AXIALLY SYMMETRIC MODES IN AN OPEN RESONATOR

Subject and Purpose. The behavior of axially symmetric oscillations in a hemispherical open resonator (OR) integrated into a waveguide transmission line and operating in pass-through mode is studied. The apertures of the OR mirrors are 60 mm. The radius of curvature of the spherical mirror is 85 mm....

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Date:	2025
Main Authors:	Kuzmychov, I. K., Lukash, O. S., Senkevych, O. B., Voitovych, O. A., Narytnyk, T. M., Churyumov, G. I.
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Language:	English
Published:	Видавничий дім «Академперіодика» 2025
Subjects:	millimeter-wave range open resonator modes coupling element transmission coefficient probe
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topic	millimeter-wave range open resonator modes coupling element transmission coefficient probe
spellingShingle	millimeter-wave range open resonator modes coupling element transmission coefficient probe Kuzmychov, I. K. Lukash, O. S. Senkevych, O. B. Voitovych, O. A. Narytnyk, T. M. Churyumov, G. I. AXIALLY SYMMETRIC MODES IN AN OPEN RESONATOR
topic_facet	millimeter-wave range open resonator modes coupling element transmission coefficient probe міліметровий діапазон відкритий резонатор типи коливань елемент зв’язку коефіцієнт передачі пробне тіло
format	Article
author	Kuzmychov, I. K. Lukash, O. S. Senkevych, O. B. Voitovych, O. A. Narytnyk, T. M. Churyumov, G. I.
author_facet	Kuzmychov, I. K. Lukash, O. S. Senkevych, O. B. Voitovych, O. A. Narytnyk, T. M. Churyumov, G. I.
author_sort	Kuzmychov, I. K.
title	AXIALLY SYMMETRIC MODES IN AN OPEN RESONATOR
title_short	AXIALLY SYMMETRIC MODES IN AN OPEN RESONATOR
title_full	AXIALLY SYMMETRIC MODES IN AN OPEN RESONATOR
title_fullStr	AXIALLY SYMMETRIC MODES IN AN OPEN RESONATOR
title_full_unstemmed	AXIALLY SYMMETRIC MODES IN AN OPEN RESONATOR
title_sort	axially symmetric modes in an open resonator
title_alt	АКСІАЛЬНО-СИМЕТРИЧНІ КОЛИВАННЯ У ВІДКРИТОМУ РЕЗОНАТОРІ
description	Subject and Purpose. The behavior of axially symmetric oscillations in a hemispherical open resonator (OR) integrated into a waveguide transmission line and operating in pass-through mode is studied. The apertures of the OR mirrors are 60 mm. The radius of curvature of the spherical mirror is 85 mm. Two 3.6×0.17 mm slot coupling elements are positioned symmetrically about the OR axis and 13.2 mm away from it. The axially symmetric oscillations excited in a hemispherical OR by slotted coupling elements are analyzed with the view of characterizing dielectric materials using resonant methods in the EHF range.Methods and Methodology. Basic quasi-optical techniques are adopted. Namely, the electric-field structures of oscillation types are measured by the perturbation method. The resonant transmission coefficients of open oscillatory systems and the physical phenomena occurring within them are experimentally studied using standard microwave measurement techniques.Results. In the experimental study conducted at 70.622 GHz, OR oscillations with large transverse indices were identifi ed from amplitude distributions. The perturbation method was used with a 1 mm diameter probe. It has been shown that in non-axial OR excitation, axially symmetric oscillations, among others, are excited. Experimentally, a distinctive feature of those axially symmetric oscillations has been established, which is an area with zero electric-field intensity at the center of the cavity. For the investigated TEM*0,1,12 oscillation, this area is 6 mm in diameter.Conclusions. It has been demonstrated that an open resonator with axially symmetric oscillations is effective for measuring the electrophysical parameters of materials, including liquids. It has been established that the placement of a disk-shaped sample or a liquid-filled cuvette at the center of the flat mirror of a hemispherical OR not only does not disrupt the working oscillation but additionally contributes to the angular mode selection of the OR oscillation spectrum. The hemispherical OR, as considered, can also be used for dynamic quality control of various liquids. In this case, the holder, like a quartz glass tube, is positioned along the OR axis.Keywords: millimeter-wave range, open resonator, modes, coupling element, transmission coefficient, probeManuscript submitted 14.09.2025Radio phys. radio astron. 2025, 30(4): 285-295REFERENCES1. Wang, Y., and Afsar, M.N., 2003. Measurement of Complex Permittivity of Liquids Using Waveguide Techniques. Progress in Electromagnetics Research (PIER), 42(1), pp. 131—142. DOI: https://doi.org/10.2528/PIER030106022. Gennarelli, G., Romeo, S., Scarfi, M.R., and Soldovieri, F., 2013. A Microwave Resonant Sensor for Concentration Measurements of Liquid Solutions. IEEE Sens. J., 13(5), pp. 1857—1864. DOI: https://doi.org/10.1109/JSEN.2013.22440353. Arumugam, J., Edhayaraj, N.R., Shanmugavadivelu, S., and Sathyanarayanan, V., 2023. Design of Microwave Electromagnetic Sensor for Liquid Characterization. Journal of High-Frequency Communication Technologies, 1(3), pp. 73—83. DOI:https://doi.org/10.58399/TLCX99004. Volkov, V.V., Suslin, M.A., and Dumbolov, J.U., 2020. Microwave Resonance Method for Measuring Microliter Volumes of Free Moisture of Aviation Fuels. Meas. Tech., 63(7), pp. 226—234. DOI: https://doi.org/10.1007/s11018-020-01775-35. Al-Mously, S.I.Y., 2012. A Modified Complex Permittivity Measurement Technique at Microwave Frequency. Int. J. New Comput. Archit. Appl. (IJNCAA), 2(2), pp. 389—401. Available from: https://scispace.com/papers/a-modified-complex-permittivity-measurement-technique-at-2mhob8 glc26. Yashchyshyn, Ye., and Godziszewski, K., 2018. A New Method for Dielectric Characterization in Sub-THz Frequency Range. IEEE Trans. Terahertz Sci. Technol., 8(1), pp. 19—26. DOI: https://doi.org/10.1109/TTHZ.2017.27713097. Jebbor, N., Bri, S., Mediavilla, A., and Chaib,i M., 2013. A Fast Calibration-Independent Method for Complex Permittivity Determination at Microwave Frequencies. Measurement, 46(7), pp. 2206—2209. DOI: 10.1016/j.measurement.2013.04.009 DOI: https://doi.org/10.1016/j.measurement.2013.04.0098. Elmajid, H., Terhzaz, J., and Ammor, H., 2014. Optimization Technique to Estimate the Complex Permittivity of Dielectric Materials at X-Band Using Rectangular Waveguide. Int. J. Appl. Eng. Res., 9(24), pp. 26709—26718. Available from: http://www.ripublication.com/Volume/ijaerv9n24.htm9. Benali, L.A., Tribak, A., Terhzaz, J., and Mediavilla, A., 2020. An Accurate Method to Estimate Complex Permittivity of Dielectric Materials at X-band Frequencies. Int. J. Microw. Opt. Technol., 15(1), pp. 10—16. Available from: https://www.ijmot.com/VOL-15-NO-1.aspx10. Krupka, J., 2021. Microwave Measurements of Electromagnetic Properties of Materials. Materials, 14(17), pp. 1—21. DOI:https://doi.org/10.3390/ma1417509711. Breslavets, A.A., Eremenko, Z.E., Rudnev, G.O., Natarov, M.P., Glamazdin, V.V., Shubnyi, O.I., Voitovych, O.A., Gang, Zhu, Rong, Li, and Prokopenko, A.A., 2022. Hemispherical X band Microwave Small Sized Open Resonator for Wide Range from 1 to 20 Permittivity Characterization of Solid-State Dielectrics. Low Temp. Phys., 48(1), pp. 43—50. DOI:https://doi.org/10.1063/10.000896312. Alimenti, A., Pittella, E., Torokhtii, K., Pompeo, N., Piuzzi, E., and Silva, E., 2023. Dielectric Loaded Resonator for the Measurement of the Complex Permittivity of Dielectric Substrates. IEEE Trans. Instrum. Meas., 72(1), pp. 1—9. DOI: https://doi.org/10.1109/TIM.2023.323630113. Drobakhin, O.O., 2025. Development of Measurement Methods in Microwave and Terahertz Ranges of Electromagnetic Waves in Ukraine (Review). Radio Electron. Commun. Syst., 67(4), pp. 161—179. DOI: https://doi.org/10.3103/S073527272404003414. Kumar, A., and Sharma, S., 2007. Measurement of Dielectric Constant and Loss Factor of the Dielectric Material at Microwave Frequencies. Prog. Electromagn. Res., 69, pp. 47—54. DOI: https://doi.org/10.2528/PIER0611120415. Bendaoued, M., Terhzaz, J., and Mandry, R., 2017. Determining the Complex Permittivity of Building Dielectric Materials using a Propagation Constant Measurement. Int. J. Electr. Comput. Eng., 7(4), pp. 1681—1685. DOI: https://doi.org/10.11591/ijece.v7i4.pp1681-168516. Stumper, U., 1973. A TE01n Cavity Resonator Method to Determine the Complex Permittivity of Low Loss Liquids at Millimeter Wavelengths. Rev. Sci. Instrum., 44(2), pp. 165—169. DOI: https://doi.org/10.1063/1.168607317. Abbas, Z., Pollard, R.D., and Kelsall, R.W., 2001. Complex Permittivity Measurements at Ka-Band Using Rectangular Dielectric Waveguide. IEEE Trans. Instrum. Meas., 50(5), pp. 1334—1342. DOI: https://doi.org/10.1109/19.96320718. Vuks, M.V., 1984. Electrical and Optical Properties of Molecules and Condensed Media. Leningrad, USSR: Leningrad University Publishing House, 1984, pp. 60—62.19. Afsar, M.N., Button, K.J., 1985. Millimeter Wave Dielectric Measurement of Materials. Proc. IEEE, 73(1), pp. 131—153. DOI: https://doi.org/10.1109/PROC.1985.1311420. Afsar, M.N., Li, X., and Chi, H., 1990. An Automated 60 GHz Open Resonator System for Precision Dielectric Measurements. IEEE Trans. Microwave Theory Tech., 38(12), pp. 1845—1853. DOI: https://doi.org/10.1109/22.6456521. Afsar, M.N., Chen, S., and Wang, Y., 2005. An Improved 60 GHz Open Resonator System for Accurate Measurement of Dielectric Permittivity. In: AP-S Int. Symp., Conf. Proc. Washington, DC, USA, 03—08 July 2005, pp. 1—5. DOI: https://doi.org/10.1109/APS.2005.155284222. Vlasov, S.N., Parshin, V.V., and Serov, E.A., 2010. Methods for Investigating Thin Dielectric Films in the Millimeter Range. Tech. Phys., 55(12), pp. 1781—1787. DOI: https://doi.org/10.1134/S106378421012012123. Yang, B.B., Katz, S.L., Willis, K.J., Weber, M.J., Knezevic, I., and Hagness, S.C., 2012. A High-Q Terahertz Resonator for the Measurement of Electronic Properties of Conductors and Low-Loss Dielectrics. IEEE Trans. Terahertz Sci. Technol., 2(4),pp. 449—459. DOI: https://doi.org/10.1109/TTHZ.2012.219957824. Parshin, V.V., and Serov, E.A., 2012. Resonance Method for Studying Dielectric Liquids in Millimeter and Submillimeter Wave Ranges. Radiophys. Quantum Electron., 54(8–9), pp. 632—637. DOI: https://doi.org/10.1007/s11141-012-9324-x25. Karpisz, T., Salski, B., Kopyt, P., and Krupka, J., 2019. Measurement of Dielectrics from 20 to 50 GHz with a Fabry–Pérot Open Resonator. IEEE Trans. Microwave Th eory Tech., 67(5), pp. 1901—1908. DOI: https://doi.org/10.1109/TMTT.2019.290554926. Givot, B.L., Gregory, A.P., Salski, B., Zentis, F., Pettit, N., and Karpisz, N., 2021. A Comparison of Measurements of the Permittivity and Loss Angle of Polymers in the Frequency Range 10 GHz to 90 GHz. In: 15th European Conf. Antennas and Propagation (EuCAP), Conf. Proc. Dusseldorf, Germany, 22—26 March 2021, pp. 1—5. DOI: https://doi.org/10.23919/EuCAP51087.2021.941129827. Kayro, N.S., Teterina, D.D., Badin, A.V., and Bilinskii, K.V., 2021. Automated system based on open resonator for measuring the electrophysical parameters of sheet dielectrics. J. Phys.: Conf. Ser., 1989(1), pp. 012020 (1—5). DOI: https://doi.org/10.1088/1742-6596/1989/1/01202028. Karpisz, T., Salski, B., Kopyt, P., Krupka, J., and Wojciechowski, M., 2022. Measurement of uniaxially anisotropic dielectrics with a Fabry-Perot open resonator in the 20—50 GHz range. IEEE Microw. Wirel. Compon. Lett., 32(5), pp. 441—444. DOI:https://doi.org/10.1109/LMWC.2022.315593829. Elwood, B.D., Grimes, P.K., Kovac, J., Eiben, M., and Meiners, G., 2024. Fabry–Perot Open Resonant Cavities for Measuring the Dielectric Parameters of mm-Wave Optical Materials. ArXiv:2411.01058v1 [physics.optics], pp. 1—12. DOI:https://doi.org/10.1117/12.301914930. Chigryai, E.E., Garin, B.M., and Denisyuk, R.N., 2018. Measurement of Dielectric Loss at Millimeter Range in the Low Loss Materials with Arbitrary Ratio of Wavelength and Sample Thickness. Journal of Radio Electronics (JRE), 10, pp. 1—7.DOI: https://doi.org/10.30898/1684-1719.2018.10.1031. Kuzmiche v, I.K., and Popkov, A.Yu., 2018. Resonant Systems for Measurement of Electromagnetic Properties of Substances at V-Band Frequencies. Chapter 3. In: Emerging Microwave Technologies in Industrial, Agricultural, Medical and Food Processing. London, United Kingdom: Intech Open Publ., 2018, pp. 27—53. DOI: https://doi.org/10.5772/intechopen.7364332. Kuzmicho v, І.К., Кogut, О.Е., Muzychishin, B.І., Popkov, O.Yu., and Senkevych, O.B., 2023. The TE01 wave excitation in a circular waveguide using higher-order modes of an open resonator. Radio Phys. Radio Astron., 28(3), pp. 243—256. DOI:https://doi.org/10.15407/rpra28.03.24333. Menzel, R., 2007. Photonics: Linear and Nonlinear Interactions of Laser Light and Matter. 2nd ed. Berlin, Germany: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, pp. 395—409. DOI: https://doi.org/10.1007/978-3-540-45158-734. Muzychishin, B.I., Kuzmichev, I.K., Senkevych, O.B., and Pogarsky, S.A., 2022. Spectrum of OR Oscillations with a Segment of a Circular Waveguide. In: 2022 IEEE 9th Int. Conf. Problems of Info communications Science and Technology (PICS&T ‘2022): Conf. Proc. Kyiv, Ukraine, 10—12 Oct. 2022, pp. 524—528. DOI: https://doi.org/10.1109/PICST57299.2022.1023866335. Valitov, R.A. (ed.), Dyubko, S.F., Kamyshan, V.V., Kuzmichev, V.M., Makarenko, B.I., Sokolov, A.V., and Sheiko, V.P., 1969. Submillimeter Wave Technique. Moscow, USSR: Sov. radio Publ., pp. 219—229.36. Yang, Z., Lin, C., and Zho, Y., 1985. A Method for Measurement of Q-Factor at Millimeter Wavelength. In: 10th Int. Conf. Infrared and Millimeter Waves, Conf. Proc. Lake Buena Vista, Florida, USA, 9—13 Dec. 1985, pp. 350—351. DOI: https://doi.org/10.1109/IRMM.1985.912671837. Kuzmiche v, I.K., 2002. The Probe Diameter Choosing for the Investigation of the Field Distribution in the Small Aperture Open resonator. Telecommunications and Radio Engineering, 58(7—8), pp. 59—63. DOI: https://doi.org/10.1615/TelecomRadEng.v58.i7-8.5038. Tarasov, L.V., 1981. Physics of processes in coherent optical radiation generators. Moscow, USSR: Radio i Svyaz’ Publ., 1981, pp. 141—212.39. Weber, H., Herziger, G., Poprawe, R. (eds.), 2006. Laser Physics and Applications. Laser Fundamentals. Part 2. Group VIII, Vol. 1. Berlin, Germany: Springer-Verlag, Berlin, Heidelberg, New York, pp. 149–161 ISSN 1619-4802.40. Kogelnik, H., 1964. Coupling and conversion coefficients for optical modes. In: Quasi-Optics, Proc. Symp. New York, NY, 8—10 June 1964. Microwave Research Institute Symposia Series. Vol. 14. Brooklyn, NY: Polytechnic Institute of Brooklyn,Polytechnic Press, pp. 333–347. ISBN 10 0470274298.
publisher	Видавничий дім «Академперіодика»
publishDate	2025
url	http://rpra-journal.org.ua/index.php/ra/article/view/1486
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spelling	rpra-journalorgua-article-14862025-12-17T13:02:08Z AXIALLY SYMMETRIC MODES IN AN OPEN RESONATOR АКСІАЛЬНО-СИМЕТРИЧНІ КОЛИВАННЯ У ВІДКРИТОМУ РЕЗОНАТОРІ Kuzmychov, I. K. Lukash, O. S. Senkevych, O. B. Voitovych, O. A. Narytnyk, T. M. Churyumov, G. I. millimeter-wave range; open resonator; modes; coupling element; transmission coefficient; probe міліметровий діапазон; відкритий резонатор; типи коливань; елемент зв’язку; коефіцієнт передачі; пробне тіло Subject and Purpose. The behavior of axially symmetric oscillations in a hemispherical open resonator (OR) integrated into a waveguide transmission line and operating in pass-through mode is studied. The apertures of the OR mirrors are 60 mm. The radius of curvature of the spherical mirror is 85 mm. Two 3.6×0.17 mm slot coupling elements are positioned symmetrically about the OR axis and 13.2 mm away from it. The axially symmetric oscillations excited in a hemispherical OR by slotted coupling elements are analyzed with the view of characterizing dielectric materials using resonant methods in the EHF range.Methods and Methodology. Basic quasi-optical techniques are adopted. Namely, the electric-field structures of oscillation types are measured by the perturbation method. The resonant transmission coefficients of open oscillatory systems and the physical phenomena occurring within them are experimentally studied using standard microwave measurement techniques.Results. In the experimental study conducted at 70.622 GHz, OR oscillations with large transverse indices were identifi ed from amplitude distributions. The perturbation method was used with a 1 mm diameter probe. It has been shown that in non-axial OR excitation, axially symmetric oscillations, among others, are excited. Experimentally, a distinctive feature of those axially symmetric oscillations has been established, which is an area with zero electric-field intensity at the center of the cavity. For the investigated TEM0,1,12 oscillation, this area is 6 mm in diameter.Conclusions. It has been demonstrated that an open resonator with axially symmetric oscillations is effective for measuring the electrophysical parameters of materials, including liquids. It has been established that the placement of a disk-shaped sample or a liquid-filled cuvette at the center of the flat mirror of a hemispherical OR not only does not disrupt the working oscillation but additionally contributes to the angular mode selection of the OR oscillation spectrum. The hemispherical OR, as considered, can also be used for dynamic quality control of various liquids. In this case, the holder, like a quartz glass tube, is positioned along the OR axis.Keywords: millimeter-wave range, open resonator, modes, coupling element, transmission coefficient, probeManuscript submitted 14.09.2025Radio phys. radio astron. 2025, 30(4): 285-295REFERENCES1. Wang, Y., and Afsar, M.N., 2003. Measurement of Complex Permittivity of Liquids Using Waveguide Techniques. Progress in Electromagnetics Research (PIER), 42(1), pp. 131—142. DOI: https://doi.org/10.2528/PIER030106022. Gennarelli, G., Romeo, S., Scarfi, M.R., and Soldovieri, F., 2013. A Microwave Resonant Sensor for Concentration Measurements of Liquid Solutions. IEEE Sens. J., 13(5), pp. 1857—1864. DOI: https://doi.org/10.1109/JSEN.2013.22440353. Arumugam, J., Edhayaraj, N.R., Shanmugavadivelu, S., and Sathyanarayanan, V., 2023. Design of Microwave Electromagnetic Sensor for Liquid Characterization. Journal of High-Frequency Communication Technologies, 1(3), pp. 73—83. DOI:https://doi.org/10.58399/TLCX99004. Volkov, V.V., Suslin, M.A., and Dumbolov, J.U., 2020. Microwave Resonance Method for Measuring Microliter Volumes of Free Moisture of Aviation Fuels. Meas. Tech., 63(7), pp. 226—234. DOI: https://doi.org/10.1007/s11018-020-01775-35. Al-Mously, S.I.Y., 2012. A Modified Complex Permittivity Measurement Technique at Microwave Frequency. Int. J. New Comput. Archit. Appl. (IJNCAA), 2(2), pp. 389—401. Available from: https://scispace.com/papers/a-modified-complex-permittivity-measurement-technique-at-2mhob8 glc26. Yashchyshyn, Ye., and Godziszewski, K., 2018. A New Method for Dielectric Characterization in Sub-THz Frequency Range. IEEE Trans. Terahertz Sci. Technol., 8(1), pp. 19—26. DOI: https://doi.org/10.1109/TTHZ.2017.27713097. Jebbor, N., Bri, S., Mediavilla, A., and Chaib,i M., 2013. A Fast Calibration-Independent Method for Complex Permittivity Determination at Microwave Frequencies. Measurement, 46(7), pp. 2206—2209. DOI: 10.1016/j.measurement.2013.04.009 DOI: https://doi.org/10.1016/j.measurement.2013.04.0098. Elmajid, H., Terhzaz, J., and Ammor, H., 2014. Optimization Technique to Estimate the Complex Permittivity of Dielectric Materials at X-Band Using Rectangular Waveguide. Int. J. Appl. Eng. Res., 9(24), pp. 26709—26718. Available from: http://www.ripublication.com/Volume/ijaerv9n24.htm9. Benali, L.A., Tribak, A., Terhzaz, J., and Mediavilla, A., 2020. An Accurate Method to Estimate Complex Permittivity of Dielectric Materials at X-band Frequencies. Int. J. Microw. Opt. Technol., 15(1), pp. 10—16. Available from: https://www.ijmot.com/VOL-15-NO-1.aspx10. Krupka, J., 2021. Microwave Measurements of Electromagnetic Properties of Materials. Materials, 14(17), pp. 1—21. DOI:https://doi.org/10.3390/ma1417509711. Breslavets, A.A., Eremenko, Z.E., Rudnev, G.O., Natarov, M.P., Glamazdin, V.V., Shubnyi, O.I., Voitovych, O.A., Gang, Zhu, Rong, Li, and Prokopenko, A.A., 2022. Hemispherical X band Microwave Small Sized Open Resonator for Wide Range from 1 to 20 Permittivity Characterization of Solid-State Dielectrics. Low Temp. Phys., 48(1), pp. 43—50. DOI:https://doi.org/10.1063/10.000896312. Alimenti, A., Pittella, E., Torokhtii, K., Pompeo, N., Piuzzi, E., and Silva, E., 2023. Dielectric Loaded Resonator for the Measurement of the Complex Permittivity of Dielectric Substrates. IEEE Trans. Instrum. Meas., 72(1), pp. 1—9. DOI: https://doi.org/10.1109/TIM.2023.323630113. Drobakhin, O.O., 2025. Development of Measurement Methods in Microwave and Terahertz Ranges of Electromagnetic Waves in Ukraine (Review). Radio Electron. Commun. Syst., 67(4), pp. 161—179. DOI: https://doi.org/10.3103/S073527272404003414. Kumar, A., and Sharma, S., 2007. Measurement of Dielectric Constant and Loss Factor of the Dielectric Material at Microwave Frequencies. Prog. Electromagn. Res., 69, pp. 47—54. DOI: https://doi.org/10.2528/PIER0611120415. Bendaoued, M., Terhzaz, J., and Mandry, R., 2017. Determining the Complex Permittivity of Building Dielectric Materials using a Propagation Constant Measurement. Int. J. Electr. Comput. Eng., 7(4), pp. 1681—1685. DOI: https://doi.org/10.11591/ijece.v7i4.pp1681-168516. Stumper, U., 1973. A TE01n Cavity Resonator Method to Determine the Complex Permittivity of Low Loss Liquids at Millimeter Wavelengths. Rev. Sci. Instrum., 44(2), pp. 165—169. DOI: https://doi.org/10.1063/1.168607317. Abbas, Z., Pollard, R.D., and Kelsall, R.W., 2001. Complex Permittivity Measurements at Ka-Band Using Rectangular Dielectric Waveguide. IEEE Trans. Instrum. Meas., 50(5), pp. 1334—1342. DOI: https://doi.org/10.1109/19.96320718. Vuks, M.V., 1984. Electrical and Optical Properties of Molecules and Condensed Media. Leningrad, USSR: Leningrad University Publishing House, 1984, pp. 60—62.19. Afsar, M.N., Button, K.J., 1985. Millimeter Wave Dielectric Measurement of Materials. Proc. IEEE, 73(1), pp. 131—153. DOI: https://doi.org/10.1109/PROC.1985.1311420. Afsar, M.N., Li, X., and Chi, H., 1990. An Automated 60 GHz Open Resonator System for Precision Dielectric Measurements. IEEE Trans. Microwave Theory Tech., 38(12), pp. 1845—1853. DOI: https://doi.org/10.1109/22.6456521. Afsar, M.N., Chen, S., and Wang, Y., 2005. An Improved 60 GHz Open Resonator System for Accurate Measurement of Dielectric Permittivity. In: AP-S Int. Symp., Conf. Proc. Washington, DC, USA, 03—08 July 2005, pp. 1—5. DOI: https://doi.org/10.1109/APS.2005.155284222. Vlasov, S.N., Parshin, V.V., and Serov, E.A., 2010. Methods for Investigating Thin Dielectric Films in the Millimeter Range. Tech. Phys., 55(12), pp. 1781—1787. DOI: https://doi.org/10.1134/S106378421012012123. Yang, B.B., Katz, S.L., Willis, K.J., Weber, M.J., Knezevic, I., and Hagness, S.C., 2012. A High-Q Terahertz Resonator for the Measurement of Electronic Properties of Conductors and Low-Loss Dielectrics. IEEE Trans. Terahertz Sci. Technol., 2(4),pp. 449—459. DOI: https://doi.org/10.1109/TTHZ.2012.219957824. Parshin, V.V., and Serov, E.A., 2012. Resonance Method for Studying Dielectric Liquids in Millimeter and Submillimeter Wave Ranges. Radiophys. Quantum Electron., 54(8–9), pp. 632—637. DOI: https://doi.org/10.1007/s11141-012-9324-x25. Karpisz, T., Salski, B., Kopyt, P., and Krupka, J., 2019. Measurement of Dielectrics from 20 to 50 GHz with a Fabry–Pérot Open Resonator. IEEE Trans. Microwave Th eory Tech., 67(5), pp. 1901—1908. DOI: https://doi.org/10.1109/TMTT.2019.290554926. Givot, B.L., Gregory, A.P., Salski, B., Zentis, F., Pettit, N., and Karpisz, N., 2021. A Comparison of Measurements of the Permittivity and Loss Angle of Polymers in the Frequency Range 10 GHz to 90 GHz. In: 15th European Conf. Antennas and Propagation (EuCAP), Conf. Proc. Dusseldorf, Germany, 22—26 March 2021, pp. 1—5. DOI: https://doi.org/10.23919/EuCAP51087.2021.941129827. Kayro, N.S., Teterina, D.D., Badin, A.V., and Bilinskii, K.V., 2021. Automated system based on open resonator for measuring the electrophysical parameters of sheet dielectrics. J. Phys.: Conf. Ser., 1989(1), pp. 012020 (1—5). DOI: https://doi.org/10.1088/1742-6596/1989/1/01202028. Karpisz, T., Salski, B., Kopyt, P., Krupka, J., and Wojciechowski, M., 2022. Measurement of uniaxially anisotropic dielectrics with a Fabry-Perot open resonator in the 20—50 GHz range. IEEE Microw. Wirel. Compon. Lett., 32(5), pp. 441—444. DOI:https://doi.org/10.1109/LMWC.2022.315593829. Elwood, B.D., Grimes, P.K., Kovac, J., Eiben, M., and Meiners, G., 2024. Fabry–Perot Open Resonant Cavities for Measuring the Dielectric Parameters of mm-Wave Optical Materials. ArXiv:2411.01058v1 [physics.optics], pp. 1—12. DOI:https://doi.org/10.1117/12.301914930. Chigryai, E.E., Garin, B.M., and Denisyuk, R.N., 2018. Measurement of Dielectric Loss at Millimeter Range in the Low Loss Materials with Arbitrary Ratio of Wavelength and Sample Thickness. Journal of Radio Electronics (JRE), 10, pp. 1—7.DOI: https://doi.org/10.30898/1684-1719.2018.10.1031. Kuzmiche v, I.K., and Popkov, A.Yu., 2018. Resonant Systems for Measurement of Electromagnetic Properties of Substances at V-Band Frequencies. Chapter 3. In: Emerging Microwave Technologies in Industrial, Agricultural, Medical and Food Processing. London, United Kingdom: Intech Open Publ., 2018, pp. 27—53. DOI: https://doi.org/10.5772/intechopen.7364332. Kuzmicho v, І.К., Кogut, О.Е., Muzychishin, B.І., Popkov, O.Yu., and Senkevych, O.B., 2023. The TE01 wave excitation in a circular waveguide using higher-order modes of an open resonator. Radio Phys. Radio Astron., 28(3), pp. 243—256. DOI:https://doi.org/10.15407/rpra28.03.24333. Menzel, R., 2007. Photonics: Linear and Nonlinear Interactions of Laser Light and Matter. 2nd ed. Berlin, Germany: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, pp. 395—409. DOI: https://doi.org/10.1007/978-3-540-45158-734. Muzychishin, B.I., Kuzmichev, I.K., Senkevych, O.B., and Pogarsky, S.A., 2022. Spectrum of OR Oscillations with a Segment of a Circular Waveguide. In: 2022 IEEE 9th Int. Conf. Problems of Info communications Science and Technology (PICS&T ‘2022): Conf. Proc. Kyiv, Ukraine, 10—12 Oct. 2022, pp. 524—528. DOI: https://doi.org/10.1109/PICST57299.2022.1023866335. Valitov, R.A. (ed.), Dyubko, S.F., Kamyshan, V.V., Kuzmichev, V.M., Makarenko, B.I., Sokolov, A.V., and Sheiko, V.P., 1969. Submillimeter Wave Technique. Moscow, USSR: Sov. radio Publ., pp. 219—229.36. Yang, Z., Lin, C., and Zho, Y., 1985. A Method for Measurement of Q-Factor at Millimeter Wavelength. In: 10th Int. Conf. Infrared and Millimeter Waves, Conf. Proc. Lake Buena Vista, Florida, USA, 9—13 Dec. 1985, pp. 350—351. DOI: https://doi.org/10.1109/IRMM.1985.912671837. Kuzmiche v, I.K., 2002. The Probe Diameter Choosing for the Investigation of the Field Distribution in the Small Aperture Open resonator. Telecommunications and Radio Engineering, 58(7—8), pp. 59—63. DOI: https://doi.org/10.1615/TelecomRadEng.v58.i7-8.5038. Tarasov, L.V., 1981. Physics of processes in coherent optical radiation generators. Moscow, USSR: Radio i Svyaz’ Publ., 1981, pp. 141—212.39. Weber, H., Herziger, G., Poprawe, R. (eds.), 2006. Laser Physics and Applications. Laser Fundamentals. Part 2. Group VIII, Vol. 1. Berlin, Germany: Springer-Verlag, Berlin, Heidelberg, New York, pp. 149–161 ISSN 1619-4802.40. Kogelnik, H., 1964. Coupling and conversion coefficients for optical modes. In: Quasi-Optics, Proc. Symp. New York, NY, 8—10 June 1964. Microwave Research Institute Symposia Series. Vol. 14. Brooklyn, NY: Polytechnic Institute of Brooklyn,Polytechnic Press, pp. 333–347. ISBN 10 0470274298. Предмет і мета роботи. Предметом досліджень є поведінка аксіально-симетричних коливань у напівсферичному відкритому резонаторі (ВР), що інтегрований до хвилевідної лінії передачі і працює в наскрізному режимі. Апертури дзеркал ВР дорівнюють 60 мм, радіус кривизни сферичного відбивача становить 85 мм. Два щілинних елементи зв›язку розміром 3.6 × 0.17 мм розташовані симетрично на відстані 13.2 мм від осі ВР. Метою роботи є дослідження аксіально-симетричних коливань, які збуджуються у такому напівсферичному ВР щілинними елементами зв’язку. Актуальність цих досліджень пов’язана з вимірюванням методом ВР параметрів діелектриків у ВВЧ-діапазоні.Методи та методологія. Для вирішення поставлених у роботі завдань використано основні методи квазіоптики. Для вимірювання структур електричних полів розглянутих типів коливань застосовано метод пробного тіла. Резонансні коефіцієнти передачі відкритих коливальних систем і фізичні явища, що в них відбуваються, досліджуються за допомогою стандартних методів НВЧ-вимірювань.Результати. Дослідження проводили на частоті 70.622 ГГц. Для вимірювання амплітудного розподілу збуджуваних у розглянутому резонаторі коливань використовували пробне тіло діаметром 1 мм. У резонаторі збуджувалися коливання з великими поперечними індексами. Показано, що при неосьовому збудженні у ВР існують аксіально-симетричні коливання. Експериментально встановлено відмінну особливість таких коливань: у центрі резонатора існує область з нульовою інтенсивністю електричного поля. Для досліджуваного коливання ТЕМ0,1,12 ця область має діаметр 6 мм.Висновки. Відкритий резонатор з аксіально-симетричними коливаннями є ефективним для вимірювання електрофізичних параметрів матеріалів, включаючи рідини. Установлено, що розміщення дископодібного зразка або кювети, заповненої рідиною, в центрі плоского дзеркала напівсферичного ВР не тільки не порушує робоче коливання, але й додатково сприяє додатковій селекції спектра коливань ВР. Розглянутий ВР також може бути використаний для динамічного контролю якості різних рідин. У цьому випадку вздовж осі резонатора розташовують тримач у вигляді кварцової скляної трубки.Ключові слова: міліметровий діапазон, відкритий резонатор, типи коливань, елемент зв’язку, коефіцієнт передачі, пробне тілоСтаття надійшла до редакції 14.09.2025Radio phys. radio astron. 2025, 30(4): 285-295БІБЛІОГРАФІЧНИЙ СПИСОК 1. Wang, Y., and Afsar, M.N., 2003. Measurement of Complex Permittivity of Liquids Using Waveguide Techniques. Progress in Electromagnetics Research (PIER), 42(1), pp. 131—142. DOI: 10.2528/PIER030106022. Gennarelli, G., Romeo, S., Scarfi, M.R., and Soldovieri, F., 2013. A Microwave Resonant Sensor for Concentration Measurements of Liquid Solutions. IEEE Sens. J., 13(5), pp. 1857—1864. DOI: 10.1109/JSEN.2013.22440353. Arumugam, J., Edhayaraj, N.R., Shanmugavadivelu, S., and Sathyanarayanan, V., 2023. Design of Microwave Electromagnetic Sensor for Liquid Characterization. Journal of High-Frequency Communication Technologies, 1(3), pp. 73—83. DOI:10.58399/TLCX99004. Volkov, V.V., Suslin, M.A., and Dumbolov, J.U., 2020. Microwave Resonance Method for Measuring Microliter Volumes of Free Moisture of Aviation Fuels. Meas. Tech., 63(7), pp. 226—234. DOI: 10.1007/s11018-020-01775-35. Al-Mously, S.I.Y., 2012. A Modified Complex Permittivity Measurement Technique at Microwave Frequency. Int. J. New Comput. Archit. Appl. (IJNCAA), 2(2), pp. 389—401. Available from: https://scispace.com/papers/a-modified-complex-permittivity-measurement-technique-at-2mhob8 glc26. Yashchyshyn, Ye., and Godziszewski, K., 2018. A New Method for Dielectric Characterization in Sub-THz Frequency Range. IEEE Trans. Terahertz Sci. Technol., 8(1), pp. 19—26. DOI: 10.1109/TTHZ.2017.27713097. Jebbor, N., Bri, S., Mediavilla, A., and Chaib,i M., 2013. A Fast Calibration-Independent Method for Complex Permittivity Determination at Microwave Frequencies. Measurement, 46(7), pp. 2206—2209. DOI: 10.1016/j.measurement.2013.04.0098. Elmajid, H., Terhzaz, J., and Ammor, H., 2014. Optimization Technique to Estimate the Complex Permittivity of Dielectric Materials at X-Band Using Rectangular Waveguide. Int. J. Appl. Eng. Res., 9(24), pp. 26709—26718. Available from: http://www.ripublication.com/Volume/ijaerv9n24.htm9. Benali, L.A., Tribak, A., Terhzaz, J., and Mediavilla, A., 2020. An Accurate Method to Estimate Complex Permittivity of Dielectric Materials at X-band Frequencies. Int. J. Microw. Opt. Technol., 15(1), pp. 10—16. Available from: https://www.ijmot.com/VOL-15-NO-1.aspx10. Krupka, J., 2021. Microwave Measurements of Electromagnetic Properties of Materials. Materials, 14(17), pp. 1—21. DOI:10.3390/ma1417509711. Breslavets, A.A., Eremenko, Z.E., Rudnev, G.O., Natarov, M.P., Glamazdin, V.V., Shubnyi, O.I., Voitovych, O.A., Gang, Zhu, Rong, Li, and Prokopenko, A.A., 2022. Hemispherical X band Microwave Small Sized Open Resonator for Wide Range from 1 to 20 Permittivity Characterization of Solid-State Dielectrics. Low Temp. Phys., 48(1), pp. 43—50. DOI:10.1063/10.000896312. Alimenti, A., Pittella, E., Torokhtii, K., Pompeo, N., Piuzzi, E., and Silva, E., 2023. Dielectric Loaded Resonator for the Measurement of the Complex Permittivity of Dielectric Substrates. IEEE Trans. Instrum. Meas., 72(1), pp. 1—9. DOI: 10.1109/TIM.2023.323630113. Drobakhin, O.O., 2025. Development of Measurement Methods in Microwave and Terahertz Ranges of Electromagnetic Waves in Ukraine (Review). Radio Electron. Commun. Syst., 67(4), pp. 161—179. DOI: 10.3103/S073527272404003414. Kumar, A., and Sharma, S., 2007. Measurement of Dielectric Constant and Loss Factor of the Dielectric Material at Microwave Frequencies. Prog. Electromagn. Res., 69, pp. 47—54. DOI: 10.2528/PIER0611120415. Bendaoued, M., Terhzaz, J., and Mandry, R., 2017. Determining the Complex Permittivity of Building Dielectric Materials using a Propagation Constant Measurement. Int. J. Electr. Comput. Eng., 7(4), pp. 1681—1685. DOI: 10.11591/ijece.v7i4.pp1681-168516. Stumper, U., 1973. A TE01n Cavity Resonator Method to Determine the Complex Permittivity of Low Loss Liquids at Millimeter Wavelengths. Rev. Sci. Instrum., 44(2), pp. 165—169. DOI: 10.1063/1.168607317. Abbas, Z., Pollard, R.D., and Kelsall, R.W., 2001. Complex Permittivity Measurements at Ka-Band Using Rectangular Dielectric Waveguide. IEEE Trans. Instrum. Meas., 50(5), pp. 1334—1342. DOI: 10.1109/19.96320718. Vuks, M.V., 1984. Electrical and Optical Properties of Molecules and Condensed Media. Leningrad, USSR: Leningrad University Publishing House, 1984, pp. 60—62.19. Afsar, M.N., Button, K.J., 1985. Millimeter Wave Dielectric Measurement of Materials. Proc. IEEE, 73(1), pp. 131—153. DOI: 10.1109/PROC.1985.1311420. Afsar, M.N., Li, X., and Chi, H., 1990. An Automated 60 GHz Open Resonator System for Precision Dielectric Measurements. IEEE Trans. Microwave Theory Tech., 38(12), pp. 1845—1853. DOI: 10.1109/22.6456521. Afsar, M.N., Chen, S., and Wang, Y., 2005. An Improved 60 GHz Open Resonator System for Accurate Measurement of Dielectric Permittivity. In: AP-S Int. Symp., Conf. Proc. Washington, DC, USA, 03—08 July 2005, pp. 1—5. DOI: 10.1109/APS.2005.155284222. Vlasov, S.N., Parshin, V.V., and Serov, E.A., 2010. Methods for Investigating Thin Dielectric Films in the Millimeter Range. Tech. Phys., 55(12), pp. 1781—1787. DOI: 10.1134/S106378421012012123. Yang, B.B., Katz, S.L., Willis, K.J., Weber, M.J., Knezevic, I., and Hagness, S.C., 2012. A High-Q Terahertz Resonator for the Measurement of Electronic Properties of Conductors and Low-Loss Dielectrics. IEEE Trans. Terahertz Sci. Technol., 2(4),pp. 449—459. DOI: 10.1109/TTHZ. 2012.219957824. Parshin, V.V., and Serov, E.A., 2012. Resonance Method for Studying Dielectric Liquids in Millimeter and Submillimeter Wave Ranges. Radiophys. Quantum Electron., 54(8–9), pp. 632—637. DOI: 10.1007/s11141-012-9324-x25. Karpisz, T., Salski, B., Kopyt, P., and Krupka, J., 2019. Measurement of Dielectrics from 20 to 50 GHz with a Fabry–Pérot Open Resonator. IEEE Trans. Microwave Th eory Tech., 67(5), pp. 1901—1908. DOI: 10.1109/TMTT.2019.290554926. Givot, B.L., Gregory, A.P., Salski, B., Zentis, F., Pettit, N., and Karpisz, N., 2021. A Comparison of Measurements of the Permittivity and Loss Angle of Polymers in the Frequency Range 10 GHz to 90 GHz. In: 15th European Conf. Antennas and Propagation (EuCAP), Conf. Proc. Dusseldorf, Germany, 22—26 March 2021, pp. 1—5. DOI: 10.23919/Eu-CAP51087.2021.941129827. Kayro, N.S., Teterina, D.D., Badin, A.V., and Bilinskii, K.V., 2021. Automated system based on open resonator for measuring the electrophysical parameters of sheet dielectrics. J. Phys.: Conf. Ser., 1989(1), pp. 012020 (1—5). DOI: 10.1088/1742-6596/1989/1/01202028. Karpisz, T., Salski, B., Kopyt, P., Krupka, J., and Wojciechowski, M., 2022. Measurement of uniaxially anisotropic dielectrics with a Fabry-Perot open resonator in the 20—50 GHz range. IEEE Microw. Wirel. Compon. Lett., 32(5), pp. 441—444. DOI:10.1109/LMWC.2022.315593829. Elwood, B.D., Grimes, P.K., Kovac, J., Eiben, M., and Meiners, G., 2024. Fabry–Perot Open Resonant Cavities for Measuring the Dielectric Parameters of mm-Wave Optical Materials. ArXiv:2411.01058v1 [physics.optics], pp. 1—12. DOI:10.48550/arXiv.2411.0105830. Chigryai, E.E., Garin, B.M., and Denisyuk, R.N., 2018. Measurement of Dielectric Loss at Millimeter Range in the Low Loss Materials with Arbitrary Ratio of Wavelength and Sample Thickness. Journal of Radio Electronics (JRE), 10, pp. 1—7.DOI: 10.30898/1684-1719.2018.10.1031. Kuzmiche v, I.K., and Popkov, A.Yu., 2018. Resonant Systems for Measurement of Electromagnetic Properties of Substances at V-Band Frequencies. Chapter 3. In: Emerging Microwave Technologies in Industrial, Agricultural, Medical and Food Processing. London, United Kingdom: Intech Open Publ., 2018, pp. 27—53. DOI: 10.5772/intechopen.7364332. Kuzmicho v, І.К., Кogut, О.Е., Muzychishin, B.І., Popkov, O.Yu., and Senkevych, O.B., 2023. The TE01 wave excitation in a circular waveguide using higher-order modes of an open resonator. Radio Phys. Radio Astron., 28(3), pp. 243—256. DOI:10.15407/rpra28.03.24333. Menzel, R., 2007. Photonics: Linear and Nonlinear Interactions of Laser Light and Matter. 2nd ed. Berlin, Germany: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, pp. 395—409. DOI: 10.1007/978-3-540-45158-734. Muzychishin, B.I., Kuzmichev, I.K., Senkevych, O.B., and Pogarsky, S.A., 2022. Spectrum of OR Oscillations with a Segment of a Circular Waveguide. In: 2022 IEEE 9th Int. Conf. Problems of Info communications Science and Technology (PICS&T ‘2022): Conf. Proc. Kyiv, Ukraine, 10—12 Oct. 2022, pp. 524—528. DOI: 10.1109/PICST57299.2022.1023866335. Valitov, R.A. (ed.), Dyubko, S.F., Kamyshan, V.V., Kuzmichev, V.M., Makarenko, B.I., Sokolov, A.V., and Sheiko, V.P., 1969. Submillimeter Wave Technique. Moscow, USSR: Sov. radio Publ., pp. 219—229.36. Yang, Z., Lin, C., and Zho, Y., 1985. A Method for Measurement of Q-Factor at Millimeter Wavelength. In: 10th Int. Conf. Infrared and Millimeter Waves, Conf. Proc. Lake Buena Vista, Florida, USA, 9—13 Dec. 1985, pp. 350—351. DOI: 10.1109/IRMM.1985.912671837. Kuzmiche v, I.K., 2002. The Probe Diameter Choosing for the Investigation of the Field Distribution in the Small Aperture Open resonator. Telecommunications and Radio Engineering, 58(7—8), pp. 59—63. DOI: 10.1615/TelecomRadEng.v58.i7-8.5038. Tarasov, L.V., 1981. Physics of processes in coherent optical radiation generators. Moscow, USSR: Radio i Svyaz’ Publ., 1981, pp. 141—212.39. Weber, H., Herziger, G., Poprawe, R. (eds.), 2006. Laser Physics and Applications. Laser Fundamentals. Part 2. Group VIII, Vol. 1. Berlin, Germany: Springer-Verlag, Berlin, Heidelberg, New York, pp. 149–161 ISSN 1619-4802.40. Kogelnik, H., 1964. Coupling and conversion coefficients for optical modes. In: Quasi-Optics, Proc. Symp. New York, NY, 8—10 June 1964. Microwave Research Institute Symposia Series. Vol. 14. Brooklyn, NY: Polytechnic Institute of Brooklyn,Polytechnic Press, pp. 333–347. ISBN 10 0470274298. Видавничий дім «Академперіодика» 2025-12-08 Article Article application/pdf http://rpra-journal.org.ua/index.php/ra/article/view/1486 10.15407/rpra30.04.285 РАДИОФИЗИКА И РАДИОАСТРОНОМИЯ; Vol 30, No 4 (2025); 285 RADIO PHYSICS AND RADIO ASTRONOMY; Vol 30, No 4 (2025); 285 РАДІОФІЗИКА І РАДІОАСТРОНОМІЯ; Vol 30, No 4 (2025); 285 2415-7007 1027-9636 10.15407/rpra30.04 en http://rpra-journal.org.ua/index.php/ra/article/view/1486/pdf Copyright (c) 2025 RADIO PHYSICS AND RADIO ASTRONOMY

AXIALLY SYMMETRIC MODES IN AN OPEN RESONATOR

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