Electrostatic solution and rayleigh approximation for small nonspherical particles in a spheroidal basis

The electrostatic problem for the case of axially symmetric particles is analyzed in a spheroidal basis. In this case, the wavenumber is zero and Maxwell’s equations are reduced to the Laplace equation for scalar potentials. An alternative approach involves solving integral equations that are similar to those obtained within the framework of the extended boundary conditions method. The scalar potentials are represented as expansions in terms of eigenfunctions of the Laplace equation in a spheroidal frame of reference, and unknown expansion coefficients are determined from an infinite set of linear algebraic equations (the separation of variables method). These two approaches yield exact solutions of the problem in the case of axially symmetric particles, which coincide with known solutions in particular cases. Investigation of infinite systems allowed finding the boundaries where these algorithms are valid. Numerical calculations showed that, for spheroidal Chebyshev particles (i.e., perturbed spheroids), the Rayleigh approximation based on the electrostatic solution is applicable in a wide range of the problem parameters and is in fair agreement with the results obtained using the discrete dipole approximation.     

On scattering of light by small axially symmetric particles

Light scattering by small dielectric particles of an arbitrary axially symmetric shape is analyzed. A simple approximate expression that governs the polarizability of the particle is found under the assumption of field homogeneity inside of these particles. The expression includes four relatively simple one-dimensional integrals that can be calculated analytically for some types of particles (except for spheroids). A comparison with the numerical data obtained for various Chebyshev particles and finite cylinders showed that the obtained approximation yields acceptable results, even when the shape of scatterers is significantly different from spheroidal. For spheroids, our approximation coincides with the Rayleigh one.     

Light scattering by dielectric particles with axial symmetry: II

A new method is developed for calculating optical characteristics of axially symmetric particles. Electromagnetic fields are separated into two (axisymmetric and non-axisymmetric) parts. The light scattering problem is formed in the integral form and solved independently for each of the parts by using specially chosen scalar potentials. The potentials are expanded into series in spherical wave functions, and the expansion coefficients are calculated from solving the infinite systems of linear algebraic equations. The applicability of the proposed method for solving the problem of light scattering by Chebyshev particles, spheroids, and finite circular cylinders is briefly discussed, and some results of calculations performed for these particles are presented.     

A T-matrix method and computer code for randomly oriented, axially symmetric coated scatterers

A computer code is described for the calculation of light-scattering properties of randomly oriented, axially symmetric coated particles, in the framework of the T-matrix theory. The underlying mathematical background is outlined briefly and convergence procedures are discussed. After outlining the input-output interaction between user and code, benchmark results are presented for two distinct shapes: coated, centered spheroids and offset coated spheres.     

Applicability of the T-matrix method and its modifications

The range of applicability of the T-matrix method and its modifications for solving the problem if the scattering of electromagnetic radiation by nonspherical, axially symmetric particles is investigated analytically and numerically. The use of this method for calculating the characteristics of scattered radiation in the farfield region (the extinction and scattering cross sections, the scattering indicatrix, etc.) is shown to be appropriate for “weak-Rayleigh-type” particles. This condition is met when the intersection of the analytic continuations of the scattered and internal fields contains a ring with the center at the origin of coordinates. For a reliable calculation of the scattered field in the near-field region, it is necessary that a particle be a “Rayleigh-type” one (i.e., the Rayleigh hypothesis be valid for it). In this case, the singularities of the scattered field must occur inside a sphere lying inside a scatterer. Spheroidal particles are weak-Rayleigh-type ones if their semiaxes ratio is $a/b < (\sqrt {2 + 1} )The range of applicability of the T-matrix method and its modifications for solving the problem if the scattering of electromagnetic radiation by nonspherical, axially symmetric particles is investigated analytically and numerically. The use of this method for calculating the characteristics of scattered radiation in the farfield region (the extinction and scattering cross sections, the scattering indicatrix, etc.) is shown to be appropriate for “weak-Rayleigh-type” particles. This condition is met when the intersection of the analytic continuations of the scattered and internal fields contains a ring with the center at the origin of coordinates. For a reliable calculation of the scattered field in the near-field region, it is necessary that a particle be a “Rayleigh-type” one (i.e., the Rayleigh hypothesis be valid for it). In this case, the singularities of the scattered field must occur inside a sphere lying inside a scatterer. Spheroidal particles are weak-Rayleigh-type ones if their semiaxes ratio is , and they are Rayleigh-type ones if . Numerical calculations for spheroids and Chebyshev particles corroborate these conclusions. However, the indicated boundaries are “ spread” (toward the expansion), because the expansion coefficients for the fields are determined with the use of the reduced (i.e., finite) systems. The limiting sizes of the particles for which the T-matrix method gives plausible results are primarily determined by their geometry (shape). __________ Translated from Optika i Spektroskopiya, Vol. 92, No. 5, 2002, pp. 813–825. Original Russian Text Copyright ? 2002 by Farafonov.     

Scattering of light by axially symmetric particles: Modification of the point-matching method

The approach based on the separation of the fields into two parts with definite properties and the proper choice of special scalar potentials for each of them is applied to the point-matching method. Earlier, such a procedure carried out within the framework of the method of separation of variables for spheroids allowed us to obtain a solution that is considerably more efficient for strongly prolate and strongly oblate particles than solutions obtained with other versions of this method. It was found that the replacement of the summation over points on the particle surface in the point-matching method by the corresponding integral leads to a faster and more exact algorithm. The applicability of the proposed method is considered in comparison with the related method of extended boundary conditions. For spheroids and Chebyshev particles with a maximum-to-minimum-size ratio exceeding 1.5–2, the efficiency of the point-matching method is not high. For other Chebyshev particles, the point-matching method is undoubtedly preferable to the commonly used method of extended boundary conditions since it allows one to increase the accuracy of calculations by several orders of magnitude. Moreover, whereas the latter method is in principle inapplicable to certain Chebyshev particles, the former lacks this disadvantage.     

含核椭球粒子后向散射特性研究

基于T矩阵方法,给出了随机取向、轴对称、含核椭球粒子的散射计算方法,散射体的核和外壳均可为非球形粒子,内层粒子和外层粒子可以为同心也可为不同心,整个粒子具有轴对称性.以含核椭球粒子为模型,计算了含有吸收性内核的水凝物气溶胶的散射特性,分析了核的大小、形状以及位置对后向散射的影响.计算结果表明,后向散射对内核的形状、大小...     

Extended boundary condition method in combination with field expansions in terms of spheroidal functions

The problem of light scattering by nonspherical particles, which arises in many applications, is nowadays most frequently solved by the method of extended boundary conditions in combination with the expansion of the fields in terms of spherical wave functions. However, such an approach encounters difficulties if the shape of particles is far from spherically symmetric, even in the simplest case of spheroids with the semiaxis ratio a/b > 5?10. A new approach to solving this problem is proposed, which also applies the extended boundary condition method but involves the expansion of the fields in terms of spheroidal functions. In this case, to obtain effective solutions for strongly prolate and oblate particles, the fields are divided in two parts with known properties and specific scalar potentials are used for each part. The basic relations of the approach are presented and some results of calculations of the optical properties of spheroids and spheroidal Chebyshev particles that are performed using computer codes realizing this approach are given. The convergence of the results for different cases and the domain of applicability of the method are discussed.     

随机取向双层椭球粒子偏振散射特性研究

基于T矩阵方法,给出了随机取向、轴对称、含核椭球粒子的散射计算方法.散射体的核和外壳均可为非球形粒子,整个粒子具有轴对称性.以含核椭球粒子为模型,计算了含有吸收性内核(黑炭,black carbon)的水凝物气溶胶的散射特性,分析了核的大小、形状对消光系数、散射系数、吸收系数、不对称因子、单次散射反照率以及Muller矩阵等的影响. 关键词： 光散射 T矩阵 Muller矩阵 椭球粒子     

Constraints on PSC particle microphysics derived from lidar observations

Based on extensive T-matrix computations of light scattering by polydispersions of randomly oriented, rotationally symmetric nonspherical particles, we analyze existing lidar observations of polar stratospheric clouds (PSCs) and derive several constraints on PSC particle microphysical properties. We show that sharp-edged nonspherical particles (finite circular cylinders) exhibit less variability of lidar backscattering characteristics with particle size and aspect ratio than particles with smooth surfaces (spheroids). For PSC particles significantly smaller than the wavelength, the backscatter color index and the depolarization color index β are essentially shape independent. Observations for type Ia PSCs can be reproduced by spheroids with aspect ratios larger than 1.2, oblate cylinders with diameter-to-length ratios greater than 1.6, and prolate cylinders with length-to-diameter ratios greater than 1.4. The effective equal-volume-sphere radius for type Ia PSCs is about 0.8 μm or larger. Type Ib PSCs are likely to be composed of spheres or nearly spherical particles with effective radii smaller than 0.8 μm. Observations for type II PSCs are consistent with large ice crystals (effective radius greater than 1 μm) modeled as cylinders or prolate spheroids.     

Can particle shape information be retrieved from light-scattering observations using spheroidal model particles?

We address the question if and how observations of scattered intensity and polarisation can be employed for retrieving particle shape information beyond a simple classification into spherical and nonspherical particles. To this end, we perform several numerical experiments, in which we attempt to retrieve shape information of complex particles with a simple nonspherical particle model based on homogeneous spheroids. The discrete dipole approximation is used to compute reference phase matrices for a cube, a Gaussian random sphere, and a porous oblate and prolate spheroid as a function of size parameter. Phase matrices for the model particles, homogeneous spheroids, are computed with the T-matrix method. By assuming that the refractive index and the size distribution is known, an optimal shape distribution of model particles is sought that best matches the reference phase matrix. Both the goodness of fit and the optimal shape distribution are analysed. It is found that the phase matrices of cubes and Gaussian random spheres are well reproduced by the spheroidal particle model, while the porous spheroids prove to be challenging. The “retrieved” shape distributions, however, do not correlate well with the shape of the target particle even when the phase matrix is closely reproduced. Rather, they tend to exaggerate the aspect ratio and always include multiple spheroids. A most likely explanation why spheroids succeed in mimicking phase matrices of more irregularly shaped particles, even if their shape distributions display little similarity to those of the target particles, is that by varying the spheroids’ aspect ratio one covers a large range of different phase matrices. This often makes it possible to find a shape distribution of spheroids that matches the phase matrix of more complex particles.     

Static and stationary solutions of the Einstein-Maxwell equations

The Weyl axially symmetric electrovac formalism for coincident gravitational and electrostatic equipotential surfaces is used to generate charged versions of some axially symmetric vacuum fields. The metric for two separated charged Curzon particles held in equilibrium by a strut is found and the condition for the removal of the strut is discussed. Kinnersley transformations applied to the two-particle metric yield spin but line singularities invariably appear along the symmetry axis and the metric is asymptotically NUT-like. It is shown that any Kinnersley transformation applied to a static axially symmetric asymptotically flat vacuum metric generates another asymptotically flat metric only if the latter is static. Moreover, the transformed metric is always undercharged (q ²<m ²) if it is asymptotically flat. A necessary and sufficient condition for asymptotic flatness in terms of the relevant parameters is found. A generalization of the Kinnersley transformation scheme is presented and illustrated by an example.     

轴对称磁透镜设计

以中国科学院近代物理研究所正在研制的轴对称磁透镜为例,设计了两种结构的轴对称磁透镜:带屏蔽铁壳的螺线管透镜和极靴形状为锥形的Glaser透镜。带屏蔽铁壳的螺线管透镜产生的轴对称磁场比较均匀,而极靴形状为锥形的Glaser透镜产生的轴对称磁场比较集中。分别采用了两种物理模型计算磁场,同时应用有限元分析软件ANSYS进行数值模拟,最后从物理和工程角度对这两种透镜作了全面比较,得出带屏蔽铁壳的螺线管透镜结构更符合设计要求。     

Diagnostics of a strong magnetic field using spectropolarimetry of the decaying emission

A method for diagnostics of a magnetic field is suggested. The method is based on spectropolarimetry of the decaying emission of an ensemble of particles whose angular momenta were ordered by pulsed axially symmetric perturbation.     

一层非球形粒子散射的标量辐射传输迭代解的求逆

给出了一层有下垫反射面的非球形粒子散射的标量辐射传输方程一、二阶迭代解,推导了相函数各阶Legendre展开系数与随机小椭球粒子相函数的对应关系,提出了一层随机小椭球粒子介电常数和单位面积粒子数的迭代反演方法.通过两次各方位角上双站散射测量,反演随机小椭球粒子的介电常数和单位面积粒子数.本方法比现有文献的一些反演方法易于实现,可应用于颗粒性复合材料介电与结构特性以及地表背景参数的反演研究 关键词： 辐射传输方程 迭代解 反演 相函数 介电常数     

On the validity of modeling rayleigh scatterers by spheroids

For single homogeneous lossy dielectric Rayleigh particles, the manner in which the particle shape affects the absorption and scattering is examined by computing the polarizability tensor elements using a general purpose program valid for any rotationally symmetric body. The results for a number of generic shapes are compared with those for the corresponding spheroids. When the dielectric constant is real and negative, the resonances attributable to bulk and to shape-dependent or surface polariton modes are tracked as functions of the length-to-width ratio of the particle and the bulk dielectric constant. The adequacy of using spheroid approximations for individual particles in a dispersion is also discussed.     

Calculation of the Parameters of Radiation Sources and the Atmosphere with Multiwavelength Optical Remote Sensing

A multiwavelength method for determining the parameters of radiation sources and the atmosphere by passive-remote sensing in the visible and near-IR spectral regions is proposed. The method relies on the obtained approximate analytical solutions of direct problems of the radiation transfer in the atmosphere for axially symmetric Planck sources. The set of these solutions is applicable to arbitrary optical atmospheric depths. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 4, pp. 491–498, July–August, 2005.     

Towards uniqueness of degenerate axially symmetric Killing horizon

For near horizon geometry we examine the linearized equations around extremal Kerr horizon (which is a unique axially symmetric near horizon geometry) and give some arguments towards stability of this horizon with respect to generic (non-symmetric) linear perturbation of near horizon geometry. The result is also applicable for other situations like Kundt’s class spacetimes or isolated horizons.     

Determination of the Disperse Composition of a PbO Suspension Containing Aggregates of Particles of Lamellar Shape by the Laser-Polarimetry Method

The results of measurements of the scattering matrix at a wavelength of 0.63 μm in the range of scattering angles of 10°–155° are presented for an aqueous suspension of lead oxide containing particles of plate form and their aggregates of monomers with dimensions of ~5 nm. The results of the measurements are compared with the results of calculations for axially symmetric scatterers (ellipsoids of rotation, cylinders). It is shown that the presence of aggregates affects the scattering properties of such a medium. The results of reconstructing the distribution of particles of a disperse medium in sizes from the measurements data of the scattering matrix are presented. The reconstruction of the distributions was carried out by solving the problem of optimizing the sum of the squared deviations of the experimental and calculated values of matrix elements in the framework of the model of axially symmetric scatterers. It is shown that the distribution of particles by sizes is more accurately reconstructed by minimizing the sum of the squares of the deviations for the sum of the diagonal elements. The obtained distribution is compared with the distribution measured by the method of dynamic light scattering.