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Article

Generalization of the Optical Theorem to an Arbitrary Multipole Excitation of a Particle near a Transparent Substrate

1
Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Leninskie Gory 1, 119991 Moscow, Russia
2
Leibniz-Institute für Werkstofforientierte Technologien, University of Bremen, Badgasteiner Str. 3, 28359 Bremen, Germany
*
Author to whom correspondence should be addressed.
Academic Editor: Nikolaos Tsitsas
Mathematics 2021, 9(24), 3244; https://doi.org/10.3390/math9243244
Received: 21 October 2021 / Revised: 29 November 2021 / Accepted: 8 December 2021 / Published: 14 December 2021
(This article belongs to the Special Issue Analytical Methods in Wave Scattering and Diffraction)
In the present paper, the generalization of the optical theorem to the case of a penetrable particle deposited near a transparent substrate that is excited by a multipole of an arbitrary order and polarization has been derived. In the derivation we employ classic Maxwell’s theory, Gauss’s theorem, and use a special representation for the multipole excitation. It has been shown that the extinction cross-section can be evaluated by the calculation of some specific derivatives from the scattered field at the position of the multipole location, in addition to some finite integrals which account for the multipole polarization and the presence of the substrate. Finally, the present paper considers some specific examples for the excitation of a particle by an electric quadrupole. View Full-Text
Keywords: optical theorem; arbitrary order of multipole; Maxwell’s theory; Gauss’s theorem; transparent substrate; extinction cross-section optical theorem; arbitrary order of multipole; Maxwell’s theory; Gauss’s theorem; transparent substrate; extinction cross-section
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MDPI and ACS Style

Eremin, Y.A.; Wriedt, T. Generalization of the Optical Theorem to an Arbitrary Multipole Excitation of a Particle near a Transparent Substrate. Mathematics 2021, 9, 3244. https://doi.org/10.3390/math9243244

AMA Style

Eremin YA, Wriedt T. Generalization of the Optical Theorem to an Arbitrary Multipole Excitation of a Particle near a Transparent Substrate. Mathematics. 2021; 9(24):3244. https://doi.org/10.3390/math9243244

Chicago/Turabian Style

Eremin, Yuri A., and Thomas Wriedt. 2021. "Generalization of the Optical Theorem to an Arbitrary Multipole Excitation of a Particle near a Transparent Substrate" Mathematics 9, no. 24: 3244. https://doi.org/10.3390/math9243244

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