E.I. Semernya1, S.P. Skobelev2

1 Moscow Aviation Institute (National Research University) (Moscow, Russia)

2 PJSC “Radiofizika” (Moscow, Russia)

2 Moscow Institute of Physics and Technology (National Research University) (Dolgoprudny, Russia)

1 poshisholina@gmail.com; 2 s.p.skobelev@mail.ru

A uniform plane electromagnetic wave propagating in free space at arbitrarily specified spherical angles with respect to Cartesian coordinates introduced in consideration is considered. Orientation of the electric field strength vector is also specified arbitrarily with respect to unit basic vectors of horizontal and vertical polarization oriented perpendicularly to the direction of the wave propagation. A technique of derivation of the formulas connecting the expansion coefficients obtained for vectors of electromagnetic field in terms of vector transversal-electric and transversal-magnetic spherical waves using the Bromwich method in general case with parameters specifying the plane wave direction of propagation and polarization is presented. The technique is based on the use of an expansion of a scalar plane wave multiplied by projections of the basic unit vectors of polarization on the direction to the observation point involving the specified vector plane wave parameters. The required expansion coefficients are then determined as a result of comparison of the expansions derived by two methods for longitudinal (radial) components of the electric and magnetic field vectors.

Semernya E.I., Skobelev S.P. Expansion of a plane electromagnetic wave over spherical waves in case of arbitrary direction of propagation. Radiotekhnika. 2024. V. 88. № 4. P. 56−62. DOI: https://doi.org/10.18127/j00338486-202404-05 (In Russian)

1. Waterman P.C. Matrix formulation of electromagnetic scattering. Proc. of IEEE. 1965. V. 53. № 8. P. 805-812.
2. Sveshnikov A.G., Il'inskij A.S. Prjamoj metod dlja zadach difrakcii na lokal'nom neodnorodnom tele. ZhVMiMF. 1971. T. 11. № 4. S. 960-968 (in Russian).
3. Stout B., Neviere M., Popov E. Light diffraction by a three dimensional object: differential theory. J. Opt. Soc. Am. A. 2005. V. 22. № 11. P. 2385-2404.
4. Semernya E.I., Skobelev S.P. Modifications of the hybrid projection method for analysis of electromagnetic scattering by inhomogeneous bodies of revolution. J. Opt. Soc. Am. A. 2020. V. 37. № 12. P. 1873-1882.
5. Mencer Dzh.R. Difrakcija i rassejanie radiovoln. M.: Sovetskoe radio. 1958 (in Russian).
6. Tsang L., Kong J.A., Shin R.T. Theory of microwave remote sensing. Wiley Interscience. 1985.
7. Mishchenko M.I., Travis L.D., Lacis A.A. Scattering, absorption, and emission of light by small particles. Cambridge, UK: Cambridge University Press. 2002.
8. Rother T. Electromagnetic wave scattering on nonspherical particles. Springer. 2009.
9. Kristensson G. Scattering of electromagnetic waves by obstacles. Edison, NJ: SciTech Publishing. 2016.
10. Frezza F., Mangini F., Tedeschi A. Introduction to electromagnetic scattering: tutorial. J. Opt. Soc. Am. A. 2018. V. 35. № 1. P. 163-173.
11. Bromwich T.S.X. Electromagnetic waves. Philosophical Magazine. 1919. V. 6. № 38. P. 143–164.
12. Vajnshtejn L.A. Jelektromagnitnye volny. M.: Radio i svjaz'. 1988 (in Russian).
13. Markov G.T., Chaplin A.F. Vozbuzhdenie jelektromagnitnyh voln. M.: Radio i svjaz'. 1983 (in Russian).