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Because of the strong electron–atom interaction, the kinematic theory of diffraction cannot be used to describe the scattering of electrons by an assembly of atoms due to the strong dynamical diffraction that needs to be taken into account. In this paper, the scattering of high‐energy electrons by a regular array of light atoms is solved exactly by applying the T‐matrix formalism to the corresponding Schrödinger's equation in spherical coordinates. The independent atom model is used, where each atom is represented by a sphere with an effective constant potential. The validity of the forward scattering approximation and the phase grating approximation, assumed by the popular multislice method, is discussed, and an alternative interpretation of multiple scattering is proposed and compared with existing interpretations. [ABSTRACT FROM AUTHOR]

Multiple scattering of parallel cylinders with arbitrary cross section is computed using the T-matrix of each single scatterer and the general translational matrix for cylindrical waves. Usually, the recommended golden rule to compute the translational matrix is Graf’s addition theorem. However, this approach cannot be properly implemented for some geometries, such as in a two-cylinder case when the center of one of them falls within the minimum circular cylinder that circumscribes the other one. In order to overcome this limitation, a transformation between cylindrical waves and plane waves, followed by propagation of the latter, is proposed. The new approach succeeds due to an adequate truncation of the evanescent plane wave spectrum. This strategy is demonstrated by studying the scattering of three infinite elliptic metallic cylinders for different electrical sizes and observing the convergence of the results as a function of the truncated spectrum. Finally, to conclusively show the interest and applicability of the approach, two more complex problems are treated: a group of infinite elliptic metallic cylinders where two different sizes are combined and a practical real-life filter in substrate integrated waveguide (SIW) technology, including several groups of rectangular dielectric cylinders. [ABSTRACT FROM AUTHOR]

Highlights • The optical characteristics of a cluster consisting of zinc sulfide (ZnS) particles doped with a nonconcentric spherical copper (Cu) cores illuminated with an arbitrarily focused Gaussian beam are investigated. • The presented aggregations of nonconcentric doped particles (i.e. core with offset origin) form linear chains or densely packed clusters. • The laser beam is modeled using angular spectrum of plane waves method and then combined with the cluster T -matrix method which is modified to solve such difficult multiple scattering problem. • This combination provides a powerful mathematical technique to obtain the phase (scattering) matrix of a cluster illuminated with any incident electromagnetic fields. • The scattering matrix provides complete descriptions of the scattering characteristics in the far field zone. • The computed results are shown for different beam waists with respect to the cluster. • The scattering processes and its results help understanding many cluster characteristics and nonlinear processes. • The presented numerical results show that the elements of the scattering matrix are sensitive to the focusing of the incident beam and characteristics of the cluster constituents. • The illustrated results are important for researches aim to improve polymer properties and to study several branches of practical sciences and industries such as nanotechnology, pharmaceuticals, chemistry, and biology. • This paper represents the first attempt to study the multiple scattering from a cluster of nonspherical particles with nonconcentric spherical cores illuminated by an arbitrarily focused laser beam. Abstract The optical characteristics of a cluster consisting of zinc sulfide (ZnS) particles doped with a nonconcentric spherical copper (Cu) cores illuminated with an arbitrarily focused Gaussian beam are investigated. The presented aggregations of nonconcentric doped particles (i.e. core with offset origin) form linear chains or densely packed clusters. The laser beam is modeled using angular spectrum of plane waves method and then combined with the cluster T -matrix method which is modified to solve such difficult multiple scattering problem. This combination provides a powerful mathematical technique to obtain the phase (scattering) matrix of a cluster illuminated with any incident electromagnetic fields. The scattering matrix provides complete descriptions of the scattering characteristics in the far field zone. The computed results are shown for different beam waists with respect to the cluster. The scattering processes and its results help understanding many cluster characteristics and nonlinear processes. The presented numerical results show that the elements of the scattering matrix are sensitive to the focusing of the incident beam and characteristics of the cluster constituents. The illustrated results are important for researches aim to improve polymer properties and to study several branches of practical sciences and industries such as nanotechnology, pharmaceuticals, chemistry, and biology. This paper represents the first attempt to study the multiple scattering from a cluster of nonspherical particles with nonconcentric spherical cores illuminated by an arbitrarily focused laser beam. [ABSTRACT FROM AUTHOR]

The simulation of light scattering by particles on a substrate with the T -matrix method relies on the expansion of the scattered field in spherical waves, followed by a plane wave expansion to allow the evaluation of the reflection from the substrate. In practice, the plane wave expansion (i.e., the Sommerfeld integrals) needs to be truncated at a maximal in-plane wavenumber κ max . An appropriate selection of κ max is essential: counter-intuitively, the overall accuracy can degrade significantly if the integrals are truncated with a too large value. In this paper, we propose an empirical formula for the selection of κ max and discuss its application using a number of example simulations with dielectric and metallic oblate spheroids on dielectric and metallic substrates. The computed differential scattering cross sections are compared to results obtained from the discrete-sources method. [ABSTRACT FROM AUTHOR]

Two methods for computing the normal incidence absorptance and hemispherical reflectance from plane parallel layers of wavelength–sized spherical particles are presented. The first method is based on an exact superposition solution to Maxwell's time harmonic wave equations for a system of randomly–positioned spherical particles excited by an incident plane wave. The second method is based upon the scalar radiative transport equation (RTE) applied to a plane parallel medium. Comparisons are made using five values of particle refractive index, sphere size parameters ranging from 1 to 4, and particle volume concentrations ranging from 0.05 to 0.4. The results indicate that the multiple sphere T matrix method (MSTM) and RTE predictions of hemispherical reflectance and absorptance converge when particle volume fraction becomes small. At higher volume fractions the RTE can yield results for hemispherical reflectance that, depending on the particle size and refractive index, significantly depart from the exact predictions. On the other hand, RTE and MSTM predictions of absorptance have a much closer agreement which is largely independent of the sphere optical properties and volume concentration. [ABSTRACT FROM AUTHOR]

A fast superposition T-matrix solution is formulated for electromagnetic scattering by a collection of arbitrarily-shaped inhomogeneous particles. The T-matrices for individual constituents are computed by expanding the Green's dyadic in the spherical vector wave functions and formulating a volume integral equation, where the equivalent electric current is the unknown and the spherical vector wave functions are treated as excitations. Furthermore, the volume integral equation and the superposition T-matrix are accelerated by the precorrected-FFT algorithm and the fast multipole algorithm, respectively. The approach allows for an efficient scattering analysis of the clusters and aggregates consisting of a large number of arbitrarily-shaped inhomogeneous particles. [ABSTRACT FROM AUTHOR]

Abstract: We consider absorption and scattering of acoustic waves from uncertain configurations comprising multiple two dimensional bodies with various material properties (sound-soft, sound-hard, absorbing and penetrable) and develop tools to address the problem of quantifying uncertainties in the acoustic cross sections of the configurations. The uncertainty arises because the locations and orientations of the particles in the configurations are described through random variables, and statistical moments of the far-fields induced by the stochastic configurations facilitate quantification of the uncertainty. We develop an efficient algorithm, based on a hybrid of the stochastic pseudospectral discretization (to truncate the infinite dimensional stochastic process) and an efficient stable truncated version of Waterman's T-matrix approach (for cost effective realization at each multiple particle configuration corresponding to the pseudospectral quadrature points) to simulate the statistical properties of the stochastic model. We demonstrate the efficiency of the algorithm for configurations with non-smooth and non-convex bodies with distinct material properties, and random locations and orientations with normal and log-normal distributions. [Copyright &y& Elsevier]

We consider multiple scattering among different groups of vias with each group of vias sharing one antipad in planar waveguide. A transformation is used that converts the 2-D discretization and 2-D surface integration of the product of Green's functions and magnetic surface currents into 1-D discretization and 1-D integration of surface charges on the vias and on the ground plane. This is used to calculate the incident fields onto the vias. Based on the incident fields, the Foldy–Lax equations can be solved to calculate the circuit parameters for the problem. We show that the results are superior to the previously used finite difference method. In addition, the group T-matrix method is used to represent a group of vias to account for the scattering among different groups of vias. Results are illustrated for various cases of multiple vias up to 20 GHz. Results show the accuracy of the method even to very closely spaced vias when they are separated by merely 1 mil. Numerical results are in excellent agreement with ANSOFT HFSS. [ABSTRACT FROM AUTHOR]

Abstract: The effects of morphological structure, water coating, dust mixing and primary particle size distribution on the radiative properties of soot fractal aggregates in atmosphere are investigated using T-matrix method. These fractal aggregates are numerically generated using a combination of the particle–cluster and cluster–cluster aggregation algorithms with fractal parameters representing soot aggregate in atmosphere. The radiative properties of compact aggregate notably deviate from that of the branched one, and the effect of morphology changes on the radiative properties in wet air cannot be neglected. However it is reasonable to use realization-averaged radiative properties to represent that of the aggregates with certain morphology. In wet air, the scattering, absorption and extinction cross-section and symmetry parameter of soot aggregates coated with water notably increase with water shell thickness. The mixing structures of dust have little effect on radiative properties of aggregates, but the volume fraction of dust has an obvious effect on extinction, scattering and absorption cross-section of aggregates when the size parameters are above the Rayleigh limit. Although the primary particle size distribution of soot aggregate has mild effect on the scattering albedo and asymmetry parameter, the deviations of the extinction, scattering, absorption cross-section among the three size distributions are significant in this study. The size distribution has a significant effect on forward scattering of phase function, while the effect can be neglected as the size parameter approaches to the Rayleigh limit. [Copyright &y& Elsevier]

Abstract: In turbid media, the partial or global orientation of anisotropic particles induces anisotropic light transport. In this study, we discuss the anisotropic incoherent transport of light in media where prolate ellipsoids are oriented in the same direction. In these anisotropic media, incoherent light transport is investigated using Monte Carlo simulations where the influence of particle anisotropy, size and optical properties are explored in a systematic way, from the local scattering event up to the diffusion limit. The database allows inverting the anisotropy of the backscattered image to yield the form factor of the particles. We then illustrate the relevance of such an analysis to assess the deformability of human erythrocytes in blood samples under normal physiological conditions. [Copyright &y& Elsevier]

The importance of the T-matrix method is well known when frequency domain scattering problems are of interest. With the relatively recent and wide-spread interest in time domain scattering problems, similar applications of the T-matrix method are expected to be useful in the time domain. In this paper, the time domain spherical scalar wave functions are introduced, translational addition theorems for the time domain spherical scalar wave functions necessary for the solution of multiple scattering problems are given, and the formulation of time domain scattering of scalar waves by two scatterers of arbitrary shape is presented. The whole analysis is performed in the time domain requiring no inverse Fourier integrals to be evaluated. Scattering by two soft spheres in free-space is studied as an application to check the numerical accuracy and demonstrate the utility of the expressions. [ABSTRACT FROM AUTHOR]

We propose an original theoretical framework to model the scattering efficiency of white paint films as a function of the volume fraction and spatial state of dispersion of rutile titanium dioxide pigments, taking into account electromagnetic couplings. Numerical calculations are performed using a multiple T matrix formalism on an “elemental” volume extracted from the bulk of the paint and which we model as pigments and fillers in a polymer matrix. Qualitative studies show that, due to the dependent scattering phenomenon, the size of fillers can modulate the magnitude of loss in scattering efficiency by modifying the spatial state of dispersion of the pigments in the polymer matrix. In particular, fillers whose size is comparable to the dimension of the pigments improve the scattering efficiency by impeding crowding. It is also shown that the optical properties of the bulk material at arbitrary concentration can be approximated by extrapolating the optical properties calculated on a limited number of scatterers. [ABSTRACT FROM AUTHOR]

• A software for the simulation of light scattering by multiple particles near planar interfaces is presented. • The usage of the software is illustrated by several application examples. • The accuracy of the results is verified by comparison to FEM and FDTD results. • Simulations with several thousand wavelength-scale particles are feasible. SMUTHI is a python package for the efficient and accurate simulation of electromagnetic scattering by one or multiple wavelength-scale objects in a planarly layered medium. The software combines the T-matrix method for individual particle scattering with the scattering matrix formalism for the propagation of the electromagnetic field through the planar interfaces. In this article, we briefly introduce the relevant theoretical concepts and present the main features of SMUTHI. Simulation results obtained for several benchmark configurations are validated against commercial software solutions. Owing to the generality of planarly layered geometries and the availability of different particle shapes and light sources, possible applications of SMUTHI include the study of discrete random media, meta-surfaces, photonic crystals and glasses, perforated membranes and plasmonic systems, to name a few relevant examples at visible and near-visible wavelengths. [ABSTRACT FROM AUTHOR]

• Superposition T-matrix method for light scattering in periodic super cells • Avoidance of artificial periodicity induced lattice resonances • Ewald summation and plane wave coupling scheme for periodic particle grids • Derivation of spectral information from large, disordered nanostructures To model and design light propagation in disordered optical nanostructures and materials, any applicable simulation technique has to cope with enormous computational challenges in a bearable time frame. To circumvent these, the introduction of an artificial periodicity to the disordered particle structure allows to rely on computational techniques that exploit periodic boundary conditions. Choosing a rather large periodicity promises to preserve randomness in form of a close-range disorder but can introduce false interferences. So far, it remains open how the artificial periodicity has to be chosen to minimize its detrimental influence. Here, we combine the superposition T-matrix scheme with an Ewald sum formulation to account for light scattering in periodic particle arrangements that contain hundreds to thousands of individual scatterers per unit cell. Simulations reveal that the periodicity's influence cannot be minimized by simply choosing one single period much longer than the excitation wavelength. The excitation of lattice induced resonances prevents so. However, choosing a periodicity that does not sustain such detrimental features allows for reliable predictions. With that, the presented approach is suitable to derive spectral information about wave-optical phenomena in large, random particle arrangements with a spatial extend beyond those accessible with other full-wave solvers. [ABSTRACT FROM AUTHOR]

Abstract: In a recent paper we proposed a decompositioning method to compute scattering by aggregated cylindrical fibres using a multiple scattering T-matrix approach. In this paper we extend this approach to scatterers lacking rotational symmetry. To investigate the capability of this method a square prism and a cube are decomposed into a number of subscatterers and scattering of the original particle shape is computed using multiple scattering. The results are validated using discrete dipole approximation (DDA). [Copyright &y& Elsevier]

A T-matrix approach is used to obtain the orientation-averaged scattering and absorption cross sections of randomly oriented particle clusters, and the average angular distribution of the radiation scattered by them. The coefficients involved in the expansion of the phase function are obtained from this T-matrix approach, and used in a multiple scattering formalism to characterize the angular distribution of the diffuse radiation propagating through a particulate coating perpendicularly illuminated with collimated visible radiation. Asymmetry between forward and backward propagating diffuse radiation intensities is taken into account by means of this multiple scattering approach, which is based on solving the radiative transfer equation for successive scattering order contributions. A four-flux model is applied to compute the reflectance in terms of wavelength of the incident radiation and particle concentration. An application of the formalism is carried out to predict the optical properties of titanium dioxide pigmented polymer coatings, in terms of the pigment volume fraction and the degree of aggregation. [Copyright &y& Elsevier]

• Review on the development of generalized Lorenz-Mie theories. • Optical theorem and structured/shaped beams. • Speed of light and nature of photons regarding particular effects. • Epistemological discussion on the underdetermination thesis of theories by experiments. As the 2020 winner of the van de Hulst Award, I have been committed to the writing of a van de Hulst Essay which is presented here. The Award has been essentially motivated by my work on laser light scattering by particles, which spreads over 40 years. During this time, I may have obtained several results of interest, but some of them made me feeling this kind of extraordinary shocks, both emotional and psychological, to which it is only possible to react by a booming "Wow !". Therefore, beside a review on my work on light scattering, the heart of the present paper is devoted to 4 wow stories related to the development of generalized Lorenz-Mie theories. They concern (i) the optical theorem (ii) the speed of laser light, slower than c (iii) the speed of light spots, faster than c and (iv) the "nature" of photons. This last issue required to extend the discussion from pure scientific issues to an epistemological discussion pertaining to the philosophy of sciences. [ABSTRACT FROM AUTHOR]