angle of three different samples of forsterite particles in random orientation at a wavelength of 632.8 nm. The three samples were prepared so that three different size distributions were obtained. The composition and reflection spectra of the three samples have been experimentally determined. The results indicate that the elements of the scattering matrix are affected in a different way by the size differences. Since light scattering by comets is probably caused by particles similar to our forsterite particles, the results potentially contain information on the size of the cometary particles.     

Semiclassical description of reactions at energies near the Coulomb barrier

The modified semiclassical approximation of Coulomb matrix elements is extended to include effects of distorting nuclear potentials in the scattering wave functions. The applicability and efficiency of the proposed semiclassical method are discussed. The advantages of this approximation are shown for a typical heavy-ion transfer reaction.     

Discontinuity of dipole-moment matrix elements in ellipsoidally shaped nanoparticles and profiles of spectral lines

The behaviour of energy levels and optical spectra of a charged particle (electron or hole) confined within a potential well of ellipsoidal shape is investigated as a function of the shape-anisotropy parameter. If two energy levels of the same symmetry intersect in a perturbation-theory approximation, they move apart on direct diagonalization of the appropriate Hamiltonian. The intersection of the energy levels leads to a discontinuity of the corresponding dipole-moment matrix element. The discontinuity of matrix elements is not reflected in the behaviour of transition probabilities which are continuous functions of the shape-anisotropy parameter. The profiles of a spectral line emitted or absorbed by an ensemble of ellipsoidally shaped nanoparticles with a Gaussian distribution of size are calculated and discussed.