Scattering matrix of arbitrarily shaped objects: combining finite elements and vector partial waves

Guillaume Demésy; Jean-Claude Auger; Brian Stout

doi:10.1364/JOSAA.35.001401

Journal of the Optical Society of America A
Vol. 35,
Issue 8,
pp. 1401-1409
(2018)
•https://doi.org/10.1364/JOSAA.35.001401

Scattering matrix of arbitrarily shaped objects: combining finite elements and vector partial waves

Guillaume Demésy, Jean-Claude Auger, and Brian Stout

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Guillaume Demésy, Jean-Claude Auger, and Brian Stout, "Scattering matrix of arbitrarily shaped objects: combining finite elements and vector partial waves," J. Opt. Soc. Am. A 35, 1401-1409 (2018)

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Abstract

We demonstrate the interest of combining finite element calculations with the vector partial wave formulation (used in $T$ -matrix and Mie theory) in order to characterize the electromagnetic scattering properties of isolated individual scatterers. This method consists of individually feeding the finite element problem with incident vector partial waves in order to numerically determine the $T$ -matrix elements of the scatterer. For a sphere and a spheroid, we demonstrate that this method determines the scattering matrix to high accuracy. Recurrence relations for a fast determination of the vector partial waves are given explicitly, and an open-source code allowing the retrieval of the presented numerical results is provided.

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Equations (74)

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Source Type	Expansion Coefficient	$T_{i, j}$	$R e {T_{i, j}}$	$I m {T_{i, j}}$	$\| 2 T_{i, j} + 1 \|$	Relative Error/Mie	$σ_{i, j}^{cuts}$
$M_{1, 1}^{(1)}$	$f_{1, 1}^{(h)}$	$T_{1, 1}$	$- 1.2385259697 \times 10^{- 02}$	$- 1.1056579997 \times 10^{- 01}$	0.999986	$1.1 \times 10^{- 03}$	$3.258 \times 10^{- 06}$
$M_{1, 0}^{(1)}$	$f_{1, 0}^{(h)}$	$T_{2, 2}$	$- 1.2385169286 \times 10^{- 02}$	$- 1.1057000518 \times 10^{- 01}$	0.999988	$1.1 \times 10^{- 03}$	$3.045 \times 10^{- 06}$
$M_{1, - 1}^{(1)}$	$f_{1, - 1}^{(h)}$	$T_{3, 3}$	$- 1.2385200511 \times 10^{- 02}$	$- 1.1056590287 \times 10^{- 01}$	0.999986	$1.1 \times 10^{- 03}$	$3.694 \times 10^{- 06}$
	Mie		$- 1.24056 \times 10^{- 02}$	$- 1.10688 \times 10^{- 01}$
$N_{1, 1}^{(1)}$	$f_{1, 1}^{(e, ∥)}$	$T_{4, 4}$	$- 8.1416217938 \times 10^{- 02}$	$- 2.7344033443 \times 10^{- 01}$	0.999964	$4.1 \times 10^{- 04}$	$2.707 \times 10^{- 05}$
$N_{1, 0}^{(1)}$	$f_{1, 0}^{(e, ∥)}$	$T_{5, 5}$	$- 8.1414532024 \times 10^{- 02}$	$- 2.7344674202 \times 10^{- 01}$	0.999974	$4.0 \times 10^{- 04}$	$3.259 \times 10^{- 05}$
$N_{1, - 1}^{(1)}$	$f_{1, - 1}^{(e, ∥)}$	$T_{6, 6}$	$- 8.1415303240 \times 10^{- 02}$	$- 2.7344188994 \times 10^{- 01}$	0.999967	$4.1 \times 10^{- 04}$	$2.776 \times 10^{- 05}$
$N_{1, 1}^{(1)}$	$f_{1, 1}^{(e, ⊥)}$	$T_{4, 4}$	$- 8.1384568157 \times 10^{- 02}$	$- 2.7343965268 \times 10^{- 01}$	1.000016	$4.7 \times 10^{- 04}$	$2.994 \times 10^{- 04}$
$N_{1, 0}^{(1)}$	$f_{1, 0}^{(e, ⊥)}$	$T_{5, 5}$	$- 8.1368265239 \times 10^{- 02}$	$- 2.7342113303 \times 10^{- 01}$	1.000023	$5.6 \times 10^{- 04}$	$5.510 \times 10^{- 04}$
$N_{1, - 1}^{(1)}$	$f_{1, - 1}^{(e, ⊥)}$	$T_{6, 6}$	$- 8.1387379353 \times 10^{- 02}$	$- 2.7344185603 \times 10^{- 01}$	1.000014	$4.6 \times 10^{- 04}$	$3.072 \times 10^{- 04}$
	Mie		$- 8.14651 \times 10^{- 02}$	$- 2.73548 \times 10^{- 01}$

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Journal of the Optical Society of America A