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.     

Direct simulation Monte Carlo ray tracing model of light scattering by a class of real particles and comparison with PROGRA experimental results

The Direct Simulation Monte Carlo (DSMC) model is presented for three-dimensional single scattering of natural light by suspended, randomly oriented, optically homogeneous and isotropic, rounded and stochastically rough cubic particles. The modelled particles have large size parameter that allows geometric optics approximation to be used. The proposed computational model is simple and flexible. It is tested by comparison with known geometric optics solution for a perfect cube and Lorenz–Mie solution for a sphere, as extreme cases of the class of rounded cubes. Scattering and polarization properties of particles with various geometrical and optical characteristics are examined. The experimental study of real NaCl crystals with new Progra² instrument in microgravity conditions is conducted. The experimental and computed polarization and brightness phase curves are compared.     

Effective dynamic properties of 3D composite materials containing rigid penny-shaped inclusions

The propagation of time-harmonic plane elastic waves in infinite elastic composite materials consisting of linear elastic matrix and rigid penny-shaped inclusions is investigated in this paper. The inclusions are allowed to translate and rotate in the matrix. First, the three-dimensional (3D) wave scattering problem by a single inclusion is reduced to a system of boundary integral equations for the stress jumps across the inclusion surfaces. A boundary element method (BEM) is developed for solving the boundary integral equations numerically. Far-field scattering amplitudes and complex wavenumbers are computed by using the stress jumps. Then the solution of the single scattering problem is applied to estimate the effective dynamic parameters of the composite materials containing randomly distributed inclusions of dilute concentration. Numerical results for the attenuation coefficient and the effective velocity of longitudinal and transverse waves in infinite elastic composites containing parallel and randomly oriented rigid penny-shaped inclusions of equal size and equal mass are presented and discussed. The effects of the wave frequency, the inclusion mass, the inclusion density, and the inclusion orientation or the direction of the wave incidence on the attenuation coefficient and the effective wave velocities are analysed. The results presented in this paper are compared with the available analytical results in the low-frequency range.     

随机取向立方粒子光散射的数值分析

用离散偶极子近似法，计算了立方粒子随机取向时在几种等效尺度参数下的光散射特性，并与等效球形粒子的光散射特性进行了比较．结果表明：立方粒子和其他非球形粒子与其等效球形粒子光散射特性之间的差别大致相同，说明对于随机取向的非球形粒子的光散射问题，粒子的内在对称性和表面的突变不会带来明显的效果． 关键词：     

Electromagnetic mixing laws: A supersymmetric approach

In this article we address the old problem of finding the effective dielectric constant of materials described either by a local random dielectric constant, or by a set of non-overlapping spherical inclusions randomly dispersed in a host. We use a unified theoretical framework, such that all the most important Electromagnetic Mixing Laws (EML) can be recovered as the first iterative step of a family of results, thus opening the way to future improvements through the refinements of the approximation schemes. When the material is described by a set of immersed inclusions characterized by their spatial correlation functions, we exhibit an EML which, being featured by a minimal approximation scheme, does not come from the multiple scattering paradigm. It is made of a pure Hori-Yonezawa formula, corrected by a power series of the inclusion density. The coefficients of the latter, which are given as sums of standard diagrams, are recast into electromagnetic quantities which calculation is amenable numerically thanks to codes available on the web. The methods used and developed in this work are generic and can be used in a large variety of areas ranging from mechanics to thermodynamics.     

非常密集随机分布球粒子相关散射的数值模拟

讨论非常密集(占空比>0.4)随机分布球粒子的散射.用Monte Carlo方法和随机搅拌产生非常密集随机分布粒子,求解电场体积分方程的解,获得散射、吸收和消光系数及有效介电常数.与现有的准晶体近似、具有相干势的准晶体近似和Maxwell-Garnett混合方程等几种方法作了比较.非常密集随机分布粒子表现出群聚性产生的大粒子散射效应.     

Effective response in nonlinear spherical coated composites under external AC and DC electric fields

By using the perturbation method,effective nonlinear direct current(DC) and alternating current(AC) responses of nonlinear composites with spherical coated inclusions randomly embedded in a host medium are studied under the action of an external electric field E a = E 0 + E 1 sin ωt + E 3 sin 3ωt with different amplitudes and frequencies.The local potentials of composites at all harmonics are given in the inclusion particles and the host regions.All effective nonlinear responses to composites and the relationship between the effective nonlinear responses at all harmonics are also deduced for the spherical coated inclusions in a dilute limit.     

High-frequency magnetic permeability of nanocomposite film

The high-frequency magnetic permeability of nanocomposite film consisting of the single-domain spherical ferromagnetic particles in the dielectric matrix is studied. The permeability is assumed to be determined by rotation of the ferromagnetic inclusion magnetic moments around equilibrium direction in AC magnetic field. The composite is modeled by a cubic array of ferromagnetic particles. The magnetic permeability tensor is calculated by solving the Landau–Lifshits–Gilbert equation accounting for the dipole interaction of magnetic particles. The permeability tensor components are found as functions of the frequency, temperature, ferromagnetic inclusions density and magnetic anisotropy. The obtained results show that nanocomposite films could have a rather high value of magnetic permeability in the microwave range.     

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.     

Polarization imaging of multiply-scattered radiation based on integral-vector Monte Carlo method

A new integral-vector Monte Carlo method (IVMCM) is developed to analyze the transfer of polarized radiation in 3D multiple scattering particle-laden media. The method is based on a “successive order of scattering series” expression of the integral formulation of the vector radiative transfer equation (VRTE) for application of efficient statistical tools to improve convergence of Monte Carlo calculations of integrals. After validation against reference results in plane-parallel layer backscattering configurations, the model is applied to a cubic container filled with uniformly distributed monodispersed particles and irradiated by a monochromatic narrow collimated beam. 2D lateral images of effective Mueller matrix elements are calculated in the case of spherical and fractal aggregate particles. Detailed analysis of multiple scattering regimes, which are very similar for unpolarized radiation transfer, allows identifying the sensitivity of polarization imaging to size and morphology.     

Estimates of the albedo of powderlike surfaces in the geometrical optics approximation

Results of computer simulation of light scattering by powderlike media composed of large semitransparent particles of different shapes are presented. The geometrical optics approach is used. The cases of particles of spherical, cubic, and random shapes are considered. The one-dimensional geometrical optics model of light scattering by powderlike media, which finds application in investigations of planetary surfaces, meteorites, and lunar samples, is briefly described. The numerical simulation allowed us to estimate the error of this model, which turned out to be within the limits of several percent. The albedo calculated by using the one-dimensional model is shown to be closest to the “three-dimensional” reflectance of the surfaces at a phase angle of about 60°. This albedo also approximates fairly well the integrated reflectance, which in laboratory measurements is determined with the help of an integrating sphere.     

Effective response and scattering cross section of spherical inclusions in a medium

The Maxwell-Garnett theory for a right-handed homogeneous system is extended in order to investigate the effective response of a medium consisting of low density distributed 3-dimensional inclusions. The polarisability factor is modified to account for inclusions with binary layered volumes and it is shown that such a configuration can yield doubly negative effective permittivity and permeability. Terms representing second-order scattering interactions between binary inclusions in the medium are derived and are used to reformulate conventional effective medium theory. In the appropriate limit, the one-body theory of Maxwell-Garnett is recovered. The scattering cross section of the spherical inclusions is determined and comparison is made to homogeneous dielectric scatterers in the Rayleigh limit. It is found that the scattering resonances can be manipulated using the inclusion parameters. Furthermore, the effect that two-interacting spherical inclusions in a medium have on the scattering cross section is investigated via higher order dipole moments while the issue of reducing the scattering cross section to zero is also examined.     

Inhomogeneous swelling in filled elastomers

An exact formulation is given for the inhomogeneous swelling of an elastomeric matrix containing a spherical inclusion, and is presented in a form amenable to solution for arbitrary free energy of mixing and network strain energy functions, rigid or soft inclusions, and finite or infinite matrix size. Specific examples of the deformation field, stress field, and composition variation are given as functions of distance from a rigid inclusion imbedded in an infinite matrix displaying Flory-Huggins/Gaussian swelling behavior. Interfacial stresses and extension ratios are given as functions of cross-link density and Flory-Huggins X parameter.

In a related study published elsewhere, Kotani and Sternstein have obtained experimental verification of the theory using birefringence techniques on model-filled elastomers. Stein and co-workers have found similar agreement of the theory with their light scattering measurements.     

Spectral Dependence of Quasi-Rayleigh Polarization Leap of Nonspherical Particles: Polystyrene Beads Application

Solid particles in Earth’s atmosphere, such as polystyrene beads, are an important factor affecting the processes of absorption and scattering of light in the atmosphere. These processes affect on the solar energy transfer in the Earth’s atmosphere, consequently they have influence on the regional and global climate changes and atmospheric visibility. In particular, great interest to study the scattering properties of small particles compared with wavelength, because of such particles experience low gravitational settlement and may have long time of life in the atmosphere. When scattering particle is much smaller than the wavelength of the scattered or absorbed light, this is the case of Rayleigh scattering. Scattering properties of these particles (such as intensity and the degree of linear polarization) at the Rayleigh scattering are simply derived from electromagnetic Maxwell’s equations. But when the particles are large enough to be comparable with the wavelength, the deviations from Rayleigh scattering law are observed. One of the clear manifestations of such deviations is the recently discovered quasi-Rayleigh polarization leap of monodisperse spherical particles. This quasi-Rayleigh polarization leap allows remote sensing of the sizes of distant particles, based on the spectral position of quasi-Rayleigh polarization leap at different phase angles of observation. In this paper, we studied the effect of the non-sphericity of a scattering polystyrene particle on the magnitude and position of the quasi-Rayleigh polarization leap. It is established that the non-sphericity shifts the position of the quasi-Rayleigh polarization leap shorter wavelengths. It is shown that for non-sphericity of particles makes the quasi-Rayleigh polarization leap becomes less pronounced. Moreover, it was found, that increasing of the phase angle and degree of non-sphericity shift the quasi-Rayleigh polarization leap position to shorter wavelength. However, in the case of not very elongated particles, the quasi-Rayleigh polarization leap is quite well manifested. Therefore, this method is suitable for remote sensing not only the size, but also the degree of non-sphericity of the scattering particles. A simple formula has been obtained for polystyrene beads that relates the degree of non-sphericity of a particle with the wavelength and phase angles at which the quasi-Rayleigh polarization leap is observed.     

Effective AC response of nonlinear spherical coated composite

An effective nonlinear response of a nonlinear composite with spherical coated inclusions randomly embedded in a host medium under the action of an external AC electric field, {{\bm E}}_a = {{\bm E}}_1 \sin (\omega t) + {{\bm E}}_3 \sin (3\omega t), is investigated using a perturbation method. The local potentials of the composite at higher harmonics are given both in the region of local inclusion particles and in the local host region under the external AC electric field. All effective nonlinear responses of the composite and the relationship between the effective nonlinear responses at the fundamental frequency and third harmonics are also studied for spherical coated inclusion in a dilute limit.     

球形雾霾粒子的紫外光散射偏振特性研究

在我国经济社会快速发展的同时,雾霾天气成为了突出的环境问题,雾霾粒子的测量非常重要。偏振紫外光与大气雾霾粒子发生散射后,散射光偏振状态(Stokes矢量以及偏振度)的改变能反映雾霾粒子的相关物理特性(粒径、复杂折射率等)。基于Mie散射理论建立了紫外光雾霾球形粒子直视和非直视单次散射模型,研究了单个球形粒子和链状结构球形粒子物理特性的改变对散射光偏振状态的影响,并用蒙特卡洛仿真分析已知粒径分布的雾霾粒子浓度对散射光偏振状态的影响。结果表明：针对单个球形粒子,随着粒子粒径的增大Stokes矢量中散射光光强(I_s)随之增强,粒子复折射率虚部为先增大后较小,偏振度也是在不断增大,且复折射率虚部较小时,偏振度增加趋势快;对于粒径分布不变的雾霾粒子,随着粒子的浓度增加,雾霾粒子的散射系数、消光系数和吸收系数均呈线性增加,但是I_s先增大后减小。针对链状球形粒子,随着粒子个数的增加,I_s均呈现增大的趋势,且偏振度可用于区分链状球形粒子是否由相同球形粒子组成; 相同球形粒子组成链状结构中,I_s随着粒子数量的增加而线性增大,偏振度不改变;不同球形粒子组成的链状结构,I_s以及偏振度的变化趋势可以区分粒子物理特性。     

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.     

Analytical description of the electrodynamic properties of metallic photonic crystals

A method of approximate calculation of the interaction inverse matrix in the method of discrete dipoles is proposed. The knowledge of this matrix makes it possible to determine the optical response of a system to the action of an electromagnetic wave with an arbitrary shape, which can be represented as a combination of vector spherical wave functions. The number of calculation operations of the matrix in the proposed method is considerably smaller than in the case of its direct calculation. In the case of a change in the refractive index of scattering particles, two methods of approximate calculation of the interaction inverse matrix are also proposed. This makes it possible to calculate the optical response of systems with new characteristics without direct solving equations of a system with a large dimension. The accuracy of the methods is numerically determined for particles with spherical and cubic shapes. It is shown that the methods are computationally efficient and can be used to calculate the values of polarization vectors inside particles and extinction and absorption cross sections of systems.     

Size dependent optical characterization of semiconductor particle: CdS embedded in polymer matrix

We report the optical investigation and analysis of both nano-sized and micrometer size Cadmium Sulphide particles which is embedded in a transparent polyvinyl alcohol (PVOH) dielectric host material. A designed and fabricated laser based light scattering system using a He-Ne laser of wavelength 632.8nm was used for the measurement and study of the scattering properties of the particles as a function of the scattering angle at this wavelength. An attempt was made to experimentally determine the most significant elements of the Mueller scattering matrix using combinations of randomly and linearly polarized incident laser beam and subsequent analyzers in corresponding orientations. The analysis of the experimental data was done by the method of comparison with theoretically generated data. Novel computational technique, involving single scattering for spherical particles using Mie-theory, was developed and applied. The theoretical data was found to be in good agreement with the experimental data within an acceptable margin of error. The results have proved that the combination of the experimental setup and associated computational method is a highly efficient and reliable in-situ system for monitoring size growth of semiconductor particles in the laboratory.