Solving problems of radiation and diffraction electromagnetic waves based on integral representations electromagnetic field


Cite item

Full Text

Abstract

Various forms of integral representations of the electromagnetic field are considered. It is shown that the use of analytically developed integral representations of the electromagnetic field instead of the vector potential method makes it possible to significantly simplify the formulation of the internal and external electrodynamic problem for specific structures. The numerical results of solving problems of radiation and diffraction of electromagnetic waves are presented. It is shown that taking into account the peculiarities of the geometry and using projection functions close to the eigenfunctions of the integral operator of the internal electrodynamic problem for basic elements make it possible to construct effective algorithms for the electrodynamic analysis of metastructures. A mathematical model of a multistage chiral frame is proposed. By the example of a tubular vibrator, the possibility of approximating the solution of an internal electrodynamic problem using eigenfunctions is demonstrated. The prospects for further development of the integral representations of the electromagnetic field method are considered.

About the authors

Dmitry P. Tabakov

Povolzhskiy State University of Telecommunications and Informatics

Author for correspondence.
Email: illuminator84@yandex.ru

Sergey V. Morozov

Povolzhskiy State University of Telecommunications and Informatics

Email: grimmxxx@gmail.com

References

  1. Gallager R. Finite Element Method. The Basics. Moscow: Mir, 1984, 428 p. (In Russ.)
  2. Mors F.M., Feshbah G. Methods of Theoretical Physics. T. 1. Moscow: Izdatel’stvo inostrannoj literatury, 1958, 931 p. (In Russ.)
  3. Neganov V.A., Nefedov E.I., Jarovoj G.P. Electrodynamic Design Methods for Microwave Devices and Antennas. Ed. by V.A. Neganov. Moscow: Radio i svjaz’, 2002, 416 p. (In Russ.)
  4. Neganov V.A., Tabakov D.P. Singular integral representations of the electromagnetic field as a means of correct solution of antenna problems. Physics of Wave Processes and Radio Systems, 2014, vol. 17, no. 3, pp. 9–23. URL: https://journals.ssau.ru/pwp/article/view/7263. (In Russ.)
  5. Neganov V.A., Tabakov D.P., Jarovoj G.P. Modern Theory and Practical Applications of Antennas. Ed. by V.A. Neganov. Moscow: Radiotehnika, 2009, 720 p. (In Russ.)
  6. Harrington R.F. Field Computation by Moment Method. New York: Macmillan, 1968, 150 p.
  7. Neganov V.A. Physical Regularization of Ill-Posed Problems in Electrodynamics: Transmission Lines, Antennas, Diffraction of Electromagnetic Waves. Moscow: Sajns-Press, 2008, 432 p. (In Russ.)
  8. Harrington R., Mautz J. Theory of characteristic modes for conducting bodies. IEEE Transactions on Antennas and Propagation, 1971, vol. 19, no. 5, pp. 622–628. DOI: https://doi.org/10.1109/TAP.1971.1139999.
  9. Garbacz R.J. Modal expansions for resonance scattering phenomena. Proceedings of the IEEE, 1965, vol. 53, no. 8, pp. 856–864. DOI: https://doi.org/10.1109/PROC.1965.4064.
  10. Tabakov D.P., Majorov A.G. On the eigenvalues of the integral operator of the singular integral equation of a thin tubular vibrator. Physics of Wave Processes and Radio Systems, 2019, vol. 22, no. 1, pp. 26–31. DOI: https://doi.org/10.18469/1810-3189.2019.22.1.26-31. (In Russ.)
  11. Tabakov D.P., Majorov A.G. Approximation of the solution of an internal electrodynamic problem for a thin tubular vibrator by the method of eigenfunctions. Trudy uchebnyh zavedenij svjazi, 2019, vol. 5, no. 4, pp. 58–64. DOI: https://doi.org/10.31854/1813-324X-2019-5-4-58-64. (In Russ.)
  12. Tabakov D.P. Fine-wire model of a symmetric fractal vibrator based on a Sierpinski napkin. Radiotehnika, 2015, no. 2, pp. 16–22. (In Russ.)
  13. Neganov V.A., Plotnikov A.M., Tabakov D.P. Electrodynamic analysis of resonant tags for radio frequency identification of objects by the method of singular integral equations. Radiotehnika i elektronika, 2012, vol. 57, no. 7, pp. 741–749. URL: https://www.elibrary.ru/item.asp?id=17794232. (In Russ.)
  14. Neganov V.A., Tabakov D.P. Correct electrodynamic analysis of chiral elements and metamaterials based on integral representations of the electromagnetic field. Physics of Wave Processes and Radio Systems, 2014, vol. 17, no. 3, pp. 29–39. URL: https://journals.ssau.ru/pwp/article/view/7265. (In Russ.)
  15. Neganov V.A., Osipov O.V. Reflective, Waveguiding and Radiating Structures with Chiral Elements. Moscow: Radio i svjaz’, 2006, 280 p. (In Russ.)
  16. Veselago V.G. Electrodynamics of substances with simultaneously negative values of e and m. Uspehi fizicheskih nauk, 1967, vol. 92, no. 7, pp. 517–526. DOI: https://doi.org/10.3367/UFNr.0092.196707d.0517. (In Russ.)
  17. Vendik I.B., Vendik O.G. Metamaterials and their Application in microwave engineering (Review). Zhurnal tehnicheskoj fiziki, 2013, vol. 83, no. 1, pp. 3–28. URL: http://journals.ioffe.ru/articles/41403. (In Russ.)
  18. Ivchenko E.L., Poddubnyj A.N. Resonant three-dimensional photonic crystals. Fizika tverdogo tela, 2006, vol. 48, no. 3, pp. 540–547. URL: https://journals.ioffe.ru/articles/3354. (In Russ.)
  19. Tabakov D.P. Application of iterative procedures to electrodynamic analysis of metamaterials. Radiotehnika, 2015, no. 7, pp. 86–94. (In Russ.)

Supplementary files

Supplementary Files
Action
1. JATS XML

Copyright (c) 2020 Tabakov D., Morozov S.

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

СМИ зарегистрировано Федеральной службой по надзору в сфере связи, информационных технологий и массовых коммуникаций (Роскомнадзор).
Регистрационный номер и дата принятия решения о регистрации СМИ: серия ФС 77 - 68199 от 27.12.2016.

This website uses cookies

You consent to our cookies if you continue to use our website.

About Cookies