Electromagnetic scattering by nonspherical particles: Recent advances

This note gives a short introduction to the reprint of the article “Numerical methods in electromagnetic scattering theory” by Kahnert, M (JQSRT 2003;79-80:775-824). Some of the most important developments in the field since the publication of this article are briefly reviewed. A list of typos that have been identified in the original article is given in the appendix.     

Using simple particle shapes to model the Stokes scattering matrix of ensembles of wavelength-sized particles with complex shapes: possibilities and limitations

We investigate to what extent the full Stokes scattering matrix of an ensemble of wavelength-sized particles with complex shapes can be modeled by employing an ensemble of simple model shapes, such as spheres, spheroids, and circular cylinders. We also examine to what extent such a simple-shape particle model can be used to retrieve meaningful shape information about the complex-shaped particle ensemble. More specifically, we compute the Stokes scattering matrix for ensembles of randomly oriented particles having several polyhedral prism geometries of different sizes and shape parameters. These ensembles serve as proxies for size-shape mixtures of particles containing several different shapes of higher geometrical complexity than the simple-shaped model particles we employ. We find that the phase function of the complex-shaped particle ensemble can be accurately modeled with a size distribution of volume-equivalent spheres. The diagonal elements of the scattering matrix are accurately reproduced with a size-shape mixture of spheroids. A model based on circular cylinders accurately fits the full scattering matrix including the off-diagonal elements. However, the modeling results provide us with only a rough estimate of the effective shape parameter of the complex-shaped particle ensemble to be modeled. They do not allow us to infer detailed information about the shape distribution of the complex-shaped particle ensemble.     

Electromagnetic wave scattering by many small particles

Scattering of electromagnetic waves by many small particles of arbitrary shapes is reduced rigorously to solving linear algebraic system of equations bypassing the usual usage of integral equations. The matrix elements of this linear algebraic system have physical meaning. They are expressed in terms of the electric and magnetic polarizability tensors. Analytical formulas are given for calculation of these tensors with any desired accuracy for homogeneous bodies of arbitrary shapes. An idea to create a “smart” material by embedding many small particles in a given region is formulated.     

Light-scattering methods for modelling algal particles as a collection of coated and/or nonspherical scatterers

Ocean reflectance or ocean colour measurements are an important tool for oceanographic studies of phytoplankton dynamics. Theoretical models based on homogeneous, spherical particles underestimate algal backscattering and thus reflectance values. It is our understanding that more advanced light-scattering methods must be employed, both for refractive index retrieval (Mie, Aden–Kerker) with inverse models, and for backscattering calculations (Extended Boundary Condition Method, EBCM). The measured optical properties of a monospecific bloom of the marine brown tide pelagophyte Aureococcus anophagefferens are used to compare the effects of assuming various simulated particle geometries. Computational results from polydisperse, coated spherical particles show results that compare better to experimental reflectance values than calculations based on homogeneous spheres. No noticeable change in simulated reflectance values is observed when a randomly oriented coated spheroidal (rather than spherical) geometry is assumed for the particle population. Our results suggest that a layered spherical geometry, based on Aden–Kerker theory, can adequately reproduce experimentally determined light-scattering properties even supposedly shape-sensitive properties such as the backscattering coefficient.     

火灾烟颗粒的分形结构形状模拟与光散射计算

针对火灾烟颗粒的形状特点，提出并建立火灾烟颗粒分形结构凝团的形状模型，并对烟颗粒扫描电镜(SEM)图像进行分析，获取分形结构模型中的单个凝团中基本颗粒个数、凝团分形维数、基本颗粒半径等参数.利用该模型对火灾烟颗粒的形状进行模拟的结果表明，该模型能够较好反映出烟颗粒的形貌特征.利用形状模型对火灾烟颗粒散射进行初步计算表明，在其他参数相同的情况下，相对于同体积的球形颗粒，分形凝团具有前向散射较弱，后向散射较强的特征.     

Scattering by randomly oriented thin ice disks with moderate equivalent-sphere size parameters

We use the T-matrix method to compute the scattering matrix for randomly oriented circular ice cylinders with diameter-to-length ratios 1 and 20 and surface-equivalent-sphere size parameters up to 12. We show that wavelength-sized, sharp-edged ice plates with extreme diameter-to-length ratios possess the same scattering properties as smooth platelike spheroids: their phase functions are similar to those of surface-equivalent compact particles, whereas all other elements of the scattering matrix are typical of Rayleigh scattering.     

T-matrix method and its applications to electromagnetic scattering by particles: A current perspective

This note serves as a short introduction to the reprint of our article “T-matrix computations of light scattering by nonspherical particles: a review” (JQSRT 1996; 55:535-75). We first discuss the motivation for writing that article and explain its historical context. This is followed by a short overview of more recent developments.     

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.     

Characteristics of light scattering by smoke particles based on spheroid models

Light scattering models of smoke particles play an important role on the development of photoelectric smoke detection. Aiming at the influence of morphology of smoke particles, spheroid models are introduced to analyze the Stokes scattering matrix of smoke particles, which are lognormal size distributions. Under the condition of random orientations, the effects of refractive indexes and mean size of smoke particles are considered. The results show that after averaging of the orientation and size, the nonsphericity of smoke particles has a considerable effect on their light scattering. Additionally, the nonsphericity of gray smoke particles generated from smoldering fires is more important than soot from flaming fires for analyzing the light scattering.     

大气气溶胶粒子光吸收系数的测量

采用核孔过滤膜累积气溶胶粒子的方法设计了气溶胶粒子光吸收系数的测量系统。该系统由双光路组成,可以减小光路损耗和电路噪声带来的各种测量误差。同时,具有体积小、光路易于调节、可进行实时测量、定标容易等特点。用200和400nm孔径的过滤膜,分别测量了实验室内大气气溶胶粒子对不同波长激光的吸收系数。随着累积时间的增加,系统的测量精度也不断的提高,在累积时间为900s时,系统测量误差为9.849×10-6/m。     

The shape influence on the overall single scattering properties of a sample in random orientation

In order to identify the type of scattering profile that corresponds to some specific shapes, we have performed calculations of some scattering properties for those shapes with a fixed size distribution. Aggregates of different numbers of spheres have been used to fit the laboratory measurements of fly ashes. The results for other shapes, such as rectangular prisms with different axial proportions, particles made of joined cubes, and particles with different fluffiness, are also shown. From all these calculations, it is concluded that the size-averaged scattering matrix elements resembles Rayleigh features, for the size distribution stopping at , when either the number of spheres or cubes of the aggregates is increased, the shape becomes flatter or the particles become fluffier. We also show the effect of the refractive index on the Q_sca vs. X curve in the case of strongly absorbing particles. A tendency to reach the geometric optic regime is observed instead of the Rayleigh regime using the same size distribution.     

椭圆截面非球形颗粒群的多重光散射

尽管非球形下一些特殊形状颗粒的单散射已被得到,球形多颗粒系（颗粒群）的多重散射也被研究,但至今仍未得到非球形颗粒群的多重散射.文中建立了一类椭圆截面非球形颗粒模型,求得其散射相位函数,借助于辐射传播方程,考虑形状及大小分布,得到了该类颗粒群的多重光散射.在两种特例情况下的结果能与已有的结果符合较好,说明了方法的可靠性.计算分析表明：非球形颗粒群的多重散射光强角分布要比球形颗粒平坦.椭圆截面颗粒的粒度或形状参数越大,多重散射光越集中于小的散射角;粒度分布或形状分布越宽,多重散射光强的角分布越平坦.随着光学厚 关键词： 多重光散射 颗粒 非球形 椭圆截面     

Light scattering by needle-type and disk-type particles

A powerful tool to analyze light scattering by 3D arbitrary-shaped homogeneous or inhomogeneous obstacles located in free space is based on volume integral equation. In this paper we apply a weak form of volume integral equation to simulate light scattering by needle- and disk-type particles such as straight and curved cylinders, cylindrical plate and hexagonal prism with high aspect ratio and low and high values of refractive indexes. For problems where discrete sources method could be applied, we calculated differential scattering cross-section using both methods and got excellent agreement in results.     

Phase function of long helical particles at normal and oblique incidence

This paper studies characteristics of the electro-magnetic wave scattering by a long helical particle in cases of oblique incidence with different polarizations. The dependence of the resonant peaks and the phase function on the incidence angle is analyzed for different values of helix parameters. The analysis is based on the model developed by the authors and presented in previous publications.     

Novel optical techniques for measurements of light extinction,scattering and absorption by single aerosol particles

Aerosol particles play important roles in a broad range of scientific disciplines, from atmospheric chemistry and physics, to the delivery of fuels for combustion and drugs to the lungs, and extending to industrial processes such as spray drying. Measurements of the light extinction, scattering and absorption by ensembles of aerosol particles can be used to non‐intrusively characterise aerosol particle samples. However, such measurements often lead to ambiguity in interpreting the properties and processes occurring on individual particles. In this review, recent developments in the use of laser based techniques to isolate and manipulate single particles and to characterise them will be highlighted. In particular, the use of cavity ring down spectroscopy, Bessel beams and optical tweezers for investigating light extinction, scattering and absorption, respectively, will be considered. The prospects for using optical techniques to interrogate the fundamental processes occurring in aerosol at the single particle level are discussed.     

Light scattering by groups of spherical particles

Light scattering by groups of spherical particles is considered. It is shown that the structure of the groups and their orientational distribution can be judged from the spectrum and polarization of the scattered light. Syktyvkar State University, 55, Oktyabr'skii Ave., Syktyvkar, 167001, Russia. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 64, No. 2, pp. 228–231, March–April, 1997.     

动态光散射研究纳米级PBA/PMMA核壳颗粒的散射特性

运用动态光散射仪研究PBA(聚丙烯酸丁脂)为核,PMMA(聚甲基丙烯酸甲脂)为壳的核壳双层结构颗粒的角度散射光,并通过测量得到的粒径分布进行理论计算,结果表明:测量结果与理论计算结果总体趋势一致,但在前向散射和后向散射两者相差较大,主要由于动态光散射仪测量粒径分布时反演算法剔除占比例很小的大颗粒造成的.