The Journal “Radio Physics and Radio Astronomy” (RPRA) is a peer-reviewed quarterly scientific journal of the National Academy of Sciences of Ukraine. RPRA was established in 1995. State Registration Certificate for printing mass media is КВ №1231, 02.02.1995; re-registration: КВ 25208-15148 ПР from 20.07.2022 ISSN 2415-7007 (Online) ISSN 1027-9636 (Print) Abbreviated key title: Radio phys. radio astron. DOI: https://doi.org/10.15407/rpra URL: http://rpra-journal.org.uа Language of publishing: Ukrainian, English Founders: The National Academy of Sciences of Ukraine Institute of Radio Astronomy of the National Academy of Sciences of Ukraine O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine Publisher: The NAS-Ukraine Academperiodyka Publishing House The NAS-Ukraine Academperiodyka Publishing House replicates the RPRA within the NAS-Ukraine Journal Support Program. RPRA publishes papers, brief information and letters to the editors relating to the modern problems of radio physics, radio astronomy and astrophysics, containing the results of fundamental and applied researches, description of research methods, hardware implementation and practical application, as well as current information such as comments, events, men of science. The RPRA is included into the List of scientific professional editions of Ukraine, approved by the Decree No. 582 of 24.04.2024 of the Ministry of Education and Science of Ukraine, in which the results of Ph.D. and Doctoral theses (in physics and mathematics) are recommended to be published. Current Issue Volume 31, No.2 (2026) CONTENT
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70 YEARS OF LOW-FREQUENCY RADIO ASTRONOMY IN UKRAINE
Subject and Purpose. The article is devoted to the birth and seventy years of successful development of low-frequency radio astronomy in Ukraine. This activity was started in the mid-50s of the prior century by the outstanding Ukrainian scientist Academician Semen Yakovych Braude with the maximum support of the also unique personality of the President of the NAS of Ukraine Boris Yevgenovych Paton. The creation of the world’s largest low-frequency radio telescopes and interferometers UTR-2 and URAN, the birth of a galaxy of outstanding scientists and a widely known radio astronomy school proved the highest world level of domestic physical, mathematical and technical sciences. The purpose of the work is a historical and scientific review of low-frequency radio astronomy in Ukraine and the income of S.Ya. Braude in its foundation. Methods and Methodology. All stages of the creation of domestic experimental base of radio astronomy on decameter-me- ter waves are analyzed in comparison with world experience. The astrophysical advantages of low-frequency radio astronomy, methodological difficulties of observations in this range and means of overcoming them are revealed. This is done on the example of the creation and use for 70 years of radio telescopes UTR-2, URAN, GURT. Results. The world’s largest low-frequency radio telescopes have been created, which are the national scientific heritage of the country. Constant innovative modernization of observation tools and methods has allowed us to obtain a large number of priority results recognized by the international community, and has made the contribution of Ukrainian scientists an import- ant component of complex highly sensitive radio astronomy research. Conclusions. For 70 years, low-frequency radio astronomy has been a priority area of research at the National Academy of Sciences of Ukraine. The scientific school created by the outstanding scientist, Academician S.Ya. Braude, is a significant con- tribution to domestic astrophysical science. Despite the hostile aggression in recent years, research continues and yields new results. There is no doubt about the post-war restoration of UTR-2 — the best monument to the outstanding radio astronomer S.Ya. Braude, and the further integration of Ukraine into the world scientific space. Keywords: radio astronomy, decameter range, radio telescope, phased array antenna, phasing system, digital and analog receiving equipment Manuscript submitted 15.04.2026 Radio phys. radio astron. 2026, 31(2): 075-097 REFERENCES 1. Smyrnov, V., 2011. Semen Yakovych Braude. Discoverer of the secrets of the Universe. Historical of Poltava. Available from: http://poltavahistory.inf.ua/mans2_7u.html (Accessed: 01.06.2026) 2. To the 100th anniversary of Academician S.Ya. Braude. 2011. Available from: https://www.youtube.com/watch?v=-Zom_0y1k1GE (Accessed: 01.06.2026) 3. Braude, S.Ya., Lebedeva, O.M., Megn, A.V., Ryabov, B.P., Zhouck, I.N., 1969. The spectra of discrete radio sources at decametric wavelengths. Mon. Not. R. Astron. Soc., 143(3), pp. 289—300. DOI: https://doi.org/10.1093/mnras/143.3.289 4. Braude, S.Ya., Megn, A.V., Ryabov, B.P., Sharykin, N.K., Zhouck, I.N., 1978. Decametric survey of discrete sources in the Northern sky. I. The UTR-2 radio telescope. Experimental techniques and data processing. Astron. Space Sci., 54, pp. 3—36. DOI: https://doi.org/10.1007/BF00637902 5. Braude, S.Ya., Megn, A.V., 1996. Radio Astronomy Researches in Ukraine in Decameter Wave Range. Radio Phys. Radio Astron., 1(1), pp. 9—24. 6. Bubnov, I.M., Stanislavsky, A.A., Shevchuk, N.V., Stanislavsky, L.A., Konovalenko, A.A., Ulyanov, O.M., Zakharenko, V.V., Reznichenko, A.M., Dorovskyy, V.V., Yerin, S.M., Selin, V.Yu., Belov, A.S., Shevchenko, V.V., Vashchishyn, R.V., Myrhorod, V.I., 2025. A solar-powered mobile phased array for radio astronomy observations at low frequencies. J. Astron. Instrum., 14(3—4), 2550009. DOI: https://doi.org/10.1142/S2251171725500096 7. Tokarskyy, P.L, Konovalenko, A.A, Modelski, J., 2023. An active ribbon dipole as an array element prototype for the lunar very low frequency radio telescope. IEEE Access, 11, pp. 75225—75235. DOI: https://doi.org/10.1109/ACCESS.2023.3294694 8. Bubnov, I.M., Stanislavsky, O.O., Yerin, S.M., Tokarsky, P.L., Konovalenko, O.O., Stanislavsky, L.O., Belov, O.S., 2026. Terrestrial investigation of the low-frequency sensitivity of a radio astronomical antenna proposed for lunar far-side observations of cosmic radio emissions. Radio Phys. Radio Astron., 31(1), pp. 35—50. DOI: https://doi.org/10.15407/rpra31.01.035 9. Braude, S.Y., Men, A.V., Sodin, L.G., 1978. Decameter wave radio telescope UTR-2. In: A.A. Pistolkors, ed. 1978. Antennas. Moscow: Svyaz’ Publ. 26, pp. 3—15. 10. Men, A.V., Sodin, L.G., Sharykin, N.K., Braude, Y.M., Melianovsky, P.A., Inyutin, G.A., Goncharov, N.Y., 1978. Design principles and characteristics of the UTR-2 radio telescope antennas. In: A.A. Pistolkors, ed. 1978. Antennas. Moscow: Svyaz’ Publ. 26, pp. 15—57. 11. van Haarlem, M.P., Wise, M.W., Gunst, A.W., et al., 2013. LOFAR: The LOw-Frequency ARray. Astron. Astrophys., 556, A2. DOI: https://doi.org/10.1051/0004-6361/201220873 12. Briand, C., Cecconi, B., Chrysaphi, N., Girard, J.N., Grießmeier, J.-M., Hariharan, K., Loh, A., Murphy, P., Sasikumar Raja, K., Zarka, P., Zhang, P., 2022. NenuFAR performance for solar radio observations. URSI Radio Sci. Lett., 4, 17. DOI: https://doi.org/10.46620/22-0017 13. Liu A., Pritchard J.R., Tegmark M., Loeb A., 2013. Global 21 cm signal experiments: A designer’s guide. Phys. Rev. D, 87(4), 043002. DOI: https://doi.org/10.1103/PhysRevD.87.043002 14. Sanidas, S., Cooper, S., Bassa, C.G., Hessels, J.W.T., Kondratiev, V.I., Michilli, D.B.W, Tan, C.M., van Leeuwen, J., Cerrigone, L., Fallows, R.A., Iacobelli, M., Orrú, E., Pizzo, R.F., Shulevski, A., Toribio, M.C., ter Veen, S., Zucca, P., Bondonneau, L., Grießmeier, J.-M., Karastergiou, A., Kramer, M., Sobey, C., 2019. The LOFAR Tied-Array All-Sky Survey (LOTA-AS): Survey overview and initial pulsar discoveries. Astron. Astrophys., 626, A104. DOI: https://doi.org/10.1051/0004-6361/201935609 15. Gurnett, D.A., Kurth, W.S., Cairns, I.H., Granroth, L.J., 1990. Whistlers in Neptune’s magnetosphere: Evidence of atmospheric lightning. J. Geophys. Res., 95(A12), pp. 20967—20976. DOI: https://doi.org/10.1029/JA095iA12p20967 16. Groeneveld, C., van Weeren, R.J., Osinga, E., Williams, W.L., Callingham, J.R., de Gasperin, F., Botteon, A., Shimwell, T., Sweijen, F., de Jong, J.M.G.H.J., Jansen, L.F., Miley, G.K., Brunetti, G., Brüggen, M., Röttgering, H.J.A., 2024. Characterization of the decametre sky at subarcminute resolution. Nat. Astron., 8, pp. 786—795. DOI: https://doi.org/10.1038/s41550-024-02266-z
Copyright (c) 2026 RADIO PHYSICS AND RADIO ASTRONOMY
COMPUTATIONAL EFFICIENCY OF AN ARTIFICIAL NEURAL NETWORK IN OPTIMIZING THE OPERATING CONDITIONS OF PATCH ANTENNAS
Subject and Purpose. Designing antennas with desired operational features is a complex optimization problem addressing a large number of parameters and nonlinear relationships. Artificial neural networks (ANNs) have had strong potential in antenna engineering. The ability to approximate nonlinear functions and capture hidden relationships enables partial automation of antenna designing. However, it requires a detailed analysis of how ANN parameters affect predictive accuracy and computational efficiency. The present study investigates the influence of ANN architecture and training configurations on the predictive accuracy of resonant frequencies for rectangular microstrip patch antennas. Methods and Methodology. A modular Python-based experimental platform is used to evaluate ANN performance for dif- ferent ANN configurations. The ANN training is on a synthetic dataset generated from a classical analytical antenna model. The number of hidden layers, neurons per layer, activation functions, and optimizers are systematically varied to assess their particular impacts on convergence, generalization performance, and execution time. Results. It has been shown that a three-layer neural network [1024, 512, 256 neurons] with ReLU activation and the Adam optimizer strikes the best balance between predictive accuracy and training rate. Simpler or excessively deep architectures, non-adaptive optimizers, and saturating activation functions can slow convergence or cause unstable training. Further analysis indicated that a smaller batch size introduces useful stochasticity into training but might also destabilize the process. Conclusions. The study has demonstrated that joint optimization of ANN architecture and training dynamics is essential for developing accurate and computationally efficient electromagnetic models. The practical results are recommendations for machine-learning-based antenna design. Keywords: artificial neural network (ANN), activation function, adaptive optimizer, microstrip patch antenna, automatic antenna design Manuscript submitted 17.10.2025 Radio phys. radio astron. 2026, 31(2): 098-107 REFERENCES 1. James, J.R., Hall, P.S., Wood, C., 1981. Microstrip Antenna. Theory and Design, London: Peter Peregrinus LTD. DOI: https://doi.org/10.1049/PBEW012E 2. Kumar, G., Kamala, P.R., 2003. Broadband Microstrip Antennas. Boston, London: Artech House. 3. Waterhouse, R.B., 2013, Microstrip Patch Antennas: A Designer’s Guide. New York: Springer Science & Business Media. 4. Patnaik, A., Anagnostou, D.E., Mishra, R.K., Christodoulou, C.G., Lyke, J.C., 2004. Applications of neural networks in wire- less communications, IEEE Antennas and Propagation Magazine, 46(3), pp. 130—137. DOI: https://doi.org/10.1109/MAP.2004.1374125 5. Feng, F., Zhang, J., Na, W., Zhang, W., Jin, J., Zhang, Q.-J., 2022. Artificial neural networks for microwave computer-aided design: The state of the art. IEEE Trans. Microw. Theory Tech., 70(11), pp. 4597—4619. DOI: https://doi.org/10.1109/TMTT.2022.3197751 6. Yu, Y., Zhang, Z., Cheng, Q.S., Liu, B., Wang, Y., Guo, C., Ye, T.T., 2022. State-of-the-art: AI-assisted surrogate mod- eling and optimization for microwave filters. IEEE Trans. Microw. Theory Tech., 70(11), pp. 4635—4651. DOI:https://doi.org/10.1109/TMTT.2022.3208898 7. Qi, S., Sarris, C.D., 2022. Deep neural networks for rapid simulation of planar microwave circuits based on their layouts. IEEE Trans. Microw. Theory Tech., 70(11), pp. 4805—4815. DOI: https://doi.org/10.1109/TMTT.2022.3210229 8. Swaminathan, M., Bhatti, O.W., Guo, Y., Huang, E., Akinwande, O., 2022. Bayesian Learning for Uncertainty Quantification, Optimization, and Inverse Design. IEEE Trans. Microw. Theory Tech., 70(11), pp. 4620—4634. DOI: https://doi.org/10.1109/TMTT.2022.3206455 9. Ma, J., Dang, S., Li, P., Watkins, G., Morris, K.A., Beach, M.A., 2023. A learning-based methodology for microwave passive component design. IEEE Trans. Microw. Theory Tech., 71(7), pp. 3037—3050. DOI: https://doi.org/10.1109/TMTT.2023.3238418 10. Thakare, V.V., Singhal, P., 2010. Microstrip antenna design using artificial neural networks. Int. J. RF Microw. Comput.-Aided Eng., 20(1), pp. 76—86. DOI: https://doi.org/10.1002/mmce.20414 11. Rawat, A., Yadav, R.N., Shrivastava, S.C., 2012. Neural network applications in smart antenna arrays: A review. AEU — Int. J. Electron. Commun., 66(11), pp. 903—912. DOI: https://doi.org/10.1016/j.aeue.2012.03.012 12. Khan, T., De, A., 2015. Modeling of microstrip antennas using neural networks techniques: a review. Int. J. RF Microw. Comput.-Aided Eng., 25(9), pp. 747—757. DOI: https://doi.org/10.1002/mmce.20910 13. Shi, D., Lian, W., Cui, K., Leong, D.S.H., 2022. An intelligent antenna synthesis method based on machine learning. IEEE Trans. Antennas Propag., 70(7), pp. 4965—4976. DOI: https://doi.org/10.1109/TAP.2022.3182693 14. Massa, A., Salucci, M., 2022. On the design of complex EM devices and systems through the system-by-design paradigm: A framework for dealing with the computational complexity. IEEE Trans. Antennas Propag., 70(2), pp. 1328—1343. DOI: https://doi.org/10.1109/TAP.2021.3111417 15. Raya, M.B., Pal, S., Ali, K., 2019. Design of inset fed rectangular shaped microstrip patch antenna using deep neural networks. In: Proc. 2019 22nd Int. Conf. on Computer and Information Technology (ICCIT). Dhaka, Bangladesh, 18—20 Dec. 2019. Dhaka: IEEE, 2019. DOI: https://doi.org/10.1109/ICCIT48885.2019.9038284 16. Pal, S., Raya, M.B., Ali, K., 2019. Computation of resonant frequency and gain from inset fed rectangular shaped microstrip patch antenna using deep neural network. In: Proc. 2019 4th Int. Con. on Electrical Information and Communication Technology (EICT). Khulna, Bangladesh, 20—22 Dec. 2019. Khulna. DOI: https://doi.org/10.1109/EICT48899.2019.9068758 17. Syahrial, S., Al Faqi, M.K., Meutia, E.D., Munadi, R., Roslidar R., 2024. Parameter estimation of two-element rectangular microstrip patch antenna using artificial neural network. In: Proc. 2024 FORTEI-Int. Conf. on Electrical Engineering (FORTEI-ICEE). Badung, Indonesia, 24—25 Oct. 2024. Badung: IEEE, pp. 216—221. DOI: https://doi.org/10.1109/FORTEI-ICEE64706.2024.10824537 18. Shereen, M.K., Liu, X., Wu, X., Niazi, S., Naseem, A., Khattak, M.I., 2025. Towards bi-directional deep learning approach in patch antenna design and optimization. In: Proc. 2025 IEEE Int. Workshop on Antenna Technology (iWAT). Cocoa Beach, FL, USA. 19—21 Feb. 2025. Cocoa Beach: IEEE. DOI: https://doi.org/10.1109/iWAT64079.2025.10931210 19. Derneryd, A., Lind, A., 1979. Extended analysis of rectangular microstrip resonator antennas. IEEE Trans. Antennas Propag., 27(6), pp. 846—849. DOI: https://doi.org/10.1109/TAP.1979.1142206 20. Garg, R., Bhartia, P., Bahl, I.J., Ittipiboon, A., 2001. Microstrip Antenna Design Handbook. Boston, London: Artech House. 21. Steer, M., 2019. Fundamentals of Microwave and RF Design, 3rd ed. USA: NC State University. DOI: https://doi.org/10.5149/9781469656892_Steer 22. Fesenko, V.I., Tkachenko, G.V., 2007. Modeling of 1-D photonic bandgap microstrip structures. In: Proc. 2007 Int. Workshop on Optoelectronic Physics and Technology (OPT’07), Kharkiv, Ukraine, 20—22 June 2007, pp. 42—43. DOI: https://doi.org/10.1109/OPT.2007.4298524 23. Mishra, R.K., Patnaik, A., 2003. Designing rectangular patch antenna using the neurospectral method. IEEE Trans. Antennas Propag., 51(8), pp. 1914—1921. DOI: https://doi.org/10.1109/TAP.2003.814748 24. Haykin, S., 2009. Neural Networks and Learning Machines. 3rd ed. NJ: Pearson Education. 25. Goodfellow, I., Bengio, Y., Courville, A., 2016. Deep Learning. Cambridge, Massachusetts London: MIT Press. 26. He, K., Zhang, X., Ren, S., Sun, J., 2015. Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification. In: Proc. 2015 IEEE Int. Conf. on Computer Vision (ICCV). Santiago, Chile, 7—13 Dec. 2015, pp. 1026—1034. DOI: https://doi.org/10.1109/ICCV.2015.123 27. Maity, B., Nayak, S.K., 2024. Artificial neural networks for optimal design parameters prediction of microstrip patch antenna with wideband harmonic suppression. In: Proc. 2024 Second Int. Conf. on Microwave, Antenna and Communication (MAC). Dehradun, India, 04—06 Oct. 2024. DOI: https://doi.org/10.1109/MAC61551.2024.10837513
A COMPARATIVE ANALYSIS OF RADIATION FROM CIRCULAR AND RECTANGULAR APERTURES: LIMITATIONS ON THEIR USE FOR BESSEL BEAM FORMATION
Subject and Purpose. Essentials of the processes for millimeter-wavelength radiation from circular apertures are analyzed, with emphasis on the formation of the field’s radiation pattern (RP) and modal structure in the aperture. The work is aimed at obtaining analytical expressions for the circular aperture’s RP and verifying these in experiments. Further aims include investi- gation of radiation characteristics and possibilities for forming up specific types of wave beams for applications like medicine, communications and interaction with aerial vehicles. Also, possible techniques of Bessel beam generation are investigated for the millimeter-wavelength range. Methods and Methodology. The electromagnetic field distribution over the waveguide aperture is assumed to be available for determining its radiated field in free space. The far-field characteristics are calculated via Kirchhoff ’s integral taken over the aperture and verified experimentally by measuring the RP and the voltage standing wave ratio (VSWR) in the wave guiding channel. Results. Explicit expressions for the RP of a circular aperture have been derived, with the use of pattern functions, for two mutually orthogonal planes. Measurements at a frequency of 34 GHz revealed that a circular aperture of a 30 mm diameter provided for a voltage standing wave ratio (VSWR) in the guiding channel close to 1.0558. The calculated and measured cross section areas of the RP, as estimated for the planes of the E and H field vectors, coincide with a Gaussian distribution to the level of −8.7 dB. The RPs produced by apertures of circular and rectangular cross-sections have been compared for antennas of equal maximum sizes. Conclusions. Analytical expressions have been derived for the radiation pattern (RP) of a circular aperture supporting the TE11 mode in two mutually orthogonal planes. As has been found, such an aperture cannot provide for formation of the far- field electric distribution required for generating a Bessel wave beam at the conical lenses’ output. Keywords: aperture method, millimeter wavelength range, circular aperture, radiation pattern, Gaussian distribution, voltage standing wave ratio (VSWR), conical lens Manuscript submitted 16.03.2026 Radio phys. radio astron. 2026, 31(2): 108-118 REFERENCES 1. Andreev D., Kuskov A., and Schamiloglu E. Review of the relativistic magnetron. Matter Radiat. Extrem. 2019. Vol. 4, Iss. 6. 067201. DOI: https://doi.org/10.1063/1.5100028 2. Xu W. Review of the high-power vacuum tube microwave sources. Preprint. Institute of Plasma Physics, Chinese Academy of Sciences. 2024. 50 p. DOI: 10.48550/arXiv.2003.04288 3. Durnin J. Exact solutions for nondiffracting beams. I. The scalar theory. J. Opt. Soc. Am. A. 1987. Vol. 4, Iss. 4. P. 651—654. DOI: https://doi.org/10.1364/JOSAA.4.000651 4. Salo J., Meltaus J., Noponen E., Westerholm J., Salomaa M.M., Lönnqvist A., Säily J., Häkli J., Ala-Laurinaho J., and Räisänen A.V. Millimetre-wave Bessel beams using computer holograms. Electron. Lett. 2001. Vol. 37, Iss. 13. P. 834—835. DOI: https://doi.org/10.1049/el:20010551 5. Cabrini S., Liberale C., Cojoc D., Carpentiero A., Prasciolu M., Mora S., Degiorgio V., De Angelis F., and Di Fabrizio, E. Axicon lens on optical fiber forming optical tweezers, made by focused ion beam milling. Microelectron. Eng. 2006. Vol. 83, Iss. 4—9. P. 804—807. DOI: https://doi.org/10.1016/j.mee.2006.01.247 6. Khonina S.N., Kazanskiy N.L., Khorin P.A., and Butt M.A. Modern Types of Axicons: New Functions and Applications. Sensors. 2021. Vol. 21, Iss. 19. 6690. DOI: https://doi.org/10.3390/s21196690 7. Mishustin B.A. Radiation from the aperture of a circular waveguide with an infinite flange. Radiophysics and Quantum Electronics. 1965. Vol. 8, Iss. 11. P. 852—858. DOI: https://doi.org/10.1007/BF01038285 8. Samaddar S.N. Theory of radiation from the open end of a circular waveguide flush-mounted to a flat ground plane. J. Eng. Math. 1967. Vol. 1, Iss. 3. P. 251—272. DOI: https://doi.org/10.1007/BF01540508 9. Lee C.S., and Lee S.W. Radar cross section of an open‐ended circular waveguide: Calculation of second‐order diffraction terms. Radio Sci. 1987. Vol. 22, Iss. 1. P. 2—12. DOI: https://doi.org/10.1029/RS022i001p00002 10. Wu T.T., and Shen H. Radiation of an Electromagnetic Pulse from the Open End of a Circular Waveguide. Proc. the Microwave and Particle Beam Sources and Propagation. Vol. 0873. (Los Angeles, CA, USA, 11—17 Jan. 1988). P. 329—337. DOI: https://doi.org/10.1117/12.965112 11. Cicchetti R., and Faraone A. 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Kharkov: Publishing House of Kharkov State University, 1960. 188 p. 26. Zhang K., Li D. Electromagnetic Theory for Microwaves and Optoelectronics. 2nd ed. Leipzig, Germany: Springer Science &Business Media, 2008. 624 p. DOI: https://doi.org/10.1007/978-3-540-74296-8
MANIPULATION OF SPATIAL FIELD DISTRIBUTION IN A PLANAR MICROWAVE PHOTON-MAGNON CONVERTER
Subject and Purpose. The research addresses planar photon-magnon (P-M) converters that efficiently convert between microwave photons and magnons and are essential components in emerging quantum technologies. Planar P-M converters benefit particularly from planar, two-dimensional (2D) resonators. Among them are asterisk-shaped resonators featuring compact geometry and strong concentration of the magnetic component of the electromagnetic (EM) field. The present work seeks an effective approach to optimizing planar P-M converters to enhance conversion efficiency and further miniaturize the device by manipulating the spatial distribution of the high-frequency magnetic field. Methods and Methodology. The proposed approach relies on numerical simulations of the electrodynamic response of the asterisk-shaped resonator coupled to the feeding microstrip line. Families of the resonance spectra are analyzed as a function of the resonator’s position relative to the microstrip line, which effectively varies the electromagnetic coupling strength. This methodology allows systematic optimization of the resonator’s geometrical and spectral parameters, enabling targeted manipulation of the magnetic field distribution across the magnetic sample location. Results. The conducted analysis has demonstrated that a fine adjustment of the P-M coupling strength can maximize the concentration of the magnetic component of the high-frequency EM field at a desired location within the resonator. Practical recommendations have been developed for designing high-performance planar P-M converters, offering a framework for the efficient integration of asterisk-shaped resonators into miniaturized quantum devices. Conclusions. Based on the numerical analysis of the spectral properties of a 2D asterisk-shaped split-ring resonator (ASRR) intended for a planar microwave P-M converter, it has been shown that selecting the optimal position for the feeding microstrip line allows a high concentration of the magnetic component of the EM field at the resonator center. Proper positioning of the mi- crostrip feeding line is important for achieving a relatively high Q-factor (Q ≈ 200) for operating modes. The calculated resonance spectra of the investigated P-M converter identify ranges of the resonator offset parameter where dynamic manipulation of the P-M coupling strength is possible and relatively simple. Keywords: microwaves, photon-magnon converter, quantum technologies, asterisk-shaped resonator, coupling strength Manuscript submitted 16.03.2026 Radio phys. radio astron. 2026, 31(2): 119-125 REFERENCES 1. Bhoi, B., and Kim, S.-K., 2019. Chapter One — Photon-magnon coupling: Historical perspective, status, and future direc- tions. Solid State Phys., 70, pp. 1—77. DOI: https://doi.org/10.1016/bs.ssp.2019.09.001 2. Girich, A., Nedukh, S., Polevoy, S., Sova, K., Tarapov, S., and Vakula, A., 2023. Enhancement of the microwave photon-mag- non coupling strength for a planar fabricated resonator. Sci. Rep., 13, 924(1—8). DOI: https://doi.org/10.1038/s41598-022-27285-6 3. Girich, A.A., Nedukh, S.V., Polevoy, S.Yu., Rami, B., Sova, K.Yu., Tarapov, S.I., and Vakula, A.S., 2024. Magnetic Nanocom- ponents for Frequency Converting in Quantum Computing Technologies. In: I. Vladymyrskyi, B. Hillebrands, A. Serga, D. Makarov and O. Prokopenko (eds.). Functional Magnetic and Spintronic Nanomaterials. Chap. 9. Dordrecht, Netherlands: Springer Nature, pp. 197—206. DOI: https://doi.org/10.1007/978-94-024-2254-2_9 4. Lan, Y., Xu, Y., Jia, Y., Mei, T., Qu, S., Yan, B., Yang, D., Chen, B., Xu, R., & Li, Y., 2017. 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SPATIAL DYNAMICS OF THE RADIALLY POLARIZED VORTEX BEAMS OF TERAHERTZ-RANGE RADIATION SUBJECTED TO TIGHT FOCUSING
Subject and Purpose. The paper concerns the effect of tight focusing of the terahertz-range vortex laser beams, formed byradially polarized TM0m modes of a dielectric waveguide-based resonator, that results from beam’s passage through a spiral phase changing plate. The work is aimed at obtaining analytical expressions to describe the field structure and determine the effect exerted by the topological charge of the plate, as well as order of the participating mode, upon the spatial-energy characteristics of the radiation within the lense’s focal region. Methods and Methodology. The propagation and focusing of the radiation are described within the framework of the Rayleigh-Sommerfeld vector theory, making use of a nonparaxial approximation. The mode structure of the resonant cavity is determined by the TM01, TM02 and TM03 modes of a hollow circular dielectric waveguide. The action of the spiral phase changing plate is taken into account in terms of a complex-valued transfer function using topological charge numbers n=0, 1, 2. Results. Analytical expressions have been obtained for components of the electric field of the laser beams as excited by the radially polarized TM0m modes passing through the spiral phase changing plate during their tight focusing. As has been found, in the absence of a phase-changing plate in the focal region of the lens, an annular field structure with a non-zero axial field’s intensity is preserved for all the modes involved. When using a phase plate with a topological charge n= 1 the field intensity maxima are localized near the axis, while in the case of n=2 an annular field distribution with a zero intensity at the axis is restored. The highest magnitudes of the maximum field intensity for the modes TM01, TM02 and TM03 correspond to the topological charge n= 1. In the case of a phase-changing plate with n=1, the phase fronts of all the three field components of the modes under study acquire a single-lobe vortex structure, while with n= 2 — a two-lobe structure. Conclusions. Making use of a TM0m mode of a certain established order, along with a spiral phase-changing plate with a selected topological charge makes it possible to control the field structure of the terahertz vortex beams involved, as well as their phase fronts, axial intensities, effective diameters and field component composition during their tight focusing in the focal region of the lens. Keywords: terahertz laser, vortex beam, spiral phase plate, topological charge, radial polarization, TM0m modes, dielectric waveguide-based resonator, tight focusing Manuscript submitted 06.05.2026 Radio phys. radio astron. 2026, 31(2): 126-137 REFERENCES 1. Pang, X., Ozolins, O., Jia, S., Zhang, L., Schatz, R., Udalcovs, A., and Yu, X., 2022. 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Aleksei A. Kostenko (to the 80th birth anniversary)