smarties: User-friendly codes for fast and accurate calculations of light scattering by spheroids

Somerville, Walter R. C.; Auguié, Baptiste; Ru, Eric C. Le

doi:10.1016/j.jqsrt.2016.01.005

Cited by 53 publications

(59 citation statements)

References 22 publications

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“…Recently, we have identified the origin of those problems in the special case of spheroids [27] and proposed an improved algorithm to overcome them [28]. This new implementation, for which user-friendly codes are freely available [29], provides unprecedented accuracy for the computation of the T-matrix and the field expansion coefficients [30]. It therefore provides a reliable basis, enabling us to study the range of validity of the RH in the context of near-field computations without the interference of numerical instabilities.…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of the Rayleigh hypothesis for electromagnetic scattering by a particle

Auguié

Somerville

Roache

et al. 2016

J. Opt.

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The validity of the Rayleigh hypothesis (RH) has been a long-standing issue in the applicability of the T-matrix method to near-field calculations, and despite numerous theoretical works, the practical consequences for numerical simulations have remained unclear. Such calculations are increasingly important in the field of nano-optics, for which accurate and efficient modeling tools are in high demand. We here tackle this challenge by investigating numerically the convergence behavior of series expansions of the electric field around spheroidal particles, which provides us with unambiguous examples to clarify the conditions of convergence. This study is made possible by the combination of alternative methods to compute near-fields accurately, and crucially, the recent improvements in the calculation of T-matrix elements free from numerical instabilities, as such errors would otherwise obfuscate the intrinsic convergence properties of the field series. The resulting numerical confirmation for the range of validity of the RH, complemented by a better understanding of the convergence behavior of the field expansions, is a crucial step toward future developments.

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Section: Introductionmentioning

confidence: 99%

Numerical investigation of the Rayleigh hypothesis for electromagnetic scattering by a particle

Auguié

Somerville

Roache

et al. 2016

J. Opt.

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“…Our implementation supports double and quad precision calculations, using Amos' library to calculate the Bessel functions [42], and BLAS/LAPACK routines to solve (5). It can also import accurate T-matrices calculated for a spheroid using our improved algorithms, [43]. Note that our discussion of the underlying formalism was based on infinite series expansions, but in practice all the series are truncated at a specified multipole order n c -an input parameter for our calculations.…”

Section: Resultsmentioning

confidence: 99%

Mind the gap: testing the Rayleigh hypothesis in T-matrix calculations with adjacent spheroids

Schebarchov

Grand

et al. 2019

Opt. Express

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The T-matrix framework offers accurate and efficient modelling of electromagnetic scattering by nonspherical particles in a wide variety of applications ranging from nano-optics to atmospheric science. Its analytical setting, in contrast to purely numerical methods, also provides a fertile ground for further theoretical developments. Perhaps the main purported limitation of the method, when extended to systems of multiple particles, is the often-stated requirement that the smallest circumscribed spheres of neighbouring scatterers not overlap. We consider here such a scenario with two adjacent spheroids whose aspect ratio we vary to control the overlap of the smallest circumscribed spheres, and compute far-field cross-sections and near-field intensities using the superposition T-matrix method. The results correctly converge far beyond the no-overlap condition, and although numerical instabilities appear for the most extreme cases of overlap, requiring high multipole orders, convergence can still be obtained by switching to quadruple precision. Local fields converge wherever the Rayleigh hypothesis is valid for each single scatterer and, remarkably, even in parts of the overlap region. Our results are validated against finite-element calculations, and the agreement demonstrates that the superposition T-matrix method is more robust and broadly applicable than generally assumed.

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“…Section III summarizes the results obtained in Ref. [11] for T 22 . Section IV modifies the approach of Ref.…”

Section: Introductionmentioning

confidence: 89%

Quasistatic limit of the electric-magnetic coupling blocks of the T-matrix for spheroids

Majic

2019

Journal of Quantitative Spectroscopy and Radiative Transfer

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The T -matrix formally describes the solution of any electromagnetic scattering problem by a given particle in a given medium at a given wavelength. As such it is commonly used in a number of contexts, for example to predict the orientation-averaged optical properties of nonspherical particles. The T -matrix for electromagnetic scattering can be divided into four blocks corresponding physically to coupling between either magnetic or electric multipolar fields. Analytic expressions were recently derived for the electrostatic limit of the electric-electric T -matrix block T 22 , of prolate spheroids. In such an electrostatic approximation, all the other blocks were zero. We here analyse the long-wavelength limit for the other blocks (T 21 , T 12 , T 11 ) corresponding to electric-magnetic, magnetic-electric, and magnetic-magnetic coupling respectively. Analytic expressions (finite sums) are obtained in the case of spheroidal particles by expressing the fields with solutions to Laplace's equation, expanding the fields in terms of spheroidal harmonics and applying the boundary conditions. Similar expressions are also presented for the auxiliary matrices in the extended boundary condition method, often used in conjunction with the T -matrix formalism.

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smarties: User-friendly codes for fast and accurate calculations of light scattering by spheroids

Cited by 53 publications

References 22 publications

Numerical investigation of the Rayleigh hypothesis for electromagnetic scattering by a particle

Numerical investigation of the Rayleigh hypothesis for electromagnetic scattering by a particle

Mind the gap: testing the Rayleigh hypothesis in T-matrix calculations with adjacent spheroids

Quasistatic limit of the electric-magnetic coupling blocks of the T-matrix for spheroids

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