Separation of variables method for multilayered nonspherical particles

A separation of variables method based on expansions of the electromagnetic fields in terms of spherical wave functions is expanded at nonspherical (axisymmetric) particles with a rather large number of layers. Commonly used alternative approaches to systems of linear algebraic equations relative to unknown field expansion coefficients for layered particles are considered in some detail. The SVM code developed is compared with the EBCM, GMT and DDA codes designed for multilayered scatterers and some numerical results obtained for nonspherical scatterers with up to 100 layers are presented as illustrations.     

Electromagnetic scattering by nonspherical particles: Recent advances

This note gives a short introduction to the reprint of the article “Numerical methods in electromagnetic scattering theory” by Kahnert, M (JQSRT 2003;79-80:775-824). Some of the most important developments in the field since the publication of this article are briefly reviewed. A list of typos that have been identified in the original article is given in the appendix.     

Radiation force caused by scattering, absorption, and emission of light by nonspherical particles

General formulas for computing the radiation force exerted on arbitrarily oriented and arbitrarily shaped nonspherical particles due to scattering, absorption, and emission of electromagnetic radiation are derived. For randomly oriented particles with a plane of symmetry, the formula for the average radiation force caused by the particle response to external illumination reduces to the standard Debye formula derived from the Lorenz–Mie theory, whereas the average radiation force caused by emission vanishes.     

Light scattering by slightly nonspherical particles on surfaces

We investigate the shape dependence of the scattering by dielectric and metallic particles on surfaces by considering particles whose free-space scattering properties are nearly identical. The scattering by metallic particles is strongly dependent on the shape of the particle in the region near where the particle touches the surface. The scattering by dielectric particles displays a weaker, but nonetheless significant, dependence on particle shape. These results have a significant effect on the use of light scattering to size and identify particles on surfaces.     

Near- and far-field light scattering by nonspherical particles: Applicability of methods that involve a spherical basis

The separation of variables method for coordinate system, the extended boundary condition method, and the point-matching method that are used to solve the problem of light scattering by nonspherical particles are considered from a unified viewpoint. It is shown that, if the mathematical correctness condition (the Rayleigh hypothesis) holds, these methods are interrelated and are equivalent. The applicability ranges of the methods in the near- and far-field zones are analyzed, discussed, and compared on both analytical (based on analytical investigations) and practical (based on numerical calculations) grounds.     

Analysis of the method of generalized separation of variables in the problem of light scattering by small axisymmetric particles

In the problem of light scattering by small axisymmetric particles, we have constructed the Rayleigh approximation in which the polarizability of particles is determined by the generalized separation of variables method (GSVM). In this case, electric-field strengths are gradients of scalar potentials, which are represented as expansions in term of eigenfunctions of the Laplace operator in the spherical coordinate system. By virtue of the fact that the separation of variables in the boundary conditions is incomplete, the initial problem is reduced to infinite systems of linear algebraic equations (ISLAEs) with respect to unknown expansion coefficients. We have examined the asymptotic behavior of ISLAE elements at large values of indices. It has been shown that the necessary condition of the solvability of the ISLAE coincides with the condition of correct application of the extended boundary conditions method (ЕВСМ). We have performed numerical calculations for Chebyshev particles with one maximum (also known as Pascal’s snails or limaçons of Pascal). The obtained numerical results for the asymptotics of ISLAE elements and for the matrix support theoretical inferences. We have shown that the scattering and absorption cross sections of examined particles can be calculated in a wide range of variation of parameters with an error of about 1–2% using the spheroidal model. This model is also applicable in the case in which the solvability condition of the ISLAE for nonconvex particles is violated; in this case, the SVM should be considered as an approximate method, which frequently ensures obtaining results with an error less than 0.1–0.5%.     

Electrostatic solution and rayleigh approximation for small nonspherical particles in a spheroidal basis

The electrostatic problem for the case of axially symmetric particles is analyzed in a spheroidal basis. In this case, the wavenumber is zero and Maxwell’s equations are reduced to the Laplace equation for scalar potentials. An alternative approach involves solving integral equations that are similar to those obtained within the framework of the extended boundary conditions method. The scalar potentials are represented as expansions in terms of eigenfunctions of the Laplace equation in a spheroidal frame of reference, and unknown expansion coefficients are determined from an infinite set of linear algebraic equations (the separation of variables method). These two approaches yield exact solutions of the problem in the case of axially symmetric particles, which coincide with known solutions in particular cases. Investigation of infinite systems allowed finding the boundaries where these algorithms are valid. Numerical calculations showed that, for spheroidal Chebyshev particles (i.e., perturbed spheroids), the Rayleigh approximation based on the electrostatic solution is applicable in a wide range of the problem parameters and is in fair agreement with the results obtained using the discrete dipole approximation.     

Development of TUSCAT: A software for light scattering studies on spherical, spheroidal and cylindrical particles

An integrated software package TUSCAT (Tezpur University SCATtering Software) incorporated with a graphical user interface (GUI) was developed for modeling electromagnetic scattering from small particles and also to yield characteristic properties of the scattering particles from experimental data. Its interactive features enable the user to observe the changes in output scattering properties in real time. In addition to its ease of use, it has high computational accuracy, efficiency, reliability and adaptability.     

Anomalous light scattering by small particles

Light scattering by a small spherical particle with a low dissipation rate is discussed based upon the Mie theory. It is shown that if close to the plasmon (polariton) resonance frequencies the radiative damping prevails over dissipative losses, sharp giant resonances with very unusual properties may be observed. In particular, the resonance extinction cross section increases with an increase in the order of the resonance (dipole, quadrupole, etc.); the characteristic values of electric and magnetic near fields for the scattered light are singular in the particle size, while energy circulation in the near field is rather complicated, so that the Poynting vector field includes singular points whose number, types, and positions are very sensitive to fine changes in the incident light frequency. The results may provide new opportunities for a giant, controlled, highly frequency-sensitive enhancement and variation of electromagnetic field at nanoscales.     

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.     

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.     

Light scattering by multilayered axisymmetric particles: Solution of the problem by the separation of variables method

A new solution to the problem of light scattering by multilayered particles possessing axial symmetry is obtained. Two methods are applied for this purpose. One is the separation of variables method with expansion of fields in terms of spherical wave functions, and the other is a novel approach based on the separation of fields into axisymmetric and nonaxisymmetric parts and on the choice of specific scalar potentials for each of them. A specific feature of the new solution is that the dimension of truncated linear algebraic systems used for determining unknown expansion coefficients of fields does not increase with an increasing number of layers. Using double-and three-layer spheroidal and Chebyshev particles of different shape and size as examples, the domain of applicability of the solution presented is compared with that of the solution previously obtained by the extended boundary conditions method. Except for nearly spherical particles, the solution presented is shown to be more favorable than the previously obtained solution.     

用蒙特卡罗方法计算光通过薄层随机分布粒子的散射

本文利用蒙特卡罗方法计算准直光束通过薄层随机分布粒子散射的透射和反射光强,并和输运理论的扩散近似结果做了比较。当散射接近各向同性时两者符合良好。当散射明显地成为各向异性时,蒙特卡罗方法的结果是合理的,而输运理论的扩散近似失效。     

Introduction to light scattering by Gaussian random particles

Background, current status, and future prospects are offered for “Light scattering by Gaussian random particles: Ray-optics approximation” [1]. The stochastic geometry of the random particle is called the Gaussian random sphere. The radial distance of the Gaussian sphere is lognormally distributed. Two logarithmic radial distances at a given great-circle angle apart relate to one another according to the covariance function. Sample Gaussian particles can be conveniently generated using a Legendre polynomial expansion for the covariance function and a spherical harmonics expansion for the logarithmic radial distance. The ray-optics approximation consists of the geometric-optics and forward-diffraction parts fully accounting for polarization. It is valid for particles much larger than the wavelength of incident light and with central phase differences much larger than unity. The numerical ray-tracing algorithms are general and, in principle, applicable computationally to arbitrarily shaped non-spherical particles.     

On scattering of light by small axially symmetric particles

Light scattering by small dielectric particles of an arbitrary axially symmetric shape is analyzed. A simple approximate expression that governs the polarizability of the particle is found under the assumption of field homogeneity inside of these particles. The expression includes four relatively simple one-dimensional integrals that can be calculated analytically for some types of particles (except for spheroids). A comparison with the numerical data obtained for various Chebyshev particles and finite cylinders showed that the obtained approximation yields acceptable results, even when the shape of scatterers is significantly different from spheroidal. For spheroids, our approximation coincides with the Rayleigh one.