Mie scattering efficiency of a large spherical particle embedded in an absorbing medium

The Mie scattering calculations are usually performed for non-absorbing spherical particles embedded in a non-absorbing medium. We consider a case of an absorbing sphere placed in an absorbing medium. We find, by numerical calculation for large size parameter of the order of 10⁴, that the scattering efficiency of a spherical particle in an absorbing medium approaches the reflectance of a plane surface at perpendicular incidence.     

Radiative properties of densely packed spheres in semitransparent media: A new geometric optics approach

This contribution presents a new Ray-tracing method for calculating effective radiative properties of densely packed spheres in non-absorbing or semitransparent host medium. The method is restricted to the geometric optic objects and neglects the wave effects. The effective radiative properties such as the absorption and scattering coefficients, and phase function are retrieved from the calculation of mean-free paths of scattering and absorption, and the angular scattering probability of radiation propagating in the dispersed medium. The model accounts for the two geometric effects called here as non-point scattering and ray transportation effects. The successful comparison of the current model with data of radiative properties and transmittances of particle beds in a non-absorbing medium reported in the literature confirm its suitability. It is shown that: (i) for opaque or absorbing particles (not systematically opaque), the non-point scattering is the dominant geometric effects whereas both non-point scattering and ray transportation effects occur for weakly absorbing and transparent particles. In the later cases, these two geometric effects oppose and may cancel out. This may explain why the Independent scattering theory works well for packed of quasi-transparent particles; (ii) the non-point scattering and ray transportation effects can be captured through the scattering and absorption coefficients while using the classical form of phase function. This enables using the standard radiative transfer equation (RTE); (iii) the surrounding medium absorption can be accounted for without any homogenization rule. It contributes to increasing the effective absorption coefficient of the composite medium as expected but, at the same time, it reduces the particle extinction; and (iv) the current transfer calculation predicts remarkably the results of direct Monte Carlo (MC) simulation. This study tends therefore to confirm that the RTE can be applied to densely packed media by using effective radiative properties.     

Scattering of electromagnetic waves by ensembles of particles and discrete random media

Current problems of the theory of multiple scattering of electromagnetic waves by discrete random media are reviewed, with an emphasis on densely packed media. All equations presented are based on the rigorous theory of electromagnetic scattering by an arbitrary system of non-spherical particles. The main relations are derived in the circular-polarization basis. By applying methods of statistical electromagnetics to a discrete random medium in the form of a plane-parallel layer, we transform these relations into equations describing the average (coherent) field and equations for the sums of ladder and cyclical diagrams in the framework of the quasi-crystalline approximation. The equation for the average field yields analytical expressions for the generalized Lorentz-Lorenz law and the generalized Ewald-Oseen extinction theorem, which are traditionally used for the calculation of the effective refractive index. By assuming that the particles are in the far-field zones of each other, we transform all equations asymptotically into the well-known equations for sparse media. Specifically, the equation for the sum of the ladder diagrams is reduced to the classical vector radiative transfer equation. We present a simple approximate solution of the equation describing the weak localization (WL) effect (i.e., the sum of cyclical diagrams) and validate it by using experimental and numerically exact theoretical data. Examples of the characteristics of WL as functions of the physical properties of a particulate medium are given. The applicability of the interference concept of WL to densely packed media is discussed using results of numerically exact computer solutions of the macroscopic Maxwell equations for large ensembles of spherical particles. These results show that theoretical predictions for spare media composed of non-absorbing or weakly absorbing particles are reasonably accurate if the particle packing density is less than ∼30%. However, a further increase of the packing density and/or absorption may cause optical effects not predicted by the low-density theory and caused by near-field effects. The origin of the near-filed effects is discussed in detail.     

Composites of resonant dielectric rods: A test of their behavior as metamaterial refractive elements

We report numerical experiments of optical wave propagation in composites of high refractive index dielectric rods at frequencies where their first electric and magnetic Mie resonances are excited. The arrays of these particles have been extensively studied and proposed as non-absorbing and isotropic metamaterials. We show that negative refraction, observed in such ordered particle arrays, is due to diffraction and that an effective medium theory (EMT) yields constitutive parameters that do not reproduce the observations in these composites, whose transmission also depends on the sample shape. This is further confirmed by disordering the arrays, a case in which large transmission losses appear due to extinction by resonant scattering from the particles. Therefore, these composites, although having little absorption, give rise to large extinction due to scattering and do not constitute an improvement, as low loss refractive elements, upon all previously designed highly absorbing metamaterials.     

Monte Carlo simulation of the interaction between an ultra-short pulse and a strongly scattering medium: The case of large particles

Simulations of the transmission of a short light pulse (50 fs) through a strongly scattering medium constituted by water droplets (50-150 μm diameter) are presented. Temporal emerging signals are computed using a Monte Carlo technique. In case of large particles with respect to the pulse duration, the time delay related to the interaction between light and individual particles has to be taken into account, in addition to the time delay related to the travel of light between particles. After careful comparisons with temporal Lorenz-Mie theory, it has been chosen to pre-calculate scattering characteristics of individual droplets using Debye series. Transmitted signals in forward direction and in a small temporal window (0-400 fs) are presented, showing that temporal information on particle size are still observable facing strongly scattering media.     

吸收性海水中气泡光散射特性的理论研究

 给出了一种适合于吸收性介质内粒子散射的Mie级数新的表示形式。利用Mie理论研究了吸收性海水中气泡的单散射特性和气泡群的相位函数。与非吸收性海水中气泡的光散射特性相比,分析了海水折射率虚部对气泡光散射的影响。结果表明：180°后向散射的增强是气泡固有的光学性质,与所处介质无关,可以利用后向散射的增强来探测气泡。     

An “exact” geometric-optics approach for computing the optical properties of large absorbing particles

Based on the principles of geometric optics, the ray-tracing technique has been extensively used to compute the single-scattering properties of particles whose sizes are much larger than the wavelength of the incident wave. However, the inhomogeneity characteristics of internal waves within an absorbing particle, which stem from a complex index of refraction, have not been fully taken into consideration in the geometric ray-tracing approaches reported in the literature for computing the scattering properties of absorbing particles. In this paper, we first demonstrate that electromagnetic fields associated with an absorbing particle can be decomposed into the TE and TM modes. Subsequently, on the basis of Maxwell's equations and electromagnetic boundary conditions for the TE-mode electric field and the TM-mode magnetic field, we derive generalized Fresnel reflection and refraction coefficients, which differ from conventional formulae and do not involve complex angles. Additionally, a recurrence formulism is developed for the computation of the scattering phase matrix of an absorbing particle within the framework of the conventional geometric ray-tracing method. We further present pertinent numerical examples for the phase function and the degree of linear polarization in conjunction with light scattering by individual absorbing spheres, and discuss the deviation of the geometric optics solutions from the exact Lorenz-Mie results with respect to size parameter and complex refractive index.     

离轴多层球对高斯波束的光散射

根据广义米氏理论，将入射的高斯波束按矢量球谐函数展开，获得了波束因子（展开系数）ｇｍｎ，ＴＭ和ｇｍｎ，ＴＥ的一般表达式。应用ｇｍｎ的局域近结果和散射系数ａｎｍ和ｂｎｍ的迭代公式与算法，研究了多层有耗介质球的光散射。讨论了波束宽度与球形粒子的尺寸和位置对散射系数和散射强度角分布的影响。     

大粒子对高斯波束散射的数值模拟

基于广义米氏理论，精确的求解了球形粒子对高斯波束和平面波的散射，采用Matlab编程， 改进了计算方法，所能够计算的粒子的尺寸参数已突破80000. 给出了平面波与高斯波入射 时，均匀粒子以及镀层粒子的散射分布，比较了吸收粒子和非吸收粒子散射分布. 关键词： 广义米氏理论 高斯波束 光散射 波束因子     

Generalized lorenz-mie theory and applications

Many optical sizing techniques rely on particle/laser interactions. The classical Lorenz-Mie theory describing sphere/plane wave interactions is therefore misleading when designing instruments and processing data when the particle size is not small enough with respect to beam diameters. In such cases the use of the generalized Lorenz-Mie theory is required. After summarizing essential features of the generalized Lorenz-Mie theory for sphere/arbitray wave interactions, this paper describes applications of the theory with some emphasis on the analysis of phase-Doppler anemometers.     

激光对含偏心核球形粒子的辐射俘获力

利用偏心球形粒子对任意角度入射有形波束散射的理论,从广义米理论出发,根据电磁场的动量守恒及麦克斯韦张量,推导了任意入射波束对偏心球形粒子辐射俘获力的级数表达式,并以高斯波束为例,就离轴入射有吸收偏心球形粒子时的辐射俘获力进行了数值模拟,讨论了束腰半径、吸收系数、内核的相对大小及位置对俘获情况的影响. 关键词： 广义米理论 偏心球 辐射俘获力 光镊     

吸收介质中微椭球体颗粒光学参数的研究

本文应用Eikonal近似将微椭球用其等效的球来近似, 结合Mie理论对吸收介质中微椭球体颗粒光学参数进行了数值计算。 结果表明, 椭球位置变化时, 散射和吸收性能发生变化。离心率增大时, 散射和吸收系数都增大, 离心率越大增大的越明显。波长增大时, 在紫光波长为0.4 μm和近红外区波长为1.58 μm处散射系数出现了峰值, 而吸收系数单调增大。相对折射率实部以及虚部变化对光学参数均有影响, 颗粒的吸收性越强, 散射相应地减弱。结果表明这种数值解析方法能有效地计算椭球体颗粒的光学参数。     

Describing small-scale structure in random media using pulse-echo ultrasound

A method for estimating structural properties of random media is described. The size, number density, and scattering strength of particles are estimated from an analysis of the radio frequency (rf) echo signal power spectrum. Simple correlation functions and the accurate scattering theory of Faran [J.J. Faran, J. Acoust. Soc. Am. 23, 405-418 (1951)], which includes the effects of shear waves, were used separately to model backscatter from spherical particles and thereby describe the structures of the medium. These methods were tested using both glass sphere-in-agar and polystyrene sphere-in-agar scattering media. With the appropriate correlation function, it was possible to measure glass sphere diameters with an accuracy of 20%. It was not possible to accurately estimate the size of polystyrene spheres with the simple spherical and Gaussian correlation models examined because of a significant shear wave contribution. Using the Faran scattering theory for spheres, however, the accuracy for estimating diameters was improved to 10% for both glass and polystyrene scattering media. It was possible to estimate the product of the average scattering particle number density and the average scattering strength per particle, but with lower accuracy than the size estimates. The dependence of the measurement accuracy on the inclusion of shear waves, the wavelength of sound, and medium attenuation are considered, and the implications for describing the structure of biological soft tissues are discussed.     

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.     

飞尘气溶胶粒子散射特性分析:对比实验和米散射方法

采用Mie散射理论计算了可见光波段等效球飞尘气溶胶粒子的Stokes散射矩阵,并与实验得到的空间随机取向的非球形飞尘气溶胶粒子结果进行了对比分析;由理论与实验方法得到的散射相函数,采用离散坐标法计算了两者的双向反射函数(BRDF),并对此结果进行了分析研究。结果表明:实验测量的非球形飞尘气溶胶粒子群的散射矩阵和基于球形粒子假设的Mie散射理论计算结果在大多数散射角上都不相同,但是不对称因子却大致相同;球形-非球形粒子群的BRDF随反射角的变化趋势基本一致,但是球形粒子群的BRDF曲线分布具有更大的波动趋势;随着光学厚度的增加,球形-非球形粒子群的BRDF曲线分布均趋于平坦,计算结果趋于一致。因此在飞尘气溶胶粒子散射特性研究中,当光学厚度较小时,用球形假设的方法会造成一定的误差,BRDF相对误差最大可以达到60%,需考虑粒子非球形特性造成的影响;而当光学厚度较大时,BRDF相对误差一般不会超过10%,采用球形假设的方法具有一定的适用性。     

On rainbows of inhomogeneous spherical droplets

The paper is devoted to the study of the intensity distributions and the angular spectra of the second and fifth rainbows of homogeneous and inhomogeneous spherical particles predicted by Lorenz-Mie theory. The results show that the distribution around the second rainbow angle for a homogeneous sphere of refractive index between 1.32 and 1.33 is due to the interference of the light after two or five internal reflections. The structure of the scattering diagram and the angular spectrum for homogeneous and radially inhomogeneous spheres are studied. For a homogeneous sphere we show that the second and fifth rainbows can be independently reconstructed by filtering the calculated spectrum. Since each order of rainbow penetrates the particle to different depths, such methods could be used to provide information about the refractive index profile or the temperature gradient of an inhomogeneous sphere. The Airy-like peaks of the second and fifth rainbows are closely connected with the refractive index profile, which is beneficial to the measurement of its refractive index profile or temperature gradient.     

Phase-Doppler Anemometry with the Dual Burst Technique for measurement of refractive index and absorption coefficient simultaneously with size and velocity

The principle of the dual burst technique (DBT) based on phase-Doppler anemometry (PDA) is proposed for simultaneous particle refractive index, size and velocity measurements. This technique used the trajectory effects in PDA systems to separate the two contributions of the different scattering processes. In the case of forward scattering and refracting particles, it is shown that from the phase of the reflected contribution, the particle diameter can be deduced, whereas from the refracted contribution the particle refractive index and velocity can be obtained. Furthermore, the intensity ratio of these two scattering processes can be used for absorption measurements. Simulations based on generalized Lorenz-Mie theory and experimental tests using monodispersed droplets of different refractive indices and absorption coefficients have validated this technique.     

Optical extinction of an assembly of spherical particles in an absorbing medium: Application to silver clusters in absorbing organic materials

The theory presented by Gerardy and Ausloos for the calculation of the linear optical response of aggregates of spherical particles is analytically continued for absorbing embedding media. The method is based on the calculation of the extinction rate by a single particle embedded in an absorbing matrix. Explicit expressions for the extinction and scattering cross-sections are given. The method is applied to calculate the energy losses in several organic matrices with embedded silver clusters. Comparison with experimental data shows a very good agreement. Received: 21 December 1998     

Scattering of a Gaussian Beam by a Sphere Using a Bromwich Formulation: Case of an arbitrary location

A complete theory of Gaussian beam scattering by a sphere is exposed. It is a generalization of the Lorenz-Mie Theory to the case of Gaussian beam illumination. The spherical, isotropic and homogeneous scatterer may be located anywhere with respect to the beam. The Bromwich Scalar Potentials are used to solve the scattering problem and expressions are obtained for the scattered field (both in the near field and far field regions), the scattered intensities and the phase angle. In the limit of special cases the expressions agree with previous works restricted to more particular problems.     

Asymptotic quantum inelastic generalized Lorenz-Mie theory

The (electromagnetic) generalized Lorenz-Mie theory describes the interaction between an electromagnetic arbitrary shaped beam and a homogeneous sphere. It is a generalization of the Lorenz-Mie theory which deals with the simpler case of a plane wave illumination. In a recent paper, we consider (i) elastic cross-sections in electromagnetic generalized Lorenz-Mie theory and (ii) elastic cross-sections in an associated quantum generalized Lorenz-Mie theory. We demonstrated that the electromagnetic problem is equivalent to a superposition of two effective quantum problems. We now intend to generalize this result from elastic cross-sections to inelastic cross-sections. A prerequisite is to build an asymptotic quantum inelastic generalized Lorenz-Mie theory, which is presented in this paper.