T-matrix method for electromagnetic scattering from scatterers with complex structure

We describe a T-matrix program for light scattering calculations from particles with complex structure. The code treats the cases of homogeneous, layered and composite scatterers. These results are combined with basic results concerning the scattering by inhomogeneous scatterers and aggregates to apply to more general types of scatterers. Some numerical simulations are presented.     

Severe loss of precision in calculations of T-matrix integrals

A severe loss of precision is unravelled in the numerical calculation of surface integrals that appear in the Extended Boundary Condition Method (EBCM), to calculate the T-matrix elements of axisymmetric particles. We systematically study the occurrence of numerical cancellations for three basic particle shapes, namely cylinders, spheroids, and offset spheres, with typical sizes, aspect ratios and materials often studied as benchmark examples in the literature. The cancellations are evidenced both for spheroids and offset spheres, and are particularly pronounced in the latter case. The resulting loss of precision is independent from the commonly asserted problems of matrix inversion. We show that the origin of these severe cancellations can be further studied and understood by numerical investigations of the scaling of the integrands and integrals with respect to the particle size parameter. This allows us to develop a detailed mathematical proof of these cancellations. The results suggest that the EBCM method, in its usual formulation, suffers important numerical instabilities which reduce the domain of convergence for specific particle shapes that are commonly used for testing and benchmarking the method.     

Modified T-matrix formulation for multiple scattering of acoustic waves

In studying the multiple scattering of acoustic waves by distributed discrete scatterers, the 'two-exterior' T-matrix or the modified T-matrix is needed. In this paper, the modified T-matrix formulae for a scatterer of arbitrary shape are derived, based on Huygen's principle and the method of optimal truncation (MOOT), respectively. Analytical expressions are given for the modified T-matrix elements of a spheroid in the low-frequency limit. The agreement with the existing results is shown to be exact to the given order of ka. It is also shown that the results based on Huygen's principle are merely the special cases of those based on MOOT.     

Linearized T-matrix and Mie scattering computations

We present a new linearization of T-Matrix and Mie computations for light scattering by non-spherical and spherical particles, respectively. In addition to the usual extinction and scattering cross-sections and the scattering matrix outputs, the linearized models will generate analytical derivatives of these optical properties with respect to the real and imaginary parts of the particle refractive index, and (for non-spherical scatterers) with respect to the “shape” parameter (the spheroid aspect ratio, cylinder diameter/height ratio, Chebyshev particle deformation factor). These derivatives are based on the essential linearity of Maxwell's theory. Analytical derivatives are also available for polydisperse particle size distribution parameters such as the mode radius. The T-matrix formulation is based on the NASA Goddard Institute for Space Studies FORTRAN 77 code developed in the 1990s. The linearized scattering codes presented here are in FORTRAN 90 and will be made publicly available.     

Modified T-matrix formulation for multiple scattering of acoustic waves

Abstract

In studying the multiple scattering of acoustic waves by distributed discrete scatterers, the ‘two-exterior’ T-matrix or the modified T-matrix is needed. In this paper, the modified T-matrix formulae for a scatterer of arbitrary shape are derived, based on Huygen's principle and the method of optimal truncation (MOOT), respectively. Analytical expressions are given for the modified T-matrix elements of a spheroid in the low-frequency limit. The agreement with the existing results is shown to be exact to the given order of ka. It is also shown that the results based on Huygen's principle are merely the special cases of those based on MOOT.     

The off-shell electromagnetic T-matrix: momentum-dependent scattering from spherical inclusions with both dielectric and magnetic contrasts

The momentum- and frequency-dependent T-matrix operator for the scattering of electromagnetic waves by a dielectric/conducting and para- or diamagnetic sphere is derived as a Mie-type series, and presented in a compact form emphasizing various symmetry properties, notably the unitarity identity. This result extends to magnetic properties one previously obtained for purely dielectric contrasts by other authors. Several situations useful to spatially-dispersive effective-medium approximations to one-body order are examined. Partial summation of the Mie series is achieved in the case of elastic scattering.     

Analytic expressions for the partial waves of the off-shell two body coulomb T-matrix

Closed form expressions for all partial waves of the pure Coulomb off-shell T-matrix p¦ T_c,l.(k ²) ¦p are obtained. All singularities appear through simple special functions, which makes it possible to study the analytic properties of p¦ T_c,l(k²) ¦p as a function not only of one of the momentap, p but even of both of them. With use of the renormalization procedure found by Zorbas the transition to half-and on-shell values is performed reproducing known expressions. By the same method simple expressions for the partial waves of the Coulomb wave function in the momentum representation are found.     

Calculation of the two-body scattering T-matrix in configuration space

In order to carry out a solution of the three-body Faddeev integral equations in configuration space, the calculation of the two-body scattering T-matrices and related integrals are required as an input. The formulation of the three-body Faddeev solution, as well as the computational steps used for the calculation of the T-matrices are presented, and results for the latter are illustrated for the case of the scattering of two helium atoms.     

Two singular integrals containing a partial wave of the two-body coulomb T-matrix

The operatorsT _C,l E+i0)[–G ₀(E+i0)]^1–i andT _C,l(E+i)G ₀[–iG ₀(E+i)]ⁱ acting on spaces of Hölder continuous, differentiable and analytic functions are investigated. The results of their action are expressed in terms of explicit singular factors and terms and Hölder (differentiable, analytic) functions. The most singular part of these operators is shown to be determined by a simple functional.     

Analytic expressions for multi-centre integrals using Slater-type orbitals

The various decay mechanisms of the lowest triplet state of α-halogenated naphthalenes have been investigated by means of polarized light spectroscopy. Contrary to pure aromatic hydrocarbons, the halogenated derivatives exhibit strong in-plane polarization in the 00-transition of the phosphorescence, which is enhanced more rapidly than the out-of-plane polarized intensity if one increases the atomic number of the substituent. The various features of the polarized emission spectra are related to a second-order Herzberg-Teller coupling. This type of interaction can provide intensity for the 00-transition via out-of-plane promoting modes. It varies with the one centre spin-orbit integral, thus explaining the strong enhancement with the heavy atom. It accounts for a deuterium isotope effect in the radiative rate of the 00-transition and in the degree of polarization.     

Simplified mobility expressions for infinite in-vacuo pipes

In this paper, closed-form expressions for the mobility of the circumferential modes in an infinite in-vacuo thin-walled pipe are derived in terms of the axial wave receptances for each mode. These expressions are valid below the ring frequency. By using simplified expressions for the wavenumbers, low-frequency approximations for the point and transfer mobilities are also derived. These new mobility expressions are validated experimentally, and are used to examine the dynamic behaviour of an in-vacuo pipe.     

T-matrix analysis of electromagnetic wave differaction from a Fourier grating

This paper is described for T-matrix analysis of the electromagnetic wave diffraction from a Fourier grating that the boundary value problem is treated by applying the extended boundary condition. The rigorous form of the expression of matrix elements is presented in the term of Bessel functions of the first kind. The error of power conservation versus the truncated number has been examined for mode number. Diffraction efficiencies versus groove depth and wavelength for a second or third harmonic wave of Fourier grating have been discussed. Numerical results are in good agreement with those obtained from other method and experimental values. Reasonable numerical results are presented for a groove depth per period of the Fourier grating less than 0.25.     

利用T-matrix计算非球形粒子散射特性的研究

本文用T-matrix方法计算了非球形气溶胶粒子的光学特性,得到了气溶胶粒子的消光截面、散射截面、吸收截面与气溶胶粒子形状的关系,不同形状气溶胶粒子的有着相同的散射相函数和不同的偏振度,非球形气溶胶粒子的散射相函数对其复折射指数的实部和虚部都不太敏感,而偏振相函数对其实部和虚部都比较敏感.此结论为研究大气辐射传输提供了较好的方法,尤其是偏振度与偏振相函数的提出为用偏振的方法进一步的反演气溶胶的光学参数提供了理论基础.     

Simplified closed form expressions for irreducible tensor operators

A general closed form expression is derived which enables one to write a spherical tensor of rank L and projection k, T_uk^L, in terms of the familiar angular momentum operators, S_z and S². The simplicity of this expression results from an intriguing relationship between these spherical tensor operators (diagonal operator equivalents) and successive derivatives of Tchebichef orthogonal polynomials.     

T-matrix for the morse potential

The s-wave part of the T-matrix on the mass shell was obtained from the well-known solution of the s-wave Schrödinger equation for the Morse potential. The result is expressed in terms of the confluent hypergeometric function.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 27–29, May, 1975.     

T-matrix for the mongan potential

The Jost functions and the T-matrix outside an energy surface are obtained by applying the method of van Leeuwen and Reiner to scattering by a nonlocal separable potential.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 27–30, 1980.     

电磁散射问题的两种反演方法研究

提出了电磁散射问题的两种反演方法:确定性梯度搜索方法和MonteCarlo随机搜索方法.给出了两种方法的基本原理,并对反演性能包括对散射体的定位能力、反演精度、反演时间进行了系统的分析与比较.数值计算结果表明,确定性方法定位精确,而随机性方法对散射体电磁参数的反演精度高且速度快,利用两者优点可以增强反演效果.     

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.     

Simplified analytical expressions for classical turning points of molecular oscillators

Simplified analytical expressions for classical turning ppoints (r_1,2) are derived by expanding the empirical potential function of Dunham and Morse in series forms. These expressions are equivalent to those obtained by Rees when the energy (E) is quadratic in the vibrational quantum number. Our first approximation approach is also found to be equivalent to Jarmain's factor f/r_e.     

Simplified universal screened Coulomb potential for ion scattering

Coulomb's interaction of ions is complicated by the presence of electronic shells. A major variety of more or less complex screening functions has been proposed over a time span of about 80 years. A simple universal screening function with only one fitting parameter is presented here.