Mathematical model of propagation of electromagnetic waves in composite media with spheroidal particles
Abstract
A mathematical model describing the propagation of monochromatic electromagnetic waves in a medium with spatial dispersion containing spheroidal particles of the along prescribed direction has been developed. The initial classical integro-differential model for electromagnetic fields in a medium with spatial dispersion is transformed, within the third-order infinitesimal, to the differential model, where the integro-differential Maxwell equations are represented as a system of second-order differential equations. In this case electrical and magnetic polarizations of the medium are given in the Laplace operators. This system of equations is analytically solved; a complete system of four forward and four backward counter-propagating electromagnetic waves is formed. The analytical representation of the fields includes a vector determining the propagation direction of plane waves. Wave numbers of the fields also depend on their propagation directions pointing to anisotropic character of the developed mathematical model.
About the Authors
V. T. Erofeenko
Institution of the Belarusian State University “Research Institute for Applied Problems of Mathematics and Informatics”
Belarus
Belarus
Viktor T. Erofeenko – Dr. Sc. (Physics and Mathematics), Professor, Chief Research Associate of the Research Laboratory of Mathematical Methods of Information Security.
4, Nezavisimosti Ave., 220030, Minsk
A. I. Urbanovich
Belarusian State University
Belarus
Belarus
Aleksandr I. Urbanovich – Ph. D. (Physics and Mathematics), Associate Professor at the Department of Mathematical Modeling and Control, Docent, Faculty of Applied mathematics and computer science.
4, Nezavisimosti Ave., 220030, Minsk
References
1. Vinogradov A. P. Jelektrodinamika kompozitnyh materialov. Electrodynamics of Composite Materials. Moscow, Editorial URSS Publ., 2001, 206 p. (in Russian).
2. Kostin M. V., Schevchenko V. V. K teorii kiralnoj sredy na osnove sfericheskikh spiralno provodyaschih chastits [The theory of the chiral medium on the spherical helically conductive particles basis]. Radiotehnika i elektronika [Radio Engineering and Electronics], 1998, vol. 43, no. 8, pp. 921–926 (in Russian).
3. Shatrov A. D. Model biizotropnoj sredy iz rezonansnyh sfericheskih chastits s idealnoj smeshannoj provodimostju poverhnosti vdol spiralnyh linij [Biisotropic medium model of resonant spherical particles with ideal mixed surface conductivity along helical line]. Radiotehnika i elektronika [Radio Engineering and Electronics], 2000, vol. 45, no. 10, pp. 1168–1170 (in Russian).
4. Erofeenko V. T., Demidchik V. I., Malyi S. V., Kornev R. V. Proniknovenie jelektromagnitnyh voln cherez kompozitnye ekrany, soderzhashhie ideal'no provodjashhie spirali [Penetration of electromagnetic waves through composite screens containing ideally conducting spirals]. Inzhenerno-fizicheskiy zhurnal [Journal of Engineering Physics and Thermophysics], 2011, vol. 84, no. 4, pp. 740–746 (in Russian).
5. Balagurov B. Y. O vliyanii formy vkluchenij na provodimost dvumernih modelej kompozitov [The inclusion forms influence on the two-dimensional composites models conductivity]. Zhurnal tehnicheskoj fiziki [Technical Physics Journal], 2011, vol. 81(5), pp. 5–8 (in Russian).
6. Erofeenko V. T. Electrodinamicheskaya model rascheta effektivnyh parametrov kompozitov iz sfericheskih biizotropnyh chastits [Electrodynamic model of calculation of effective parameters of composites from spherical isotropic particles]. Informatika [Informatics], 2014, no. 1(41), pp. 45–58 (in Russian).
7. Erofeenko V. T., Bondarenko V. F. Ekranirovanie elekrtomagnitnyh voln ploskim odnoslojnym ekranom iz materialov s prostranstvennoj dispersiej [Shielding of electromagnetic waves by a flat single-layer screen of materials with spatial dispersion]. Informatika [Informatics], 2017, vol. 4(56), pp. 5–15 (in Russian).
8. Erofeenko V. T., Bondarenko V. F. Ekranirovanie elektromagnitnyh polej ekranami iz matrichnyh kompozitov, soderzhashhih biizotropnye chasticy [Screening of electromagnetic fields by screens from matrix composites containing bi-isotropic particles]. Informatika [Informatics], 2014, no. 3(43), pp. 28–43 (in Russian).
9. Agranovich V. M., Ginzburg V. L. Kristallooptika s uchetom prostranstvennoj dispersii i teorija jeksitonov. Crystal Optics with Allowance for Spatial Dispersion and the Theory of Excitons. Moscow, Nauka Publ., 1979, 432 p. (in Russian).
10. Silin R. A., Timoshina I. R. Obratnye volny i prostranstvennaja dispersija [Reverse waves and spatial dispersion]. Radiotekhnika i elektronika [Radio Engineering and Electronics], 2012, vol. 57, no. 7, pp. 725–733 (in Russian).
11. Erofeenko V. T., Kozlovskaja I. S. Analiticheskoe modelirovanie v jelektrodinamike. Analytical Modeling in Electrodynamics. Minsk, BGU, 2010, 304 p. (in Russian).
12. Erofeenko V. T. Modelirovanie rasprostranenija jelektromagnitnyh voln v sredah s prostranstvennoj dispersiej [Modeling the propagation of electromagnetic waves in media with spatial dispersion]. Informatika [Informatics], 2017, no. 3(55), pp. 5–12 (in Russian).
13. Ivanov E. A. Difraktsiya electromagnitnyh voln na dvuh telah. Diffraction of Electromagnetic Waves on Two Bodies. Minsk, Nauka i tehnika Publ., 1968, 584 р. (in Russian).
Review
For citations:
Erofeenko V.T., Urbanovich A.I. Mathematical model of propagation of electromagnetic waves in composite media with spheroidal particles. Informatics. 2018;15(3):102-112. (In Russ.)
Views: 934
Email this article 