Journal of Radio Electronics. eISSN 1684-1719. 2026. ¹4
Full text in Russian (pdf)
DOI: https://doi.org/10.30898/1684-1719.2026.4.8
Analytical and numerical solutionS
TO the PROBLEM OF NONSTATIONARY SCATTERING
FROM a Perfectly Conducting Triangle
in Physical Optics Approximation
A.M. Lebedev 1, I.S. Suyundukov 1,2
1 Institute for Theoretical and Applied Electromagnetics RAS,
125412, Russia, Moscow, Izhorskaya, 13
2 Moscow Institute of Physics and Technology (National Research University),
141701, Russia, Moscow Region, Dolgoprudny, Institutskiy per., 9
The paper was received March 12, 2026.
Abstract. Using physical optics approximation, the analytical expression of the nonstationary field, bistatically scattered from the triangle on the surface of a metallic object, was obtained for an arbitrary time dependence of the incident wave field. The solution is a set of the scattered field expressions in the far zone 1) in direction of the beam specular reflection, in the shadow direction and in small angular neighborhoods of these directions (first-order maxima of scattering intensity), 2) in direction belonging to the cone of diffracted rays around one of the sides of the triangle, and in the small angular neighborhood of this direction (second-order maximum of scattering intensity), 3) in general case of scattering outside the above-mentioned directions of maxima of scattering intensity. On this basis the procedure of calculating the nonstationary scattered field, produced in the far zone by a metallic triangle, has been developed. Optimal condition of transition between calculations based on general and particular formulas has been determined and tested. Accuracy of calculations in time domain using the developed numerical procedure was demonstrated by comparing the scattered field for a monochromatic problem with the steady-state amplitude of scattered field oscillations under excitation by a radio impulse with rectangular envelope and high-frequency filling. In contrast to the monochromatic problem, for which the amplitude of the scattered field is characterized by a single complex number, in time domain the signal, scattered from the triangle, consists of five intervals of oscillations. The intervals correspond to the initial, intermediate and final parts of time dependence of the field at the observation point. They are related to expansion of the triangle’s part, which forms the scattered field, starting from infinitely small neighborhood of a vertex to the full coverage of the triangle’s surface, then to steady-state scattering, and finally to reduction of the triangle’s part, which contributes to the scattered field, to zero starting from deceasing by infinitely small neighborhood of the same vertex. Scattered field changes continuously in transitions between intervals, but the amplitude, phase, and constant components of oscillations undergo abrupt changes on transitions between intervals. The character of the time evolution of the field, scattered by a triangle, indicates the dominant role of the neighborhoods of its vertices in the formation of time response. The developed computer program can be considered as the basic component of combined numerical procedure to calculate scattering from a complex object in time domain, when scattering from one part of the object is determined in physical optics approximation, while scattering from the remaining part is calculated within a rigorous approach.
Key words: triangle on the surface of a metallic object, nonstationary field, bistatic scattering, physical optics approximation, radio impulse.
Corresponding author: Lebedev Andrey Mikhaylovich, lebedev_am@mail.ru
References
1. Landau L.D. and Lifshitz E.M. Theoretical Physics. Vol. 2. Field Theory. Moscow: Fizmatlit. 536 p. (In Russian)
2. Lebedev A.M., Obukhov M.L., Selin I.A., Furmanova T.A. Regularities of Bistatic Scattering from a Metallic Triangle // Journal of Radio Electronics. – 2019. – ¹. 12. https://doi.org/10.30898/1684-1719.2019.12.15 (In Russian)
3. FEKO : electromagnetic simulation software : [site] / Altair Engineering, Inc. – Electronic data. – Troy, Michigan, USA : Altair Engineering, Inc., 1997. – URL: https://altair.com/feko
For citation:
Lebedev A.M., Suyundukov I.S. Analytical and numerical solutions to the problem of nonstationary scattering from a perfectly conducting triangle in physical optics approximation // Journal of Radio Electronics. – 2026. – ¹. 4. https://doi.org/10.30898/1684-1719.2026.4.8 (In Russian)