Abstract
Different variants of the problem of diffraction of spherical electromagnetic wave by axial-symmetric bodies are researched in the work. These problems are reduced to infinite sets of linear algebraic equations. The joining method is used. The conductive bodies, dielectric bodies and spherical conductive screens on the coordinate and non-coordinate boundaries are considered. The results of the computational experiment are presented.
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REFERENCES
G. Mie, ‘‘Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen,’’ Ann. Phys. 330, 337–445 (1908).
T. Wriedt, ‘‘Mie theory: A review,’’ in The Mie Theory, Vol. 169 of Springer Series in Optical Sciences (Springer, Berlin, 2012).
V. Kerker, D. S. Wang, and C. L. Giles, ‘‘Electromagnetic scattering by magnetic spheres,’’ J. Opt. Soc. Am. 73, 765–767 (1983).
O. P. Ponomarev, ‘‘Solutions of Maxwell set in the spherical coordinate systems using rotation group. Appendix for spherical mirror antennas,’’ Radiotekhnika 4, 77–78 (2006).
I. T. Selezov and Iu. G. Kryvonos, ‘‘On mathematical modeling of interaction of electromagnetic field with biological systems,’’ J. Aut. Inf. Sci. 45, 4–13 (2013).
H. Hönl, A. W. Maue, and K. Westpfahl, Theorie der Beugung (Springer, Berlin, 1961) [in German].
A. Angot, Compléments de mathématiques a l’usage des ingénieurs de l’électrotechnique et des télecommunications (Paris, 1957) [in French].
J. A. Stratton, Electromagnetic Theory (McGraw-Hill, New York, 1941).
I. E. Pleshchinskaya and N. B. Pleshchinskii, ‘‘Infinite sets of linear algebraic equations in the problems of diffraction of electromagnetic waves by the non-coordinate periodic media interfaces,’’ Lobachevskii J. Math. 40 (10), 1685–1694 (2019).
I. E. Pleshchinskaya and N. B. Pleshchinskii, ‘‘On the scattering of electromagnetic waves by cylindrical bodies with non-coordinate boundaries,’’ Lobachevskii J. Math. 41, 1385–1395 (2020).
N. B. Pleshchinskii and D. N. Tumakov, ‘‘A new approach to investigation of Maxwell equations in spherical coordinates,’’ Lobachevskii J. Math. 36 (1), 15–27 (2015).
M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1972).
G. V. Abgaryan and N. B. Pleshchinskii, ‘‘On the eigen frequencies of rectangular resonator with a hole in the wall,’’ Lobachevskii J. Math. 40 (10), 1631–1639 (2019).
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This paper has been supported by the Kazan Federal University Strategic Academic Leadership Program.
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(Submitted by E. E. Tyrtyshnikov)
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Pleshchinskaya, I.E., Pleshchinskii, N.B. On the Scattering of Electromagnetic Waves by Axial-Symmetric Bodies. Lobachevskii J Math 42, 1381–1390 (2021). https://doi.org/10.1134/S1995080221060226
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DOI: https://doi.org/10.1134/S1995080221060226