AN OPEN RESONATOR WITH INTERNAL INHOMOGENEITIES
Subject and Purpose. Investigations on axially symmetric oscillations excited in a hemispherical open resonator (OR) are presented with a specific focus on the effects exerted by internal inhomogeneities in the OR structure. In this context, a waveguide section is inserted in the center of one of th...
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| author | Kuzmychov, I. K. Lukash, O. S. Voitovych, O. A. Prokopenko, Yu. V. Churyumov, G. I. |
| author_facet | Kuzmychov, I. K. Lukash, O. S. Voitovych, O. A. Prokopenko, Yu. V. Churyumov, G. I. |
| author_sort | Kuzmychov, I. K. |
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| description | Subject and Purpose. Investigations on axially symmetric oscillations excited in a hemispherical open resonator (OR) are presented with a specific focus on the effects exerted by internal inhomogeneities in the OR structure. In this context, a waveguide section is inserted in the center of one of the OR mirrors, and the field distributions of axially symmetric oscillations and the OR oscillation spectrum selection are examined. The motivation behind this study is to minimize the geometric size of the inserted waveguide while still accommodating a small-diameter dielectric sample, thereby ensuring that the measurement results are as little affected by diffraction loss as possible.Methods and Methodology. The electric-field distribution of OR eigenoscillations is studied in the framework of quasi-optic methods of probe perturbations. The OR resonance characteristics and the physical phenomena occurring within the OR are examined using established and validated techniques to measure transmission coefficients along the EHF path.Results.It has been established that in a circular waveguide with radius ɑ = 0.6042w0 (w0 is the TEM00q mode field spot radius), the TE11 mode is excited with an efficiency of 0.8993 by the central spot of the TEM10q mode. The oscillation amplitude distribution was measured at a frequency of 74.98 GHz. The axial symmetry of the OR structure is broken, but axially symmetric oscillations are still excited due to the flat insert. The circular waveguide section provides angular selection of the oscillation spectrum. The loss introduced by this waveguide to the OR does not exceed −2 dB.Conclusions. A hemispherical open resonator incorporating specific inhomogeneities that facilitate axially symmetric OR oscillations has shown potential for measuring the electrophysical parameters of materials. For this, a disk-shaped sample is placed at the bottom of a circular waveguide section inserted into the OR flat mirror in its center.Keywords: extremely high frequency (EHF) range, open resonator, axially symmetric oscillations, circular waveguide, coupling element, transmission coefficientManuscript submitted 07.02.2026Radio phys. radio astron. 2026, 31(1): 051-064REFERENCES1. 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-x2. 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. Microw. Theory Tech., 67(5), pp. 1901—1908. DOI: 10.1109/TMTT.2019.29055493. Givot, B.L., Gregory, A.P., Salski, B., Zentis, F., Pettit, N., and Karpisz, T.A., 2021. Comparison of Measurements of the Permittivity and Loss Angle of Polymers in the Frequency Range 10 GHz to 90 GHz. In: 15th European Conf. on Antennas and Propagation (EuCAP). Dusseldorf, Germany, 22—26 March 2021. P. 1—5. DOI: 10.23919/EuCAP51087.2021.94112984. 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), 012020. DOI: 10.1088/1742-6596/1989/1/0120205. Afsar, M.N., Chen, S., and Wang, Y., 2005. An Improved 60 GHz Open Resonator System for Accurate Measurement of Dielectric Permittivity. In: Proc. the AP-S Int. Symp. Washington, DC, USA, 3-8 July 2005. P. 1—5. DOI: 10.1109/APS.2005.15528426. Rahman, R., Taylor, P.C., and Scales, J.A., 2013. A System for Measuring Complex Dielectric Properties of Thin Films at Submillimeter Wavelengths Using an Open Hemispherical Cavity and a Vector Network Analyzer. Rev. Sci. Instrum., 84(8), 083901. DOI: 10.1063/1.48168287. Breslavets, A.A., Eremenko, Z.E., Rudnev, G.O., Natarov, M.P., Glamazdin, V.V., Shubnyi, O.I., Voitovych, O.A., Gang, Z., Rong, L., 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:10.1063/10.00089638. Dudorov, S.N., Lioubtchenko, D.V., Mallat, J.A., and Räisänen, A.V., 2005. Differential Open Resonator Method for Permittivity Measurements of Thin Dielectric Film on Substrate. IEEE Trans. Instrum. Meas., 54(5), pp. 1916—1920. DOI: 10.1109/TIM.2005.8533529. 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 Thicness. J. Radio Electron., 10, pp. 1—7. DOI: 10.30898/1684-1719.2018.10.1010. Kuzmichev, I.K., Melezhik, P.N., and Poyedinchuk, A.Ye., 2006. An open resonator for physical studies. Int. J. Infrared Millimeter Waves, 27(6), pp. 857—869. DOI: 10.1007/s10762-006-9122-711. Kuzmichev, I.K., and Popkov, A.Yu., 2018. Resonant Systems for Measurement of Electromagnetic Properties of Substances at V-Band Frequencies. Chap. 3. In: Emerging Microwave Technologies in Industrial, Agricultural, Medical and Food Processing. London, United Kingdom: IntechOpen Publishing house, pp. 27—53. DOI: 10.5772/intechopen.7364312. Kuzmichev, I.K., 2014. Open resonator with a section of rectangular waveguide. Radio Phys. Radio Astron., 19(3), pp. 249—257. DOI: 10.15407/rpra19.03.24913. Auston, D.H., Primich, R.I., and Hayami, R.A., 1964. Further considerations of the use of Fabry–Perot resonators in microwave plasma diagnostics. In: Quasi-Optics, Symposium on Quasi-Optics Proceedings. Brooklyn, NY: Polytechnic Press, pp. 273—304.14. Giri, D.V., 2004. High-Power Electromagnetic Radiators: Nonlethal Weapons and Other Applications. Cambridge, Massachusetts: Harvard University Press. 198 p. ISBN 9780674015692.15. Giri, D.V., Hoad, R., and Sabath, F., 2020. High-Power Electromagnetic Effects on Electronic Systems. Boston, London: Artech House. 320 p. ISBN: 9781630815882.16. Schwan, H.P., and Foster, K.R., 1977. Microwave Dielectric Properties of Tissue. Some Comments on the Rotational Mobility of Tissue Water. Biophys., 17(2), pp. 193—197. DOI: 10.1016/S0006-3495(77)85637-317. Birx, D., Dick, G.J., Little, W.A., Mercereau, J.E., and Scalapino, D.J., 1978. Pulsed frequency modulation of superconducting resonators. Appl. Phys. Lett., 33(5), pp. 466—468. DOI: http://dx.doi.org/10.1063/1.9038118. Alvarez, R.A., Birx, D., Byrne, D., Mendonca, M., and Johnson, R.M., 1981. Generation of high-power microwave pulses using a spherical superconducting cavity and interference-type switch. IEEE Trans. Magn., 17(1), pp. 935—938. DOI: 10.1109/TMAG.1981.106106719. Danilov, Yu.Yu., Kuzikov, S.V., Pavel’ev, V.G., Koshurinov, Yu.I., and Shchegol’kov, D.Yu., 2005. Linear Frequency-Modulated Pulse Compressor Based on a Three-Mirror Ring Cavity. Tech. Phys., 75(4), pp. 523—525. DOI: 10.1134/1.190179720. Kuzmichev, I.K., Popkov, A.Yu., and Rud, L.A., 2012. Excitation of TE11 and TE01 Waves in a Coaxial Waveguide Incorporated into an Open Resonator. Part 2. Switch Modeling. Phys. Bases Instrum., 1(4), pp. 14—23. DOI: 10.25210/jfop-1204-01402321. Artemenko, S.N., Kaminskii, V.L., Yushkov, Yu.G., and Dellis, A.N., 1993. Extraction of the energy in large axisymmetric resonators through an oversized coaxial line. Tech. Phys., 38(2), pp. 111—114.22. Avgustinovich, V. A., Artemenko, S. N., and Zhukov, A. A., 2013. Microwave-energy extraction from a resonator via oversized interference switch. Tech. Phys. Lett., 39(5), pp. 492—494. DOI: 10.1134/S106378501305016723. Kühn R., 1964. Mikrowellenantennen. Berlin: Veb Berlag Technik Publ., pp. 231—236.24. Bronstein, I.N., Semendyaev, K.A., Musiol, G., and Muehlig, H., 2007. Mathematics Handbook. 5th ed. Berlin, Heidelberg, New York: Springer Publishing house. ISBN 978-3-540-72121-5.25. Kogelnik, H., 1964. Coupling and convertion coefficients for optical modes. In: Quasi-Optics, Symposium on Quasi-Optics Proceedings. Brooklyn, NY: Polytechnic Press, pp. 333—347.26. Kuzmichev, I.K., 2009. Quasi-Optical Resonance Systems with Internal Inhomogeneities. Telecommunications and Radio Engineering, 68(4), pp. 299—317. DOI: 10.1615/TelecomRadEng.v68.i4.3027. Kuzmichev, I.K., 2002. The Probe Diameter Choosing for the Investigation of the Field Distribution in the Small Aperture Open Resonator. Telecommunication and Radio Engineering, 58(7—8), pp. 59—63. DOI: 10.1615/TelecomRadEng.v58.i7-8.5028. Pozar, D.M., 2012. Microwave Engineering. 4th ed. New York: Wiley & Sons, Limited, John, pp. 124—129. ISBN 978-0-470-63155-3.29. Kuzmychov, I.K., Lukash, O.S., Senkevych, O.B., Voitovych, O.A., Narytnyk, T.M., and Churyumov, G.I., 2025. Axially symmetric modes in an open resonator. Radio Phys. Radio Astron., 30(4), pp. 285—295. DOI: 10.15407/rpra30.04.28530. Marcuse, D., 1982. Light Transmission Optics. 2th ed. New York, Scarborough, Mitcham, Wokingham: Published by Van Nostrand Reinhold Company Inc., pp. 253—262. ISBN 13- 9780442263096.31. Korn, G.A., and Korn, T.M., 2000. Mathematical Handbook for Scientists and Engineers: Definitions, Th eorems, and Formulas for Reference and Review. Mineola, New York: Courier Corporation Publishing House, pp. 849—856. ISBN 0486411478,9780486411477. |
| first_indexed | 2026-03-25T02:00:05Z |
| format | Article |
| id | rpra-journalorgua-article-1491 |
| institution | Radio physics and radio astronomy |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-03-25T02:00:05Z |
| publishDate | 2026 |
| publisher | Видавничий дім «Академперіодика» |
| record_format | ojs |
| spelling | rpra-journalorgua-article-14912026-03-24T09:03:48Z AN OPEN RESONATOR WITH INTERNAL INHOMOGENEITIES ВІДКРИТИЙ РЕЗОНАТОР ІЗ ВНУТРІШНІМИ НЕОДНОРІДНОСТЯМИ Kuzmychov, I. K. Lukash, O. S. Voitovych, O. A. Prokopenko, Yu. V. Churyumov, G. I. extremely high frequency (EHF) range; open resonator; axially symmetric oscillations; circular waveguide; coupling element; transmission coefficient вкрай високочастотний діапазон; відкритий напівсферичний резонатор; аксіально-симетричні коливання; круглий хвилевід; елемент зв’язку; коефіцієнт передачі; пробне тіло Subject and Purpose. Investigations on axially symmetric oscillations excited in a hemispherical open resonator (OR) are presented with a specific focus on the effects exerted by internal inhomogeneities in the OR structure. In this context, a waveguide section is inserted in the center of one of the OR mirrors, and the field distributions of axially symmetric oscillations and the OR oscillation spectrum selection are examined. The motivation behind this study is to minimize the geometric size of the inserted waveguide while still accommodating a small-diameter dielectric sample, thereby ensuring that the measurement results are as little affected by diffraction loss as possible.Methods and Methodology. The electric-field distribution of OR eigenoscillations is studied in the framework of quasi-optic methods of probe perturbations. The OR resonance characteristics and the physical phenomena occurring within the OR are examined using established and validated techniques to measure transmission coefficients along the EHF path.Results.It has been established that in a circular waveguide with radius ɑ = 0.6042w0 (w0 is the TEM00q mode field spot radius), the TE11 mode is excited with an efficiency of 0.8993 by the central spot of the TEM10q mode. The oscillation amplitude distribution was measured at a frequency of 74.98 GHz. The axial symmetry of the OR structure is broken, but axially symmetric oscillations are still excited due to the flat insert. The circular waveguide section provides angular selection of the oscillation spectrum. The loss introduced by this waveguide to the OR does not exceed −2 dB.Conclusions. A hemispherical open resonator incorporating specific inhomogeneities that facilitate axially symmetric OR oscillations has shown potential for measuring the electrophysical parameters of materials. For this, a disk-shaped sample is placed at the bottom of a circular waveguide section inserted into the OR flat mirror in its center.Keywords: extremely high frequency (EHF) range, open resonator, axially symmetric oscillations, circular waveguide, coupling element, transmission coefficientManuscript submitted 07.02.2026Radio phys. radio astron. 2026, 31(1): 051-064REFERENCES1. 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-x2. 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. Microw. Theory Tech., 67(5), pp. 1901—1908. DOI: 10.1109/TMTT.2019.29055493. Givot, B.L., Gregory, A.P., Salski, B., Zentis, F., Pettit, N., and Karpisz, T.A., 2021. Comparison of Measurements of the Permittivity and Loss Angle of Polymers in the Frequency Range 10 GHz to 90 GHz. In: 15th European Conf. on Antennas and Propagation (EuCAP). Dusseldorf, Germany, 22—26 March 2021. P. 1—5. DOI: 10.23919/EuCAP51087.2021.94112984. 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), 012020. DOI: 10.1088/1742-6596/1989/1/0120205. Afsar, M.N., Chen, S., and Wang, Y., 2005. An Improved 60 GHz Open Resonator System for Accurate Measurement of Dielectric Permittivity. In: Proc. the AP-S Int. Symp. Washington, DC, USA, 3-8 July 2005. P. 1—5. DOI: 10.1109/APS.2005.15528426. Rahman, R., Taylor, P.C., and Scales, J.A., 2013. A System for Measuring Complex Dielectric Properties of Thin Films at Submillimeter Wavelengths Using an Open Hemispherical Cavity and a Vector Network Analyzer. Rev. Sci. Instrum., 84(8), 083901. DOI: 10.1063/1.48168287. Breslavets, A.A., Eremenko, Z.E., Rudnev, G.O., Natarov, M.P., Glamazdin, V.V., Shubnyi, O.I., Voitovych, O.A., Gang, Z., Rong, L., 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:10.1063/10.00089638. Dudorov, S.N., Lioubtchenko, D.V., Mallat, J.A., and Räisänen, A.V., 2005. Differential Open Resonator Method for Permittivity Measurements of Thin Dielectric Film on Substrate. IEEE Trans. Instrum. Meas., 54(5), pp. 1916—1920. DOI: 10.1109/TIM.2005.8533529. 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 Thicness. J. Radio Electron., 10, pp. 1—7. DOI: 10.30898/1684-1719.2018.10.1010. Kuzmichev, I.K., Melezhik, P.N., and Poyedinchuk, A.Ye., 2006. An open resonator for physical studies. Int. J. Infrared Millimeter Waves, 27(6), pp. 857—869. DOI: 10.1007/s10762-006-9122-711. Kuzmichev, I.K., and Popkov, A.Yu., 2018. Resonant Systems for Measurement of Electromagnetic Properties of Substances at V-Band Frequencies. Chap. 3. In: Emerging Microwave Technologies in Industrial, Agricultural, Medical and Food Processing. London, United Kingdom: IntechOpen Publishing house, pp. 27—53. DOI: 10.5772/intechopen.7364312. Kuzmichev, I.K., 2014. Open resonator with a section of rectangular waveguide. Radio Phys. Radio Astron., 19(3), pp. 249—257. DOI: 10.15407/rpra19.03.24913. Auston, D.H., Primich, R.I., and Hayami, R.A., 1964. Further considerations of the use of Fabry–Perot resonators in microwave plasma diagnostics. In: Quasi-Optics, Symposium on Quasi-Optics Proceedings. Brooklyn, NY: Polytechnic Press, pp. 273—304.14. Giri, D.V., 2004. High-Power Electromagnetic Radiators: Nonlethal Weapons and Other Applications. Cambridge, Massachusetts: Harvard University Press. 198 p. ISBN 9780674015692.15. Giri, D.V., Hoad, R., and Sabath, F., 2020. High-Power Electromagnetic Effects on Electronic Systems. Boston, London: Artech House. 320 p. ISBN: 9781630815882.16. Schwan, H.P., and Foster, K.R., 1977. Microwave Dielectric Properties of Tissue. Some Comments on the Rotational Mobility of Tissue Water. Biophys., 17(2), pp. 193—197. DOI: 10.1016/S0006-3495(77)85637-317. Birx, D., Dick, G.J., Little, W.A., Mercereau, J.E., and Scalapino, D.J., 1978. Pulsed frequency modulation of superconducting resonators. Appl. Phys. Lett., 33(5), pp. 466—468. DOI: http://dx.doi.org/10.1063/1.9038118. Alvarez, R.A., Birx, D., Byrne, D., Mendonca, M., and Johnson, R.M., 1981. Generation of high-power microwave pulses using a spherical superconducting cavity and interference-type switch. IEEE Trans. Magn., 17(1), pp. 935—938. DOI: 10.1109/TMAG.1981.106106719. Danilov, Yu.Yu., Kuzikov, S.V., Pavel’ev, V.G., Koshurinov, Yu.I., and Shchegol’kov, D.Yu., 2005. Linear Frequency-Modulated Pulse Compressor Based on a Three-Mirror Ring Cavity. Tech. Phys., 75(4), pp. 523—525. DOI: 10.1134/1.190179720. Kuzmichev, I.K., Popkov, A.Yu., and Rud, L.A., 2012. Excitation of TE11 and TE01 Waves in a Coaxial Waveguide Incorporated into an Open Resonator. Part 2. Switch Modeling. Phys. Bases Instrum., 1(4), pp. 14—23. DOI: 10.25210/jfop-1204-01402321. Artemenko, S.N., Kaminskii, V.L., Yushkov, Yu.G., and Dellis, A.N., 1993. Extraction of the energy in large axisymmetric resonators through an oversized coaxial line. Tech. Phys., 38(2), pp. 111—114.22. Avgustinovich, V. A., Artemenko, S. N., and Zhukov, A. A., 2013. Microwave-energy extraction from a resonator via oversized interference switch. Tech. Phys. Lett., 39(5), pp. 492—494. DOI: 10.1134/S106378501305016723. Kühn R., 1964. Mikrowellenantennen. Berlin: Veb Berlag Technik Publ., pp. 231—236.24. Bronstein, I.N., Semendyaev, K.A., Musiol, G., and Muehlig, H., 2007. Mathematics Handbook. 5th ed. Berlin, Heidelberg, New York: Springer Publishing house. ISBN 978-3-540-72121-5.25. Kogelnik, H., 1964. Coupling and convertion coefficients for optical modes. In: Quasi-Optics, Symposium on Quasi-Optics Proceedings. Brooklyn, NY: Polytechnic Press, pp. 333—347.26. Kuzmichev, I.K., 2009. Quasi-Optical Resonance Systems with Internal Inhomogeneities. Telecommunications and Radio Engineering, 68(4), pp. 299—317. DOI: 10.1615/TelecomRadEng.v68.i4.3027. Kuzmichev, I.K., 2002. The Probe Diameter Choosing for the Investigation of the Field Distribution in the Small Aperture Open Resonator. Telecommunication and Radio Engineering, 58(7—8), pp. 59—63. DOI: 10.1615/TelecomRadEng.v58.i7-8.5028. Pozar, D.M., 2012. Microwave Engineering. 4th ed. New York: Wiley & Sons, Limited, John, pp. 124—129. ISBN 978-0-470-63155-3.29. Kuzmychov, I.K., Lukash, O.S., Senkevych, O.B., Voitovych, O.A., Narytnyk, T.M., and Churyumov, G.I., 2025. Axially symmetric modes in an open resonator. Radio Phys. Radio Astron., 30(4), pp. 285—295. DOI: 10.15407/rpra30.04.28530. Marcuse, D., 1982. Light Transmission Optics. 2th ed. New York, Scarborough, Mitcham, Wokingham: Published by Van Nostrand Reinhold Company Inc., pp. 253—262. ISBN 13- 9780442263096.31. Korn, G.A., and Korn, T.M., 2000. Mathematical Handbook for Scientists and Engineers: Definitions, Th eorems, and Formulas for Reference and Review. Mineola, New York: Courier Corporation Publishing House, pp. 849—856. ISBN 0486411478,9780486411477. Предмет і мета роботи. Предметом роботи є аксіально-симетричні коливання у напівсферичному відкритому резонаторі (ВР), що містить внутрішні неоднорідності. Метою роботи є дослідження розподілу поля аксіально-симетричних коливань, які збуджуються в напівсферичному ВР у разі наявності неоднорідностей, та їх селекція. Актуальність цих досліджень пов’язана з необхідністю зменшити геометричні розміри хвилеводу, виконаного в центрі одного з дзеркал резонатора. Це дозволить досліджувати зразки діелектриків невеликих поперечних розмірів, поміщаючи їх у хвилевід, і завдяки цьому виключити вплив дифракційних втрат на результати вимірювань.Методи та методологія. Дослідження розподілу електричного поля власного коливання ВР здійснювалося із застосуванням квазіоптичного методу пробного тіла. Резонансні характеристики ВР та фізичні явища в ньому досліджувались за допомогою відомих і перевірених методів вимірювання коефіцієнта передачі НВЧ-тракту на ділянці резонатора.Результати. Установлено, що у круглому хвилеводі, радіус перерізу якого ɑ=0.6042w0, де w0 — радіус плями поля коливання ТЕМ00q, збуджується мода ТЕ11 з ефективністю 0.8993 за допомогою центральної плями поля коливання ТЕМ10q. Дослідження проводили на частоті 74.98 ГГц. Завдяки плоскій вставці у резонаторі збуджувалися аксіально-симетричні коливання, хоча резонатор не мав аксіальної симетрії. Відрізок круглого хвилеводу забезпечував модову селекцію коливань. Втрати, що були внесені в резонатор цим хвилеводом, не перевищували 2 дБ.Висновок. Відкритий резонатор, який містить зазначені неоднорідності та в якому завдяки цьому збуджуються аксіально-симетричні коливання, може бути використаний для визначення електрофізичних параметрів речовин. Для цього зразок діелектрика дископодібної форми поміщають на дно відрізка круглого хвилеводу, розташованого в центрі плоского дзеркала напівсферичного ВР.Ключові слова: вкрай високочастотний діапазон, відкритий напівсферичний резонатор, аксіально-симетричні коливання, круглий хвилевід, елемент зв’язку, коефіцієнт передачі, пробне тілоСтаття надійшла до редакції 07.02.2026Radio phys. radio astron. 2026, 31(1): 051-064БІБЛІОГРАФІЧНИЙ СПИСОК1. Parshin V.V., and Serov E.A. Resonance Method for Studying Dielectric Liquids in Millimeter and Submillimeter Wave Ranges. Radiophys. Quantum Electron. 2012. Vol. 54, Iss. 8—9. P. 632—637. DOI: 10.1007/s11141-012-9324-x2. Karpisz T., Salski B., Kopyt P., and Krupka J. Measurement of Dielectrics from 20 to 50 GHz with a Fabry–Pérot Open Resonator. 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Видавничий дім «Академперіодика» 2026-03-24 Article Article http://rpra-journal.org.ua/index.php/ra/article/view/1491 РАДИОФИЗИКА И РАДИОАСТРОНОМИЯ; Vol 31, No 1 (2026); 64 RADIO PHYSICS AND RADIO ASTRONOMY; Vol 31, No 1 (2026); 64 РАДІОФІЗИКА І РАДІОАСТРОНОМІЯ; Vol 31, No 1 (2026); 64 2415-7007 1027-9636 uk Copyright (c) 2026 RADIO PHYSICS AND RADIO ASTRONOMY |
| spellingShingle | extremely high frequency (EHF) range open resonator axially symmetric oscillations circular waveguide coupling element transmission coefficient Kuzmychov, I. K. Lukash, O. S. Voitovych, O. A. Prokopenko, Yu. V. Churyumov, G. I. AN OPEN RESONATOR WITH INTERNAL INHOMOGENEITIES |
| title | AN OPEN RESONATOR WITH INTERNAL INHOMOGENEITIES |
| title_alt | ВІДКРИТИЙ РЕЗОНАТОР ІЗ ВНУТРІШНІМИ НЕОДНОРІДНОСТЯМИ |
| title_full | AN OPEN RESONATOR WITH INTERNAL INHOMOGENEITIES |
| title_fullStr | AN OPEN RESONATOR WITH INTERNAL INHOMOGENEITIES |
| title_full_unstemmed | AN OPEN RESONATOR WITH INTERNAL INHOMOGENEITIES |
| title_short | AN OPEN RESONATOR WITH INTERNAL INHOMOGENEITIES |
| title_sort | open resonator with internal inhomogeneities |
| topic | extremely high frequency (EHF) range open resonator axially symmetric oscillations circular waveguide coupling element transmission coefficient |
| topic_facet | extremely high frequency (EHF) range open resonator axially symmetric oscillations circular waveguide coupling element transmission coefficient вкрай високочастотний діапазон відкритий напівсферичний резонатор аксіально-симетричні коливання круглий хвилевід елемент зв’язку коефіцієнт передачі пробне тіло |
| url | http://rpra-journal.org.ua/index.php/ra/article/view/1491 |
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