Wave-amplitude synthesis applied to Gaussian-beam scattering by an off-axis sphere

Dimitrios P. Chrissoulidis; Elodie Richalot

doi:10.1364/JOSAA.34.000558

Journal of the Optical Society of America A
Vol. 34,
Issue 4,
pp. 558-567
(2017)
•https://doi.org/10.1364/JOSAA.34.000558

Wave-amplitude synthesis applied to Gaussian-beam scattering by an off-axis sphere

Dimitrios P. Chrissoulidis and Elodie Richalot

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Dimitrios P. Chrissoulidis and Elodie Richalot, "Wave-amplitude synthesis applied to Gaussian-beam scattering by an off-axis sphere," J. Opt. Soc. Am. A 34, 558-567 (2017)

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Abstract

Electromagnetic scattering of a Gaussian beam by an off-axis dielectric sphere is treated by the sum-of-waves formulation, which is inherent in Lorenz–Mie theory. Each “wave” is a spherical eigenvector, defined in the natural frame of the scatterer, and the coefficient of that wave is the “wave amplitude.” Decomposition of the beam into homogeneous plane waves lays the ground for a synthesis of the wave amplitudes, which is done by an integration over the polar angle that defines the direction of propagation of the plane-wave constituents of the beam. Concise analytical results are developed for (a) the electric-field intensity in every part of space, (b) the bistatic and monostatic radar cross sections of the scatterer, and (c) the power extracted from the beam by scattering and absorption. Numerical calculations are made for a spherical glycerol droplet of radius 1.5 μm that is excited by an adjacent, infrared, Gaussian beam of wavelength 1.1424 μm and spot size 2 μm. The numerical application manifests (a) how the beam is coupled with the droplet and (b) the effect of the droplet on the power intercepted by a receiver-end fiber placed on the beam axis, beyond the focal plane. Comparisons to numerical results obtained by a finite-element method software (a) validate the sum-of-waves theory, (b) evaluate the performance of the code implementing that theory, and, succinctly, (c) manifest the limits of the plane-wave decomposition of the beam.

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$d$ (μm)	0	2	4	6	8
$ν_{\max} = 30$	−7.92	−6.14	−5.38	−12.74	−33.05
$ν_{\max} = 40$	−7.92	−6.17	−4.37	−5.48	−13.72
$ν_{\max} = 50$	−7.91	−6.17	−4.38	−4.26	−5.78
$ν_{\max} = 60$	−7.91	−6.17	−4.38	−4.27	−4.27
$ν_{\max} = 70$	−7.92	−6.17	−4.38	−4.27	−4.27
$ν_{\max} = 80$	−7.92	−6.17	−4.38	−4.27	−4.27
$ν_{\max} = 90$	−7.91	−6.17	−4.38	−4.27	−4.27
HFSS	−7.49	−6.04	−4.44	−4.35	−4.35
error (%)	−9.43	−2.93	1.39	1.88	1.88

$d$ (μm)	0	2	4	6	8
$ν_{\max} = 30$	−23.16	−21.52	−21.37	−28.62	−48.89
$ν_{\max} = 40$	−23.09	−21.38	−19.95	−21.42	−29.87
$ν_{\max} = 50$	−23.03	−21.36	−19.90	−19.93	−21.88
$ν_{\max} = 60$	−23.08	−21.44	−20.01	−19.89	−19.97
$ν_{\max} = 70$	−23.43	−21.73	−20.16	−19.84	−19.68
$ν_{\max} = 80$	−24.09	−22.10	−20.17	−19.70	−19.68
$ν_{\max} = 90$	−24.42	−22.14	−20.05	−19.73	−19.88
HFSS	−22.70	−21.29	−19.96	−19.78	−19.78
error (%)	−7.45	−1.6	0.18	1.14	−2.28

$L$ (μm)	20	150	450
$ν_{\max} = 30$	−4.27	−19.66	−29.16
$ν_{\max} = 40$	−4.27	−19.62	−29.11
$ν_{\max} = 50$	−4.26	−19.58	−29.00
$ν_{\max} = 60$	−4.26	−19.63	−28.84
$ν_{\max} = 70$	−4.27	−19.88	−28.63
$ν_{\max} = 80$	−4.27	−20.31	−28.40
$ν_{\max} = 90$	−4.26	−20.48	−27.45

$d$ (μm)	0	2	4	6	8
$ν_{\max} = 30$	−7.92	−6.14	−5.38	−12.74	−33.05
$ν_{\max} = 40$	−7.92	−6.17	−4.37	−5.48	−13.72
$ν_{\max} = 50$	−7.91	−6.17	−4.38	−4.26	−5.78
$ν_{\max} = 60$	−7.91	−6.17	−4.38	−4.27	−4.27
$ν_{\max} = 70$	−7.92	−6.17	−4.38	−4.27	−4.27
$ν_{\max} = 80$	−7.92	−6.17	−4.38	−4.27	−4.27
$ν_{\max} = 90$	−7.91	−6.17	−4.38	−4.27	−4.27
HFSS	−7.49	−6.04	−4.44	−4.35	−4.35
error (%)	−9.43	−2.93	1.39	1.88	1.88

$d$ (μm)	0	2	4	6	8
$ν_{\max} = 30$	−23.16	−21.52	−21.37	−28.62	−48.89
$ν_{\max} = 40$	−23.09	−21.38	−19.95	−21.42	−29.87
$ν_{\max} = 50$	−23.03	−21.36	−19.90	−19.93	−21.88
$ν_{\max} = 60$	−23.08	−21.44	−20.01	−19.89	−19.97
$ν_{\max} = 70$	−23.43	−21.73	−20.16	−19.84	−19.68
$ν_{\max} = 80$	−24.09	−22.10	−20.17	−19.70	−19.68
$ν_{\max} = 90$	−24.42	−22.14	−20.05	−19.73	−19.88
HFSS	−22.70	−21.29	−19.96	−19.78	−19.78
error (%)	−7.45	−1.6	0.18	1.14	−2.28

Abstract

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Figures (10)

Tables (3)

Equations (36)

Journal of the Optical Society of America A