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The norm for analyzing radiative transfer in randomly dispersed particulate medium is to use the independent scattering assumption, where the radiative characteristics of the system are derived from the superposition of the individual particles' radiative characteristics. This assumption is valid when the particles are sparsely distributed. There are established regime maps that are used to identify if the independent scattering assumption is valid. However, these maps which are based on experimental data have been recently questioned and updates are proposed by studies relying on direct solution of Maxwell's equations, in which scattering coefficients, cross-sections and/or efficiencies of particle ensembles are considered to identify presence of dependent scattering effects. Notably, both directionality of the scattering phenomenon and the presence of coherent scattering occurring on the free-space - particle cloud boundary are overlooked while identifying transition between independent and dependent scattering regimes. This study provides a critical overview of recent numerical approaches and shows that a regime map cannot be drawn relying solely on scattering cross section estimated by electromagnetic field solvers. The dependent scattering effects for dielectric particulate medium can be well represented using static structure factor including the directionality of scattering. Transport scattering coefficient that accounts for both magnitude and directionality of the scattering can be used to represent the radiative behavior adequately. Therefore, it can be used as the single intrinsic characteristic for identifying the transition between dependent and independent scattering, rather than the scattering coefficient and the asymmetry parameter alone. [Display omitted] • SSF estimates scattering coefficient and asymmetry parameter for dielectric particulate medium. • Transport scattering coefficient is the proper metric for representing scattering regime. • Solution of Maxwell's equations is possible for finite sized particulate media. • Coherent scattering leads to overestimation of scattering coefficient. • Calculated asymmetry parameter depends on considered ensemble size. [ABSTRACT FROM AUTHOR]

• Radiative transfer problems for three different cases of refractive indexes for spherical particles embedded in an absorbing medium are systematically investigated. • The errors of the directional-hemispherical reflectance and transmittance caused by neglecting the effect of host medium absorption on particle scattering are analyzed. • Neglecting the effect of host medium absorption on particle scattering will underestimate the directional-hemispherical reflectance and transmittance to some extent. • For the case of monodisperse particles embedded in an absorbing thin layer considered in this paper, the relative error of hemispherical reflectances increases approximate linearly from 5.9% to 59.4% with the particle size parameter increases from 1.0 to 40. For many practical radiative transfer problems in dispersed media, the host medium surrounding the particles is absorbing rather than lossless, therefore it may lead to inaccurate results when the effect of host medium absorption on particle scattering is neglected. This paper presents a systematical investigation on the radiative transfer problems for three different cases of refractive indexes for spherical particles embedded in an absorbing medium. The single-scattering properties of the particles are calculated using the recently developed public-domain Lorenz-Mie program for the case of an absorbing host medium. The directional-hemispherical reflectance and transmittance for a plane-parallel layer of spherical particles are obtained by using the Monte Carlo method. The effects of host medium absorption, particle size parameter and size distribution on the radiative transfer characteristics are discussed. The results show that neglecting the effect of host medium absorption on particle scattering will underestimate the directional-hemispherical reflectance and transmittance to some extent. Meanwhile, the errors caused by using the conventional Lorenz–Mie theory increase obviously with increase of host medium absorption index and particle size parameter. For the case of monodisperse particles embedded in an absorbing thin layer (i.e., with layer thickness of 0.05 mm and host medium absorption index of 0.01), the relative error of hemispherical reflectances increases approximate linearly from 5.9% to 59.4% with the particle size parameter increases from 1.0 to 40. [ABSTRACT FROM AUTHOR]

Ηighlights • Electromagnetic torque on spheres in circularly polarized illumination reviewed. • Humblet-decomposition applied to spin and orbital angular momentum of scattered radiation. • Spin angular momentum of scattered radiation related to Stokes parameters. • Numerical examples from Lorenz-Mie theory for metallic spheres using the Hagen–Rubens approximation. • Orbital angular momentum of scattered radiation can exceed spin angular momentum in Mie theory. • Development of Hagen–Rubens approximation for the complex refractive index of metals reviewed. Abstract When a circularly polarized electromagnetic wave is scattered by an isotropic sphere, Humblet's decomposition from 1943 is helpful for understanding why the axial projection of the spin-angular momentum gives incomplete information concerning the total radiated angular momentum. Humblet asserted that some field angular momentum is orbital angular momentum (OAM). This distinction, applied here to Mie scattering, gives insight into why classical electromagnetic radiation torque is proportional to absorbed power for isotropic spheres. It also reveals the direct measurability (from Stokes parameters) of spin contributions to the radiated angular momentum. This approach is applied to metallic spheres in circularly polarized illumination modeled with Lorenz–Mie theory using the Hagen–Rubens approximation (1903) in which the real and imaginary components of the sphere's refractive index are equal in magnitude. That approximation is often useful for terahertz and lower frequencies. It was helpful to compare a spin efficiency factor Q spin with the canonical scattering efficiency factor Q sca for varying sphere sizes at a fixed frequency. A small-size limiting case Q sca /Q spin = 2 is recovered associated with a common interpretation of electric dipole-related torque. For larger sizes, the OAM contribution increases giving Q sca /Q spin > 2. Van de Hulst's scattering calculations for metal spheres are also reproduced. Dedicated in memory of Seattle Pacific University Professor James H. Crichton (1937–1999). [ABSTRACT FROM AUTHOR]

A recently developed FORTRAN program computing far-field optical observables for spherical particles in an absorbing medium has exhibited numerical instability arising when the product of the particle vacuum size parameter and the imaginary part of the refractive index of the host becomes sufficiently large. We offer a simple analytical explanation of this instability and propose a compact numerical algorithm for the stable computation of Lorenz–Mie coefficients based on an upward recursion formula for spherical Hankel functions of a complex argument. Extensive tests confirm an excellent accuracy of this algorithm approaching machine precision. The improved public-domain FORTRAN program is available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html . [ABSTRACT FROM AUTHOR]

Many applications of electromagnetic scattering involve particles immersed in an absorbing rather than lossless medium, thereby making the conventional scattering theory potentially inapplicable. To analyze this issue quantitatively, we employ the FORTRAN program developed recently on the basis of the first-principles electromagnetic theory to study far-field scattering by spherical particles embedded in an absorbing infinite host medium. We further examine the phenomenon of negative extinction identified recently for monodisperse spheres and uncover additional evidence in favor of its interference origin. We identify the main effects of increasing the width of the size distribution on the ensemble-averaged extinction efficiency factor and show that negative extinction can be eradicated by averaging over a very narrow size distribution. We also analyze, for the first time, the effects of absorption inside the host medium and ensemble averaging on the phase function and other elements of the Stokes scattering matrix. It is shown in particular that increasing absorption significantly suppresses the interference structure and can result in a dramatic expansion of the areas of positive polarization. Furthermore, the phase functions computed for larger effective size parameters can develop a very deep minimum at side-scattering angles bracketed by a strong diffraction peak in the forward direction and a pronounced backscattering maximum. [ABSTRACT FROM AUTHOR]

Avogadro constant determines the number of particles in one mole of a substance, thus relating the molar mass of the substance to the mass of this substance. Avogadro constant is related to Système Internationale base units by defining the very concept of chemical quantity. Revisions of the base units created a need to redefine the Avogadro constant, where a collaborative work called the Avogadro Project is established to employ optical interferometry to measure the diameter of high quality 100 mm silicon spheres. We propose far-infrared spectroscopy for determining the Avogadro constant by using elastic scattering from the 100 mm Avogadro Project silicon spheres. Similar spectroscopic methods are already in use in the near-infrared, relating whispering gallery modes of the 1 mm silicon spheres to the diameter of the spheres. We present numerical simulations in the far-infrared and the near-infrared, as well as spatially scaled down elastic scattering measurements in the near-infrared. These numerical and experimental results show that, the diameter measurements of 100 mm single crystal silicon spheres with elastic scattering in the far-infrared can be considered as an alternative to optical interferometry. [ABSTRACT FROM AUTHOR]

In this paper we make practical use of the recently developed first-principles approach to electromagnetic scattering by particles immersed in an unbounded absorbing host medium. Specifically, we introduce an actual computational tool for the calculation of pertinent far-field optical observables in the context of the classical Lorenz–Mie theory. The paper summarizes the relevant theoretical formalism, explains various aspects of the corresponding numerical algorithm, specifies the input and output parameters of a FORTRAN program available at https://www.giss.nasa.gov/staff/mmishchenko/Lorenz-Mie.html , and tabulates benchmark results useful for testing purposes. This public-domain FORTRAN program enables one to solve the following two important problems: (i) simulate theoretically the reading of a remote well-collimated radiometer measuring electromagnetic scattering by an individual spherical particle or a small random group of spherical particles; and (ii) compute the single-scattering parameters that enter the vector radiative transfer equation derived directly from the Maxwell equations. [ABSTRACT FROM AUTHOR]

A statistical approach in defining particle morphology in terms of an ensemble of hexahedra of distorted shapes is employed for modeling the Inherent Optical Properties (IOPs) of aquatic particles. The approach is inspired by the rich variability in shapes of real aquatic particles that cannot be represented by one particular shape. Two methods, the Invariant Imbedding T-matrix (II-TM) and Physical Geometric Optics Hybrid (PGOH) method, are combined to simulate the IOPs for aquatic particles of sizes ranging from the Rayleigh scattering to geometric optics regimes. Nonspherical effects on the IOPs are examined by comparing the results with predictions based on the Lorenz-Mie theory to explore the limitations of assuming the particles to be spherical. We pay special attention to backscattering-related and polarimetric scattering properties, particularly the backscattering ratio, Gordon parameter, backscattering volume scattering function and the degree of linear polarization. The simulated IOPs are compared with the in-situ measurements to assess the feasibility of using a hexahedral ensemble in modeling the IOPs of the aquatic particles. [ABSTRACT FROM AUTHOR]

In this paper we present a theoretical analysis of the generalized Lorenz–Mie theory for negative refractive index (NRI) media and spherical scatterers, extending the well-known concepts and definitions found in the literature involving dielectric or positive refractive index (PRI) particles. The consequences of a negative phase velocity and an anti-parallelism of the wave vector with respect to the Poynting vector are investigated and interpreted in this framework and, together with the symmetries found for the beam-shape coefficients when compared to the conventional PRI case, it is shown that the description of plane waves, Gaussian beams and, more generally, on-axis azimuthally symmetric waves along a NRI medium, their fields and all physical properties can be conveniently correlated with that of dielectric media once the electromagnetic response functions are replaced by their corresponding dielectric counterparts. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present some new developments in particle characterization. More precisely, the paper will be focused on the description of some progresses in the characterization of particles by interferometric methods which are generally considered as the most accurate ones. Three standard configurations will be presented and discussed: i) Interference between scattered light from a particle and a single reference beam (holography), ii) Interference between different kinds of light scattered by a single particle (ILIDS), iii) Interference between the light scattered from different particles. A special attention will be devoted to the possibility to obtain 3D information on the particle location. [ABSTRACT FROM AUTHOR]

In the field of combustion, the characterization of particles (such as 3D-location, particle shape, particle size, particle component and temperature) is a challenge. Newly developed technique, Fourier Interferometric Imaging (FII), have been proposed for characterizing a field of spherical particles. Based on the analysis of the interference field recorded on 2D detectors, information on the size, shape, temperature and relative position of the particles can be extracted. This article is devoted to the numerical and experimental validation of the FII approach on a line of monodispersed droplets. A simple model is introduced for efficient and fast computations of Fourier interferometric images. The predictions issue from that model are compared to Lorenz–Mie computations and experimental images. Good agreement between both the numerical and experimental behavior is obtained. [ABSTRACT FROM AUTHOR]

Abstract: We develop an orders-of-scattering approximation, termed the “screened cylindrical void/core” (SCV) approximation, for a composite cylinder. The composite cylinder consists of a large host cylinder that contains a small, eccentrically embedded, core cylinder. The SCV approximation is developed via separation of variables in conjunction with addition theorems for cylindrical functions. We show that the SCV approximation is in good agreement with the numerically exact solution. A simple physical interpretation of the SCV approximation is also presented. [Copyright &y& Elsevier]

Abstract: In this paper, we analyze a monochromatic plane wave scattering from an infinite homogeneous cylindrical annulus. In particular, we study the effect that the inner part of the cylindrical annulus (cylindrical void, if you will) has on the scattered field. This is done by isolating the cylindrical void's contribution to the scattered field. We show that if the cylindrical void is small, then its contribution to the scattered field may be approximated by the “screened cylindrical void” (SCV) approximation. We first develop the SCV approximation in a physically intuitive manner, and then show that it could also be obtained in a more mathematically rigorous manner. Numerical results comparing the SCV approximation to the exact solution are also presented. [Copyright &y& Elsevier]

Abstract: In liquid combustion, the evaporation process is one of the key parameters which controls combustion efficiency. To understand the combustion process, and to be able to develop an efficient combustor which produces less pollutant, it is necessary to be able to measure evaporation properties. Several techniques exist to measure the physical properties of fuel droplets, but very few exist to measure the thermo-chemical properties. The global rainbow technique (GRT) has been proposed and successfully used to measure the average temperature and the size distribution of sprays under the assumption that all the droplets are at the same temperature. This paper explores the applicability of GRT to sprays where the refractive index is a function of the particle size. A first result proves that the refractive index measured by GRT is weighted by the droplet diameter to the power of 7/3. This result permits accurate and fast comparisons between the numerical simulations and the experiments. A second result is the measurement of the refractive index by the size class by coupling GRT and Phase Doppler Anemometry (PDA) measurements (or another measurement technique with a low sensitivity to the refractive index such as holography, diffractometry, etc). [Copyright &y& Elsevier]

Abstract: We report on the results of theoretical investigation of the parameters of photonic nanojets formed near the shadow surface of micron-sized dielectric spheres irradiated by a laser radiation. The longitudinal and transversal dimensions of the photonic nanojet and its peak intensity also are calculated as the functions of particle size, index of absorption, and optical contrast of the particulate material. The photonic nano-flux was simulated numerically in composite particles made of a core and a shell with different refractive indices and variable shell thickness. Some practical conclusions are drawn concerning the possible ways to gain the control over the nanojet parameters in micron-sized spherical particles. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Simulations of the transmission of a short light pulse (50fs) through a strongly scattering medium constituted by water droplets (50–150μm 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 (0–400fs) are presented, showing that temporal information on particle size are still observable facing strongly scattering media. [Copyright &y& Elsevier]

A simple and robust method for the inversion of the laser diffraction diagrams of small transparent fibres is introduced. Based on Lorenz-Mie theory (LMT) calculations and the definition of a correlation estimator, it allows the particle diameter to be determined without the classical size ambiguity problem due to morphological-dependent resonances (MDRs). Experimentally, when sizing single reinforcement glass fibres during their forming process, the typical resolution obtained is about σ≈0.02 μm for the size range D=7–42 μm. This inversion method is thought to be also applicable for the diagnosis of other highly symmetrical and transparent particles as well as other particle characteristics. [Copyright &y& Elsevier]

This paper is devoted to the research on the characteristics of angular spectra of the intensity distributions near rainbow angles of a homogeneous cylinder where different orders of rainbow appear. The geometric optics predicts that two or more different orders of rainbow can appear at the same angle for certain refractive index. In the point of view of physical optics, the rays undergone different paths (corresponding to different orders of rainbow) interfere. By using the FFT and inverse FFT to the intensity distributions simulated by Lorenz–Mie theory and the Debye series, we can recognize the contributions of each order. This means that we can extract the information of different orders of rainbow from the signal collected by only one detector. Since the rays of different orders of rainbow pass through different paths and provide information of different parts in the particle, we can measure the parameters such as diameter, (gradient of) refractive index and non-circularity/non-sphericity of the particle from the unique signal. The results are also validated by experiments for a cylinder of diameter d=125 μm and refractive index m=1.4571. [Copyright &y& Elsevier]

• Scattering by non-absorbing bispheres and particle suspensions and aggregates was studied systematically. • A wide range of size parameter, refractive index, and interparticle distance-to-wavelength ratio was explored. • New transition criteria between independent/dependent scattering regimes were established. • The scattering cross-section and asymmetry factor feature different transition criteria. • Criteria for bispheres cannot be extended to suspensions and aggregates of small particles. Independent scattering refers to situations when particles are sufficiently distant that some of the radiation characteristics of particle systems can be determined by adding the contributions of each particle. When particles are in close proximity, however, dependent scattering prevails and is affected by near-field interactions and far-field interferences among scattered waves from nearby particles. The dimensionless parameters governing the scattering cross-section and asymmetry factor of non-absorbing bispheres, disordered and ordered suspensions and aggregates with up to 8 spherical particles were found to be the particle size parameter χ s , the relative index of refraction m , the interparticle distance-to-wavelength ratio d *, and the number of particles. Here, χ s ranged from 0.031 to 8.05, m varied from 0.667 to 2.6, and d * reached up to 30. Dependent effects were observed in aggregates with particles of all sizes and were strongly affected by the relative index of refraction in particle systems with χ s ≥ 2 due to large phase shifts across the particles. Moreover, new criteria for the transition between the dependent and independent scattering regimes for the scattering cross-section and the asymmetry factor were derived. For the scattering cross-section of structures with a narrow interparticle distance distribution, the independent scattering regime prevailed when the average interparticle distance-to-wavelength ratio d ¯ * exceeded (i) 2 for particles with χ s ≤ 2 and (ii) 5 for particles with χ s > 2. For the asymmetry factor, the transition from the dependent to the independent regimes for particles with χ s ≤ 2 was achieved for d ¯ * as high as 25. These transition criteria could be extended to particle systems with a broad interparticle distance distribution when based on the minimum interparticle distance-to-wavelength ratio. Finally, the relative index of refraction m did not affect these transition criteria. [ABSTRACT FROM AUTHOR]