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...
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Radio physics and radio astronomy| _version_ | 1868203880251129856 |
|---|---|
| author | Kuzmychov, I. K. Voitovych, O. A. Lukash, O. S. Khutorian, E. M. Maltsev, V. P. May, O. V. |
| author_facet | Kuzmychov, I. K. Voitovych, O. A. Lukash, O. S. Khutorian, E. M. Maltsev, V. P. May, O. V. |
| author_institution_txt_mv | [] |
| author_sort | Kuzmychov, I. K. |
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| datestamp_date | 2026-06-16T11:44:37Z |
| description | 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 lensManuscript submitted 16.03.2026Radio phys. radio astron. 2026, 31(2): 108-118REFERENCES1. Andreev D., Kuskov A., and Schamiloglu E. Review of the relativistic magnetron. Matter Radiat. Extrem. 2019. Vol. 4, Iss. 6. 067201. DOI: 10.1063/1.51000282. 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.2003.042883. 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: 10.1364/JOSAA.4.0006514. 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: 10.1049/el:200105515. 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: 10.1016/j.mee.2006.01.2476. 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: 10.3390/s211966907. 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: 10.1007/BF010382858. 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: 10.1007/BF015405089. 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: 10.1029/RS022i001p0000210. 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: 10.1117/12.96511211. Cicchetti R., and Faraone A. Radiation from Open-Ended Circular Waveguides: a Formulation Based on the Incomplete Hankel Functions. Progress in Electromagnetics Research (PIER). 2008. Vol. 78. P. 285—300. DOI: 10.2528/PIER0709140512. Galyamin S.N., and Vorobev V.V. Diffraction at the Open End of Dielectric-Lined Circular Waveguide. IEEE Trans. Microw. Theory Tech. 2022. Vol. 70, Iss. 6. P. 3087—3095. DOI: 10.1109/TMTT.2022.3167639 13. Dong H., Doc J.-B., and Félix S. Maximum Directivity of Flanged Open-Ended Waveguides. J. Acoust. Soc. Am. 2023. Vol. 154, Iss. 1. P. 115—125. DOI: 10.1121/10.002005214. Bai Y., Ming Y., Yang F., Wang C., Dong Y., Yang J., Zhou G., and Xie Y. Noncontact Rotational Speed Measurement with Near-Field Microwave of Open-Ended Waveguide. Electronics. 2024. Vol. 13, Iss. 15, 3012, P. 1—18. DOI: 10.3390/electronics131 5301215. Dash T., Prinsloo D., and Yarovoy A. Radiation from the Open-ended Over-moded Cylindrical Waveguide. Proc. the 4th URSI Atlantic Radio Science Conference (AT-RASC 2024). (Gran Canaria, Spain, 19—24 May 2024). P. 1—4. ISBN (Electronic) 978-9-4639-6-8102. DOI: 10.46620/ursiatrasc24/qeut461116. Xu S., Heo J., Ahn B.K., Lee C.S., and Ahn B.C. Simulation-Based Approach to the Matching of a Dielectric-Filled Circular Waveguide Aperture. Sensors. 2024. Vol. 24, Iss. 3. P. 841—860. DOI: 10.3390/s2403084117. Pozar D.M. Microwave Engineering. 4th ed. New York: Wiley & Sons, Limited, John, 2012. P. 123—128.18. Nikitin P.V., Stancil D.D., and Erosheva E.A. Estimating the number of modes in multimode waveguide propagation environment. Proc. the 2011 IEEE Int. Symp. on Antennas and Propagation (APSURSI). (Spokane, WA, USA, 03—08 July 2011). P. 1—4. DOI: 10.1109/APS.2011.599662319. R. Kühn. Mikrowellenantennen. Berlin: Veb Berlag Technik Publ., 1964. P. 198—203.20. Bird T.S. Fundamentals of aperture antennas and arrays: from theory to design, fabrication and testing. United Kingdom: John Wiley & Sons Limited Publishing House, 2016. P. 154—157.21. Bronstein I.N., Semendyaev K.A., Musiol G., and Muehlig H. Mathematics Handbook. 5th ed. Berlin, Heidelberg, New-York: Springer Publishing house, 2007. 647 p.22. Gradshtein I.S., and Ryzhik I.M. Table of Integrals, Series, and Products. 7th ed., edited by A. Jeffrey and D. Zwillinger. Amsterdam, London, New York, Paris: Academic Press is an imprint of Elsevier, 2014. P. 892—910.23. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Edited by M. Abramowitz and I.A. Stegun. 10th print. Washington, D.C.: U.S. Dept. of Commerce: U.S. G.P.O., 1972. 361 p.24. Balanis C.A. Antenna Theory. Analysis and Design. Canada: Published by John Wiley & Sons, Inc., Hoboken, New Jersey, 2005. 35 p.25. Shubarin Yu.V. Ultra-high frequency antennas. 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: 10.1007/978-3-540-74296-8 |
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| spelling | rpra-journalorgua-article-14952026-06-16T11:44:37Z A COMPARATIVE ANALYSIS OF RADIATION FROM CIRCULAR AND RECTANGULAR APERTURES: LIMITATIONS ON THEIR USE FOR BESSEL BEAM FORMATION ПОРІВНЯЛЬНИЙ АНАЛІЗ ВИПРОМІНЮВАННЯ З КРУГЛОЇ ТА ПРЯМОКУТНОЇ АНТЕННИХ АПЕРТУР. ОБМЕЖЕННЯ, ЩО ПЕРЕШКОДЖАЮТЬ ФОРМУВАННЮ БЕССЕЛЕВИХ ПУЧКІВ Kuzmychov, I. K. Voitovych, O. A. Lukash, O. S. Khutorian, E. M. Maltsev, V. P. May, O. V. aperture method; millimeter wavelength range; circular aperture; radiation pattern; Gaussian distribution; voltage standing wave ratio (VSWR); conical lens апертурний метод; міліметровий діапазон; кругла апертура; діаграма спрямованості; гауссів розподіл; коефіцієнт стоячої хвилі за напругою (КСХН); конічна лінза 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 lensManuscript submitted 16.03.2026Radio phys. radio astron. 2026, 31(2): 108-118REFERENCES1. Andreev D., Kuskov A., and Schamiloglu E. Review of the relativistic magnetron. Matter Radiat. Extrem. 2019. Vol. 4, Iss. 6. 067201. DOI: 10.1063/1.51000282. 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.2003.042883. 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: 10.1364/JOSAA.4.0006514. 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: 10.1049/el:200105515. 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: 10.1016/j.mee.2006.01.2476. 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: 10.3390/s211966907. 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: 10.1007/BF010382858. 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: 10.1007/BF015405089. 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: 10.1029/RS022i001p0000210. 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: 10.1117/12.96511211. Cicchetti R., and Faraone A. Radiation from Open-Ended Circular Waveguides: a Formulation Based on the Incomplete Hankel Functions. Progress in Electromagnetics Research (PIER). 2008. Vol. 78. P. 285—300. DOI: 10.2528/PIER0709140512. Galyamin S.N., and Vorobev V.V. Diffraction at the Open End of Dielectric-Lined Circular Waveguide. IEEE Trans. Microw. Theory Tech. 2022. Vol. 70, Iss. 6. P. 3087—3095. DOI: 10.1109/TMTT.2022.3167639 13. Dong H., Doc J.-B., and Félix S. Maximum Directivity of Flanged Open-Ended Waveguides. J. Acoust. Soc. Am. 2023. Vol. 154, Iss. 1. P. 115—125. DOI: 10.1121/10.002005214. Bai Y., Ming Y., Yang F., Wang C., Dong Y., Yang J., Zhou G., and Xie Y. Noncontact Rotational Speed Measurement with Near-Field Microwave of Open-Ended Waveguide. Electronics. 2024. Vol. 13, Iss. 15, 3012, P. 1—18. DOI: 10.3390/electronics131 5301215. Dash T., Prinsloo D., and Yarovoy A. Radiation from the Open-ended Over-moded Cylindrical Waveguide. Proc. the 4th URSI Atlantic Radio Science Conference (AT-RASC 2024). (Gran Canaria, Spain, 19—24 May 2024). P. 1—4. ISBN (Electronic) 978-9-4639-6-8102. DOI: 10.46620/ursiatrasc24/qeut461116. Xu S., Heo J., Ahn B.K., Lee C.S., and Ahn B.C. Simulation-Based Approach to the Matching of a Dielectric-Filled Circular Waveguide Aperture. Sensors. 2024. Vol. 24, Iss. 3. P. 841—860. DOI: 10.3390/s2403084117. Pozar D.M. Microwave Engineering. 4th ed. New York: Wiley & Sons, Limited, John, 2012. P. 123—128.18. Nikitin P.V., Stancil D.D., and Erosheva E.A. Estimating the number of modes in multimode waveguide propagation environment. Proc. the 2011 IEEE Int. Symp. on Antennas and Propagation (APSURSI). (Spokane, WA, USA, 03—08 July 2011). P. 1—4. DOI: 10.1109/APS.2011.599662319. R. Kühn. Mikrowellenantennen. Berlin: Veb Berlag Technik Publ., 1964. P. 198—203.20. Bird T.S. Fundamentals of aperture antennas and arrays: from theory to design, fabrication and testing. United Kingdom: John Wiley & Sons Limited Publishing House, 2016. P. 154—157.21. Bronstein I.N., Semendyaev K.A., Musiol G., and Muehlig H. Mathematics Handbook. 5th ed. Berlin, Heidelberg, New-York: Springer Publishing house, 2007. 647 p.22. Gradshtein I.S., and Ryzhik I.M. Table of Integrals, Series, and Products. 7th ed., edited by A. Jeffrey and D. Zwillinger. Amsterdam, London, New York, Paris: Academic Press is an imprint of Elsevier, 2014. P. 892—910.23. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Edited by M. Abramowitz and I.A. Stegun. 10th print. Washington, D.C.: U.S. Dept. of Commerce: U.S. G.P.O., 1972. 361 p.24. Balanis C.A. Antenna Theory. Analysis and Design. Canada: Published by John Wiley & Sons, Inc., Hoboken, New Jersey, 2005. 35 p.25. Shubarin Yu.V. Ultra-high frequency antennas. 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: 10.1007/978-3-540-74296-8 Предмет і мета роботи. Аналізуються особливості процесу випромінювання радіохвиль міліметрового діапазону з круглої антенної апертури та формування її діаграми направленості (ДН) з урахуванням модової структури поля в розкриві. Метою роботи є отримання аналітичних виразів для ДН круглої апертури та їх експериментальна перевірка, дослідження характеристик та методів формування заданих типів хвильових пучків для застосувань у медицині, системах зв’язку та для впливу на літальні апарати. Досліджується можливість формування бесселевих пучків у міліметровому діапазоні довжин хвиль.Методи та методологія. Розподіл електромагнітного поля в апертурі хвилеводу вважається відомим і вико- ристовується для визначення полів у вільному просторі. Поля в дальній зоні розраховуються через інтеграл Кірхгофа по апертурі та перевіряються експериментально шляхом вимірювання ДН та коефіцієнта стоячої хвилі за напругою (КСХН) у хвилевідному тракті.Результати. З використанням діаграмних функцій виведено вирази для ДН круглої апертури у двох ортогональних площинах. Вимірювання на частоті 34 ГГц показали, що для круглої апертури діаметром 30мм КСХН у хвилевід-ному тракті становить 1.0558. Розраховані та вимірювані перерізи ДН у площинах векторів та збігаються з гауссовим розподілом до рівня −8.7 дБ. Проведено порівняння ДН круглої та прямокутної апертур з однаковим макси-мальним розміром.Висновки. Отримано формульні вирази для ДН круглої апертури з ТЕ11-модою у двох ортогональних площинах. Така апертура не дозволяє сформувати у дальній зоні структуру поля, необхідну для отримання на виході з конічної лінзи бесселевого хвильового пучка.Ключові слова: апертурний метод, міліметровий діапазон, кругла апертура, діаграма спрямованості, гауссів розподіл, коефіцієнт стоячої хвилі за напругою (КСХН), конічна лінзаСтаття надійшла до редакції 16.03.2026Radio phys. radio astron. 2026, 31(2): 108-118БІБЛІОГРАФІЧНИЙ СПИСОК1. Andreev D., Kuskov A., and Schamiloglu E. Review of the relativistic magnetron. Matter Radiat. Extrem. 2019. Vol. 4, Iss. 6. 067201. DOI: 10.1063/1.51000282. 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.2003.042883. 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: 10.1364/JOSAA.4.0006514. 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: 10.1049/el:200105515. 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: 10.1016/j.mee.2006.01.2476. 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: 10.3390/s211966907. Mishustin B.A. Radiation from the aperture of a circular waveguide with an infinite flange. Radiophysics and QuantumElectronics. 1965. Vol. 8, Iss. 11. P. 852—858. DOI: 10.1007/BF010382858. 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: 10.1007/BF015405089. 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: 10.1029/RS022i001p0000210. Wu T.T., and Shen H. Radiation of an Electromagnetic Pulse from the Open End of a Circular Waveguide. Proc. the Micro-wave and Particle Beam Sources and Propagation. Vol. 0873. (Los Angeles, CA, USA, 11—17 Jan. 1988). P. 329—337. DOI: 10.1117/12.96511211. Cicchetti R., and Faraone A. Radiation from Open-Ended Circular Waveguides: a Formulation Based on the Incomplete Hankel Functions. Progress in Electromagnetics Research (PIER). 2008. Vol. 78. P. 285—300. DOI: 10.2528/PIER0709140512. Galyamin S.N., and Vorobev V.V. Diffraction at the Open End of Dielectric-Lined Circular Waveguide. IEEE Trans. Mi-crow. Theory Tech. 2022. Vol. 70, Iss. 6. P. 3087—3095. DOI: 10.1109/TMTT.2022.3167639 13. Dong H., Doc J.-B., and Félix S. Maximum Directivity of Flanged Open-Ended Waveguides. J. Acoust. Soc. Am. 2023. Vol. 154, Iss. 1. P. 115—125. DOI: 10.1121/10.002005214. Bai Y., Ming Y., Yang F., Wang C., Dong Y., Yang J., Zhou G., and Xie Y. Noncontact Rotational Speed Measurement with Near-Field Microwave of Open-Ended Waveguide. Electronics. 2024. Vol. 13, Iss. 15, 3012, P. 1—18. DOI: 10.3390/electronics131 5301215. Dash T., Prinsloo D., and Yarovoy A. Radiation from the Open-ended Over-moded Cylindrical Waveguide. Proc. the 4thURSI Atlantic Radio Science Conference (AT-RASC 2024). (Gran Canaria, Spain, 19—24 May 2024). P. 1—4. ISBN (Electronic) 978-9-4639-6-8102. 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DOI: 10.1007/978-3-540-74296-8 Видавничий дім «Академперіодика» 2026-06-16 Article Article http://rpra-journal.org.ua/index.php/ra/article/view/1495 РАДИОФИЗИКА И РАДИОАСТРОНОМИЯ; Vol 31, No 2 (2026); 108 RADIO PHYSICS AND RADIO ASTRONOMY; Vol 31, No 2 (2026); 108 РАДІОФІЗИКА І РАДІОАСТРОНОМІЯ; Vol 31, No 2 (2026); 108 2415-7007 1027-9636 uk Copyright (c) 2026 RADIO PHYSICS AND RADIO ASTRONOMY |
| spellingShingle | aperture method millimeter wavelength range circular aperture radiation pattern Gaussian distribution voltage standing wave ratio (VSWR) conical lens Kuzmychov, I. K. Voitovych, O. A. Lukash, O. S. Khutorian, E. M. Maltsev, V. P. May, O. V. A COMPARATIVE ANALYSIS OF RADIATION FROM CIRCULAR AND RECTANGULAR APERTURES: LIMITATIONS ON THEIR USE FOR BESSEL BEAM FORMATION |
| title | A COMPARATIVE ANALYSIS OF RADIATION FROM CIRCULAR AND RECTANGULAR APERTURES: LIMITATIONS ON THEIR USE FOR BESSEL BEAM FORMATION |
| title_alt | ПОРІВНЯЛЬНИЙ АНАЛІЗ ВИПРОМІНЮВАННЯ З КРУГЛОЇ ТА ПРЯМОКУТНОЇ АНТЕННИХ АПЕРТУР. ОБМЕЖЕННЯ, ЩО ПЕРЕШКОДЖАЮТЬ ФОРМУВАННЮ БЕССЕЛЕВИХ ПУЧКІВ |
| title_full | A COMPARATIVE ANALYSIS OF RADIATION FROM CIRCULAR AND RECTANGULAR APERTURES: LIMITATIONS ON THEIR USE FOR BESSEL BEAM FORMATION |
| title_fullStr | A COMPARATIVE ANALYSIS OF RADIATION FROM CIRCULAR AND RECTANGULAR APERTURES: LIMITATIONS ON THEIR USE FOR BESSEL BEAM FORMATION |
| title_full_unstemmed | A COMPARATIVE ANALYSIS OF RADIATION FROM CIRCULAR AND RECTANGULAR APERTURES: LIMITATIONS ON THEIR USE FOR BESSEL BEAM FORMATION |
| title_short | A COMPARATIVE ANALYSIS OF RADIATION FROM CIRCULAR AND RECTANGULAR APERTURES: LIMITATIONS ON THEIR USE FOR BESSEL BEAM FORMATION |
| title_sort | comparative analysis of radiation from circular and rectangular apertures: limitations on their use for bessel beam formation |
| topic | aperture method millimeter wavelength range circular aperture radiation pattern Gaussian distribution voltage standing wave ratio (VSWR) conical lens |
| topic_facet | aperture method millimeter wavelength range circular aperture radiation pattern Gaussian distribution voltage standing wave ratio (VSWR) conical lens апертурний метод міліметровий діапазон кругла апертура діаграма спрямованості гауссів розподіл коефіцієнт стоячої хвилі за напругою (КСХН) конічна лінза |
| url | http://rpra-journal.org.ua/index.php/ra/article/view/1495 |
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