Theory and practical application of Riemann-Zilberstein vectors for the tasks of antenna technology

 

B. L. Kogan, I. V. Bel’kovich

National Research University Moscow Power Engineering Institute, Krasnokazarmennaya 14, Moscow 11250, Russia

 

The paper is received on October 5, 2018

 

Abstract. Exact vector solution of Maxwell’s equations describing an electromagnetic field in electrically large tasks as large antennas or beam-waveguides are always time-consuming, requiring substantial computational resources. There exist many asymptotic methods simplifying the problem but having significant assumptions and inaccuracies. In this paper, a theoretical foundation and solution of some practical problems utilizing unconventional electromagnetics vectors are presented. The vectors are the Riemann-Silberstein vectors (the RS vectors), which are a linear combination of the electric and magnetic field vectors. In homogeneous space, utilizing the RS vectors Maxwell’s Equations are converted into a system of two independent equations, with each vector describing the total electromagnetic field of an ideal circular polarization. One of the most effective methods of rigorous numerical and analytical solution of Maxwell's equations is multipole series expansion. The method of electromagnetic field expansion into a series of vector spherical harmonics of the Riemann-Silberstein vectors in helical coordinates is presented in the paper. Such expansion has a simpler mathematical representation compared to the traditional multipole expansion, it is symmetric and has a clear physical meaning. Solution of field scattering and diffraction problems of aperture antennas is described. The amount of computational work compared to the traditional method of TE and TM multipole expansion is reduced due to the initial independence of the Riemann-Silberstein vectors and the direct vector spherical expansion.

Key words: antennas, aperture antennas, computational electromagnetics, electromagnetic fields, electromagnetic radiation, spherical harmonics, spherical wave expansion.

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For citation:
B. L. Kogan, I. V. Bel’kovich. Theory and practical application of Riemann-Zilberstein vectors for the tasks of antenna technology. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2018. No. 12. Available at http://jre.cplire.ru/jre/dec18/11/text.pdf

DOI  10.30898/1684-1719.2018.12.11