Near-field calculation based on the T-matrix method with discrete sources

We propose a novel approach to compute the field scattered by a particle in the near-zone, in the framework of the transition matrix formulation. This method is based on the expansion of the total near-field in terms of discrete sources vector spherical wave functions and turns out to be particularly effective to model strongly elongated or flattened particles with high permittivity. The performances are evaluated on gold spheroids with several aspect ratios. This method results very useful to understand the complex behavior of enhanced plasmon fields in resonant metallic nanostructures.     

T-matrix method for electromagnetic scattering from scatterers with complex structure

We describe a T-matrix program for light scattering calculations from particles with complex structure. The code treats the cases of homogeneous, layered and composite scatterers. These results are combined with basic results concerning the scattering by inhomogeneous scatterers and aggregates to apply to more general types of scatterers. Some numerical simulations are presented.     

Extended calculation of polarization and intensity of fractal aggregates based on rigorous method for light scattering simulations with numerical orientation averaging

The intensity and polarization of fractal aggregates have been investigated using both rigorous and approximate methods for light scattering simulations. However, previous studies using the analytical orientation averaging version of the rigorous method were generally limited to a few hundred monomers when the monomer size parameter was around 1.7. In this study, we propose using numerical orientation averaging instead of analytical orientation averaging. The numerical averaging is performed together with a fixed orientation version of the rigorous T-matrix method for clusters of spheres. This approach enables increasing the number of monomers by a factor of 2-7 or the size of monomers by a factor of 8-10 compared to the analytical orientation averaging version.We investigated the influence of monomer size and the number of monomers on the light scattering of silicate aggregates (refractive index m=1.68+0.03i) for incident light with a wavelength of . We considered ballistic particle-cluster aggregates (BPCA) and ballistic cluster-cluster aggregates (BCCA) composed of 128, 256, 512, and 1024 monomers with radii between 0.11 and .Our results show that the size of monomers plays an important role in reproducing the negative polarization branch for all the BPCA and BCCA. Silicate aggregates with the monomer radius of less than contribute to reproducing the negative polarization branch, while aggregates with monomers larger than do not have the negative polarization branch. Polarization oscillation with scattering angle occurs for larger monomers (i.e., monomer radius ).The maximum polarization decreases for increasing monomer radius between 0.11 and . However, the negative polarization branch is generally enhanced for monomer radii up to around , and reduced for further increase of monomer size.The number of monomers also has a large influence on the negative polarization branch in the case of BPCA. The increase in the number of monomers from 128 to 1024 shifts the scattering angle of minimum polarization to larger angles for BPCA. In addition, the increase in the number of monomers reduces the values of negative polarization for BPCA while the variation with the number of monomers for BCCA is small and is not monotonic.     

Derivatives of light scattering properties of a nonspherical particle computed with the T-matrix method

Based on the T-matrix formalism, we analytically calculate derivatives of light scattering quantities by a nonspherical particle with respect to its microphysical parameters. Illustrative computations are performed for a spheroid, and the results agree with those obtained by finite differencing. The proposed formalism also predicts correctly derivatives for a sphere obtained by linearized Lorenz-Mie theory.     

Efficient numerical orientation averaging of light scattering properties with a quasi-Monte-Carlo method

We studied numerical orientation averaging with three methods for selection of orientations: lattice-grid division, crude Monte-Carlo (CMC) method, and quasi-Monte-Carlo (QMC) method. Numerical orientation averaging with these methods are carried out with a fixed orientation version of the T-matrix method for clusters of spheres. The errors of numerical orientation averaging as a function of number of orientations are investigated by comparison with results from analytical orientation averaging of the T-matrix method.We studied four types of aggregates: a bisphere, ballistic cluster-cluster aggregates of 4 and 128 monomers (BCCA4 and BCCA128), and a ballistic particle-cluster aggregate of 128 monomers (BPCA128).We studied convergence of the scattering efficiency Q_sca, absorption efficiency Q_abs, asymmetry parameter g, intensity , and degree of linear polarization P=-S₁₂/S₁₁. For the polarization, scattering angles of maximum (Θ_max) and minimum (Θ_min) polarization in results of analytical orientation averaging are considered. For the intensity, in addition to Θ_max and Θ_min, forward scattering angle (Θ=10^°) is also considered.Q_sca, Q_abs and g of bisphere, BCCA4, and BPCA128 can be obtained accurately with smallest number of orientations by using QMC among three methods. Errors in Q_sca, Q_abs and g of BCCA128 were already small for smaller number of orientations (e.g., 100) with all the three methods.P(Θ_min) generally shows slow convergence requiring several thousands of orientations to have errors less than 1%. There are also cases where convergence of P(Θ_min) within 1% error is not attained even for largest number of orientations studied in this paper (i.e., BCCA4 with lattice-grid, BCCA128 with lattice-grid, BCCA128 with CMC).Intensity of Θ=10^°, Θ_max and Θ_min, and polarization of Θ_max generally show convergence within 1% error for several hundreds to 1000 orientations with three methods for selection of orientation angles. Among three methods, QMC requires smallest number of orientations for intensity and polarization.We also investigated convergence of Θ_max and Θ_min. Convergence of Θ_max and Θ_min is generally attained for 100-1000 orientations.We also described the application of the method to the discrete dipole approximation. In these calculations, we considered three shape models with different number of dipoles and different dipole representations to describe BCCA4. The results show that scattering and absorption efficiencies, and asymmetry parameter can generally be obtained within 1% errors for all the three shape models. On the other hand, errors are larger for intensity (up to 10%) and polarization (up to 50-70%).     

Computer programs for light scattering by particles with inclusions

We present a comparison of computational results from light scattering by spherical particles with inclusions. The different simulation methods like the T-matrix method, multiple multipole method and the method of separation of variables are presented shortly. Exemplary numerical simulations involve scattering by particles with one or two spherical inclusions and scattering by particles with non-spherical inclusions.     

基于递归T矩阵的离散随机散射体散射特性研究

本文根据电磁场矢量球波函数多极点展开原理及矢量叠加定理提出了递归T矩阵算法的矢量形式,并且基于矢量递归T矩阵算法建立了多散射球模拟离散随机散射体散射的三维电磁散射模型.通过计算不同尺寸、随机分布散射球的散射以及分析散射球间的高阶散射效应,结果表明:矢量递归T矩阵算法具有很高的计算精度,算法中包含多散射体间的高阶散射效应,因此能够精确计算多散射体总的散射效应.本文所建模型可应用于土壤湿度探测工程中评估地表下掩埋离散随机散射体散射对雷达回波信号产生的影响.     

水下任意刚性散射体对Bessel波的散射特性分析

本文利用Bessel波的谐波展开式, 采用T矩阵方法的推导思路, 建立了水下任意刚性散射体在Bessel波照射下的声散射场计算公式. 以水下刚性椭球体和两端附连半球的刚性圆柱体为例, 计算了在不同波锥角β 下的反向散射形态函数, 同时, 依据镜反射波和绕行波的干涉物理模型, 给出了预报Bessel波照射下的反向散射形态函数峰峰间隔值的计算模型. 仿真结果表明本文提出的Bessel波照射下反向散射形态函数峰峰间隔值预报方法是准确有效的, 同时也说明, 本文建立的基于T矩阵法计算水下任意刚性散射体在Bessel波束下的声散射场方法是有效的, 这拓展了T矩阵法的应用领域.     

Null-field method with discrete sources to electromagnetic scattering from composite objects

A novel formulation for improving the numerical stability of the null-field method for highly elongated and flattened composite scatterers is presented. The key step in this approach is to approximate the surface current densities by the lowest-order multipoles located in the complex plane. The accuracy of the proposed method is investigated from a numerical point of view.     

Light scattering simulation for the characterization of sintered silver nanoparticles

Light scattering is a useful tool in optical particle characterization. It can help to understand the nature of single particles as well as systems or clusters of particles; information about particle sizes, materials or shapes can be gathered. In this paper we investigate the application of light scattering studies to the analysis of a sintering process of silver nanoparticles. For this we first simulate the scattering behavior of two silver spheres. Then we assume sintering between them, leading to a single particle with a concave, peanut-like shape. We approximate this shape by a Cassini-oval. For light scattering studies we use an advanced T-matrix algorithm, the Nullfield Method with Discrete Sources. This method proved to be capable of simulating light scattering by concave particles. To make sure that the calculated data are correct we do comparative simulations using the Discrete Sources Method.     

Analysis of the light scattering properties of a gold nanorod on a plane surface via discrete sources method

The Discrete Sources Method has been extended to analyze the scattering behavior of a gold nanorod deposited on a plane surface in an evanescent wave field. In this case the system particle-surface demonstrates no axial symmetry and it is not possible to apply the conventional DSM approach for axisymmetric systems used before. In this paper DSM algorithm for non-axisymmetric systems is presented. The rigorous computer model based on DSM, which allows to take into account all features of the scattering problem including particle-surface interaction has been realized. Computer simulation analysis of the scattering spectra of gold nanorod is presented.     

Cross section calculations of randomly oriented bispheres in the small particle regime

The T-matrix is used to calculate the extinction cross section of bispherical particle systems in random orientation for a monospherical size parameter x=0.01. Differences between bispherical and monospherical (Mie) results are shown for a range of values of the refractive index. It is found that the size of the T-matrix that needs to be calculated can be large, thus preventing simple dipole approximations from being used. Once the T-matrix is computed, however, only a small number of terms is needed to obtain cross section values.     

光滑粒子动力学方法中粒子分布与数值稳定性分析

光滑粒子动力学(SPH)作为一种拉格朗日型无网格粒子方法,已经成功地应用于包括含多相流动界面以及移动边界的可压缩和不可压缩流体运动的研究中.通过对Poiseuille流动的深入研究,探索了SPH方法中粒子分布对计算精度的影响,揭示了一种因为粒子不规则分布而导致的数值不稳定现象.研究显示,这种数值不稳定性起源于SPH方法粒子近似过程中的不连续性.使用了一种新的粒子近似格式以确保SPH方法中粒子近似的连续性.计算结果表明,这种新的粒子近似格式对于规则和不规则的粒子分布都能得到稳定精度的结果.     

Different shape models for erythrocyte: Light scattering analysis based on the discrete sources method

In practical applications a precise and fast detection of the shape of a single erythrocyte from its scattering characteristics is needed. For this reason detailed investigations of light scattering properties of erythrocyte and their relation to shape is of great interest in recent years. In this paper we analyze light scattering behavior of different shape models of erythrocyte using the discrete sources method. For this we compare scattering results for oblate spheroid, disk-sphere, Cassini-based shape and a shape for a real strainless erythrocyte introduced by Skalak. Numerical results for the scattering indicatrix and the differential cross section by different shape models and its orientations are presented.     

Application of the T-matrix method to determine the structure of spheroidal cell nuclei with angle-resolved light scattering

We demonstrate an inverse light-scattering analysis procedure based on using the T-matrix method as a light-scattering model. We measure light scattered by in vitro cell monolayers using angle-resolved low-coherence interferometry (a/LCI) and compare the data to predictions of the T-matrix theory. The comparison yields measurements of the equal volume diameter and aspect ratio of the spheroid cell nuclei with accuracy comparable to quantitative image analysis of fixed and stained samples. These improvements represent a significant upgrade for the a/LCI technique, expanding both the range of tissue in which it is applicable and potentially increasing its value as a diagnostic tool.     

细菌觅食优化算法在光散射法颗粒粒度反演中的应用

针对函数约束算法中传统的智能算法反演时存在鲁棒性差和易陷入局部最优的缺点,提出了将正则化理论与细菌觅食优化算法相结合应用在颗粒粒度的测量中。引入Tikhonov平滑泛函来构建算法的目标函数,采用L曲线法确定正则化参数;再利用细菌觅食优化算法通过趋向、聚群、复制和迁徙等四种智能行为,迭代计算来搜寻函数的最优解。实验仿真结果表明:利用细菌觅食优化算法实现了在不同程度的随机噪声下的服从J-SB分布的单峰分布的均匀球形颗粒粒度分布反演,其反演结果更稳定,反演精度高,对于实现稳定、快速、准确的颗粒粒度在线测量具有重要的意义。     

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.     

Simulations of light scattering spectra of a nanoshell on plane interface based on the discrete sources method

The resonance properties of nanoshells are of great interest in nanosensing applications such as surface enhanced Raman scattering or biological sensing. In this paper the discrete sources method has been applied to analyze the spectrum of evanescent light scattering from a nanoshell particle deposited near a plane surface. Based on the rigorous theoretical model, which allows to take into account all features of the scattering problem as: medium with frequency dispersion, presence of the interface, the objective aperture and its location and core-shell asphericity, the scattering spectrum of nanoshells was calculated. The dependence of the local nanoshell spectral density behavior on its properties is discussed.     

Computation of direct intensity and medium intensity by using the discrete ordinates method

On the basis of the discrete ordinate scheme with (an) infinitely small weight(s), an easy-to-use and comprehensive method, named multi-rays method, is developed to calculate total, direct and medium intensities in arbitrarily specified directions. In doing this, for each of the specified directions, three identical discrete directions with infinitely small weights are employed to represent the three intensities. The new method is verified with two standard test problems, and is used to compute the intensities in two anisotropically scattering problems.     

Discrete sources method for light scattering analysis from 3D asymmetrical features on a substrate

The discrete sources method is extended to analyze polarized light scattering by three-dimensional asymmetrical features on a plane penetrable substrate. The strict mathematical model and corresponding numerical scheme are described. Computer simulation results of non-spherical micro-particle scattering show that particle shape has a stronger effect on measured response for normal incident scanners.