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OPERATOR METHOD IN THE PROBLEM OF A PLANE ELECTROMAGNETIC WAVE DIFFRACTION BY AN ANNULAR SLOT IN THE PLANE OR BY A RING

OPERATOR METHOD IN THE PROBLEM OF A PLANE ELECTROMAGNETIC WAVE DIFFRACTION BY AN ANNULAR SLOT IN THE PLANE OR BY A RING

Purpose: The problem of a plane electromagnetic wave diffraction by an annular slot in the perfectly conducting zero thickness plane is considered. As a dual problem, the problem of diffraction by a perfectly conducting zero thickness ring is also considered. The paper aims at developing the operato...

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Main Authors: Kaliberda, M. E., Lytvynenko, L. M., Pogarsky, S. A.
Format: Article
Language:Ukrainian
Published: Видавничий дім «Академперіодика» 2021
Subjects:
circular hole
disk
annular slot
ring
operator method
diffraction
круглий отвір
диск
кільцева щілина
кільце
операторний метод
дифракція
Online Access:http://rpra-journal.org.ua/index.php/ra/article/view/1372
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record_format ojs
institution Radio physics and radio astronomy
collection OJS
language Ukrainian
topic circular hole
disk
annular slot
ring
operator method
diffraction
circular hole
disk
annular slot
ring
operator method
diffraction
круглий отвір
диск
кільцева щілина
кільце
операторний метод
дифракція
spellingShingle circular hole
disk
annular slot
ring
operator method
diffraction
circular hole
disk
annular slot
ring
operator method
diffraction
круглий отвір
диск
кільцева щілина
кільце
операторний метод
дифракція
Kaliberda, M. E.
Lytvynenko, L. M.
Pogarsky, S. A.
OPERATOR METHOD IN THE PROBLEM OF A PLANE ELECTROMAGNETIC WAVE DIFFRACTION BY AN ANNULAR SLOT IN THE PLANE OR BY A RING
topic_facet circular hole
disk
annular slot
ring
operator method
diffraction
circular hole
disk
annular slot
ring
operator method
diffraction
круглий отвір
диск
кільцева щілина
кільце
операторний метод
дифракція
format Article
author Kaliberda, M. E.
Lytvynenko, L. M.
Pogarsky, S. A.
author_facet Kaliberda, M. E.
Lytvynenko, L. M.
Pogarsky, S. A.
author_sort Kaliberda, M. E.
title OPERATOR METHOD IN THE PROBLEM OF A PLANE ELECTROMAGNETIC WAVE DIFFRACTION BY AN ANNULAR SLOT IN THE PLANE OR BY A RING
title_short OPERATOR METHOD IN THE PROBLEM OF A PLANE ELECTROMAGNETIC WAVE DIFFRACTION BY AN ANNULAR SLOT IN THE PLANE OR BY A RING
title_full OPERATOR METHOD IN THE PROBLEM OF A PLANE ELECTROMAGNETIC WAVE DIFFRACTION BY AN ANNULAR SLOT IN THE PLANE OR BY A RING
title_fullStr OPERATOR METHOD IN THE PROBLEM OF A PLANE ELECTROMAGNETIC WAVE DIFFRACTION BY AN ANNULAR SLOT IN THE PLANE OR BY A RING
title_full_unstemmed OPERATOR METHOD IN THE PROBLEM OF A PLANE ELECTROMAGNETIC WAVE DIFFRACTION BY AN ANNULAR SLOT IN THE PLANE OR BY A RING
title_sort operator method in the problem of a plane electromagnetic wave diffraction by an annular slot in the plane or by a ring
title_alt OPERATOR METHOD IN THE PROBLEM OF A PLANE ELECTROMAGNETIC WAVE DIFFRACTION BY AN ANNULAR SLOT IN THE PLANE OR BY A RING
ОПЕРАТОРНИЙ МЕТОД В ЗАДАЧІ ПРО ДИФРАКЦІЮ ПЛОСКОЇ ЕЛЕКТРОМАГНІТНОЇ ХВИЛІ НА КІЛЬЦЕВІЙ ЩІЛИНІ В ПЛОЩИНІ АБО НА КІЛЬЦІ
description Purpose: The problem of a plane electromagnetic wave diffraction by an annular slot in the perfectly conducting zero thickness plane is considered. As a dual problem, the problem of diffraction by a perfectly conducting zero thickness ring is also considered. The paper aims at developing the operator method for the axially symmetric structures placed in free space.Design/methodology/approach: The problem is considered in the spectral domain. The scattered field is expressed in terms of unknown Fourier amplitudes (spectral functions). The annular slot is given as a unity of two simple discontinuities, namely of a disk and a circular hole in the plane, which interact with each other. The Fourier amplitude of the scattered field is sought as a sum of two amplitudes, the Fourier amplitude of the field of currents on the disk and Fourier amplitude of the field of currents on the perfectly conducting plane with circular hole. The operator equations are written for these amplitudes, which take into account the electromagnetic coupling of the disk and the hole in the plane. The equations use the reflection operators of a single isolated disk and a single hole in the plane. They are supposed to be known and can be obtained for example by the method of moments.The reflection operators can have singularities. After transformations, the equations are obtained, which are equivalent to the Fredholm integral equations of second kind and they can be solved numerically.Findings: The operator equations relative to the Fourier amplitudes of the field scattered by the discussed structure are obtained. The far zone scattered field for an annular slot and a ring for different values of parameters are studied.Conclusions: The rigorous solution of the problem of the electromagnetic wave diffraction by an annular slot in the plane and by a circular ring is obtained. The problem is reduced to the Fredholm integral equations of second kind. The far field distribution for different parameters is studied. The developed approach is an effective instrument for a number of problems of antenna technique to be solved.Key words: circular hole; disk; annular slot; ring; operator method; diffractionManuscript submitted 01.09.2021Radio phys. radio astron. 2021, 26(4): 350-357REFERENCES1. BLACK, D. N. and WILTSE, J. C., 1987. Millimeter-Wave Characteristics of Phase-Correcting Fresnel Zone Plates. IEEE Trans. Microw. Theory Techn. vol. 35, is. 12, pp. 1122–1129. DOI: https://doi.org/10.1109/TMTT.1987.11338262. JI, Y. and FUJITA, M., 1994. Design and Analysis of a Folded Fresnel Zone Plate Antenna. Int. J. Infrared Milli. Waves. vol. 15, is. 8, pp. 1385–1406. DOI: https://doi.org/10.1007/BF020960663. SAIDOGLU, N. Y. and NOSICH, A. I., 2020. Method ofanalytical regularization in the analysis of axially symmetricexcitation of imperfect circular disk antennas. Comput. Math. Appl. vol. 79, is. 10, pp. 2872–2884. DOI: https://doi.org/10.1016/j.camwa.2019.12.0204. DIKMEN, F., KARACHUHA, E. and TUCHKIN, Y. A., 2001. Scalar Wave Diffraction by a Perfectly Soft Infi nitely Thin Circular Ring. Turk. J. Elec. Eng. Comp. Sci. vol. 9, no. 2, pp. 199–219.5. AGAFONOVA, M. A., 2013. Methods of Integral Equations in Problems of Diffraction on Strip and Slots. T-comm.no. 11, pp. 21–24. (in Russian).6. DIKMEN, F. and TUCHKIN, Y. A., 2009. Analytical Regularization Method for Electromagnetic Wave Diffraction by Axially Symmetrical Thin Annular Strips. Turk. J. Elec. Eng. Comp. Sci. vol. 17, no. 2, pp. 107–124. DOI: 10.3906/elk-0811-107. KAZ’MIN, I. A., LERER, A. M. and SHEVCHENKO, V. N., 2008. Electromagnetic-Wave Diffraction by a 2D Periodic Grating of Circular and Ring Slots. J. Commun. Technol. Electron. vol. 53, no. 2, pp. 177–183. DOI: https://doi.org/10.1134/S10642269080200718. LI, S. and SCHARSTEIN, R. W., 2005. High Frequency Scattering by a Conducting Ring. IEEE Trans. Antennas Propag. vol. 53, is. 6, pp. 1927–1938. DOI: https://doi.org/10.1109/TAP.2005.8485069. LYTVYNENKO, L. M. and PROSVIRNIN, S. L., 2009. Wave reflection by a periodic layered metamaterial. Eur. Phys. J. Appl. Phys. vol. 46, no. 3, id. 32608. DOI: https://doi.org/10.1051/epjap:200812810. KALIBERDA, M. E., LYTVYNENKO, L. M. and POGARSKY, S. A., 2021. Operator Method in the Problem of the the H-Polarized Wave Diffraction by Two Semi-Infinite Gratings Placed in the Same Plane. Radio Phys. Radio Astron. vol. 26, no. 3, pp. 239–249. (in Ukrainian). DOI: https://doi.org/10.15407/rpra26.03.23911. KALIBERDA, M. E., LYTVYNENKO, L. M. and POGARSKY, S. A., 2018. Operator Method in the Scalar Wave Diffraction by Axially-Symmetric Discontinuities in the Screen. Radio Phys. Radio Astron. vol. 23, no. 1, pp. 36–42. (in Russian). DOI: https://doi.org/10.15407/rpra23.01.03612. KALIBERDA, M. E., POGARSKY, S. A. and LYTVYNENKO, L. M., 2020. Operator Method in Scalar Wave Scatteringby Circular Slot in Screen in Case of Dirichlet Conditions. In: 2020 IEEE Ukrainian Microwave Week (UkrMW) Proceedings. Kharkiv, Ukraine, 21-25 Sept., 2020. pp. 1–4.DOI: https://doi.org/10.1109/UkrMW49653.2020.925263213. NOMURA, Y. and KATSURA, S., 1955. Diffraction of Electromagnetic Waves by Circular Plate and Circular Hole. J. Phys. Soc. Jpn. vol. 10, no. 4, pp. 285–304. DOI: https://doi.org/10.1143/JPSJ.10.28514. LYTVYNENKO, L. M., PROSVIRNIN, S. L. and KHIZHNYAK, A. N., 1988. Semiinversion of the Operator with the Using of Method of Moments in the Scattering Problems by the Structures Consisting of the Thin Disks. Preprint No. 19. Institute of Radio Astronomy, Academy of Sciences of Ukrainian SSR. 31 p. (in Russian). 
publisher Видавничий дім «Академперіодика»
publishDate 2021
url http://rpra-journal.org.ua/index.php/ra/article/view/1372
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spelling oai:ri.kharkov.ua:article-13722023-06-19T05:28:33Z OPERATOR METHOD IN THE PROBLEM OF A PLANE ELECTROMAGNETIC WAVE DIFFRACTION BY AN ANNULAR SLOT IN THE PLANE OR BY A RING OPERATOR METHOD IN THE PROBLEM OF A PLANE ELECTROMAGNETIC WAVE DIFFRACTION BY AN ANNULAR SLOT IN THE PLANE OR BY A RING ОПЕРАТОРНИЙ МЕТОД В ЗАДАЧІ ПРО ДИФРАКЦІЮ ПЛОСКОЇ ЕЛЕКТРОМАГНІТНОЇ ХВИЛІ НА КІЛЬЦЕВІЙ ЩІЛИНІ В ПЛОЩИНІ АБО НА КІЛЬЦІ Kaliberda, M. E. Lytvynenko, L. M. Pogarsky, S. A. circular hole; disk; annular slot; ring; operator method; diffraction circular hole; disk; annular slot; ring; operator method; diffraction круглий отвір; диск; кільцева щілина; кільце; операторний метод; дифракція Purpose: The problem of a plane electromagnetic wave diffraction by an annular slot in the perfectly conducting zero thickness plane is considered. As a dual problem, the problem of diffraction by a perfectly conducting zero thickness ring is also considered. The paper aims at developing the operator method for the axially symmetric structures placed in free space.Design/methodology/approach: The problem is considered in the spectral domain. The scattered field is expressed in terms of unknown Fourier amplitudes (spectral functions). The annular slot is given as a unity of two simple discontinuities, namely of a disk and a circular hole in the plane, which interact with each other. The Fourier amplitude of the scattered field is sought as a sum of two amplitudes, the Fourier amplitude of the field of currents on the disk and Fourier amplitude of the field of currents on the perfectly conducting plane with circular hole. The operator equations are written for these amplitudes, which take into account the electromagnetic coupling of the disk and the hole in the plane. The equations use the reflection operators of a single isolated disk and a single hole in the plane. They are supposed to be known and can be obtained for example by the method of moments.The reflection operators can have singularities. After transformations, the equations are obtained, which are equivalent to the Fredholm integral equations of second kind and they can be solved numerically.Findings: The operator equations relative to the Fourier amplitudes of the field scattered by the discussed structure are obtained. The far zone scattered field for an annular slot and a ring for different values of parameters are studied.Conclusions: The rigorous solution of the problem of the electromagnetic wave diffraction by an annular slot in the plane and by a circular ring is obtained. The problem is reduced to the Fredholm integral equations of second kind. The far field distribution for different parameters is studied. The developed approach is an effective instrument for a number of problems of antenna technique to be solved.Key words: circular hole; disk; annular slot; ring; operator method; diffractionManuscript submitted 01.09.2021Radio phys. radio astron. 2021, 26(4): 350-357REFERENCES1. BLACK, D. N. and WILTSE, J. C., 1987. Millimeter-Wave Characteristics of Phase-Correcting Fresnel Zone Plates. IEEE Trans. Microw. Theory Techn. vol. 35, is. 12, pp. 1122–1129. DOI: https://doi.org/10.1109/TMTT.1987.11338262. JI, Y. and FUJITA, M., 1994. Design and Analysis of a Folded Fresnel Zone Plate Antenna. Int. J. Infrared Milli. Waves. vol. 15, is. 8, pp. 1385–1406. DOI: https://doi.org/10.1007/BF020960663. SAIDOGLU, N. Y. and NOSICH, A. I., 2020. Method ofanalytical regularization in the analysis of axially symmetricexcitation of imperfect circular disk antennas. Comput. Math. Appl. vol. 79, is. 10, pp. 2872–2884. DOI: https://doi.org/10.1016/j.camwa.2019.12.0204. DIKMEN, F., KARACHUHA, E. and TUCHKIN, Y. A., 2001. Scalar Wave Diffraction by a Perfectly Soft Infi nitely Thin Circular Ring. Turk. J. Elec. Eng. Comp. Sci. vol. 9, no. 2, pp. 199–219.5. AGAFONOVA, M. A., 2013. Methods of Integral Equations in Problems of Diffraction on Strip and Slots. T-comm.no. 11, pp. 21–24. (in Russian).6. DIKMEN, F. and TUCHKIN, Y. A., 2009. Analytical Regularization Method for Electromagnetic Wave Diffraction by Axially Symmetrical Thin Annular Strips. Turk. J. Elec. Eng. Comp. Sci. vol. 17, no. 2, pp. 107–124. DOI: 10.3906/elk-0811-107. KAZ’MIN, I. A., LERER, A. M. and SHEVCHENKO, V. N., 2008. Electromagnetic-Wave Diffraction by a 2D Periodic Grating of Circular and Ring Slots. J. Commun. Technol. Electron. vol. 53, no. 2, pp. 177–183. DOI: https://doi.org/10.1134/S10642269080200718. LI, S. and SCHARSTEIN, R. W., 2005. High Frequency Scattering by a Conducting Ring. IEEE Trans. Antennas Propag. vol. 53, is. 6, pp. 1927–1938. DOI: https://doi.org/10.1109/TAP.2005.8485069. LYTVYNENKO, L. M. and PROSVIRNIN, S. L., 2009. Wave reflection by a periodic layered metamaterial. Eur. Phys. J. Appl. Phys. vol. 46, no. 3, id. 32608. DOI: https://doi.org/10.1051/epjap:200812810. KALIBERDA, M. E., LYTVYNENKO, L. M. and POGARSKY, S. A., 2021. Operator Method in the Problem of the the H-Polarized Wave Diffraction by Two Semi-Infinite Gratings Placed in the Same Plane. Radio Phys. Radio Astron. vol. 26, no. 3, pp. 239–249. (in Ukrainian). DOI: https://doi.org/10.15407/rpra26.03.23911. KALIBERDA, M. E., LYTVYNENKO, L. M. and POGARSKY, S. A., 2018. Operator Method in the Scalar Wave Diffraction by Axially-Symmetric Discontinuities in the Screen. Radio Phys. Radio Astron. vol. 23, no. 1, pp. 36–42. (in Russian). DOI: https://doi.org/10.15407/rpra23.01.03612. KALIBERDA, M. E., POGARSKY, S. A. and LYTVYNENKO, L. M., 2020. Operator Method in Scalar Wave Scatteringby Circular Slot in Screen in Case of Dirichlet Conditions. In: 2020 IEEE Ukrainian Microwave Week (UkrMW) Proceedings. Kharkiv, Ukraine, 21-25 Sept., 2020. pp. 1–4.DOI: https://doi.org/10.1109/UkrMW49653.2020.925263213. NOMURA, Y. and KATSURA, S., 1955. Diffraction of Electromagnetic Waves by Circular Plate and Circular Hole. J. Phys. Soc. Jpn. vol. 10, no. 4, pp. 285–304. DOI: https://doi.org/10.1143/JPSJ.10.28514. LYTVYNENKO, L. M., PROSVIRNIN, S. L. and KHIZHNYAK, A. N., 1988. Semiinversion of the Operator with the Using of Method of Moments in the Scattering Problems by the Structures Consisting of the Thin Disks. Preprint No. 19. Institute of Radio Astronomy, Academy of Sciences of Ukrainian SSR. 31 p. (in Russian).  Purpose: The problem of a plane electromagnetic wave diffraction by an annular slot in the perfectly conducting zero thickness plane is considered. As a dual problem, the problem of diffraction by a perfectly conducting zero thickness ring is also considered. The paper aims at developing the operator method for the axially symmetric structures placed in free space.Design/methodology/approach: The problem is considered in the spectral domain. The scattered field is expressed in terms of unknown Fourier amplitudes (spectral functions). The annular slot is given as a unity of two simple discontinuities, namely of a disk and a circular hole in the plane, which interact with each other. The Fourier amplitude of the scattered field is sought as a sum of two amplitudes, the Fourier amplitude of the field of currents on the disk and Fourier amplitude of the field of currents on the perfectly conducting plane with circular hole. The operator equations are written for these amplitudes, which take into account the electromagnetic coupling of the disk and the hole in the plane. The equations use the reflection operators of a single isolated disk and a single hole in the plane. They are supposed to be known and can be obtained for example by the method of moments.The reflection operators can have singularities. After transformations, the equations are obtained, which are equivalent to the Fredholm integral equations of second kind and they can be solved numerically.Findings: The operator equations relative to the Fourier amplitudes of the field scattered by the discussed structure are obtained. The far zone scattered field for an annular slot and a ring for different values of parameters are studied.Conclusions: The rigorous solution of the problem of the electromagnetic wave diffraction by an annular slot in the plane and by a circular ring is obtained. The problem is reduced to the Fredholm integral equations of second kind. The far field distribution for different parameters is studied. The developed approach is an effective instrument for a number of problems of antenna technique to be solved.Key words: circular hole; disk; annular slot; ring; operator method; diffractionManuscript submitted 01.09.2021Radio phys. radio astron. 2021, 26(4): 350-357REFERENCES1. BLACK, D. N. and WILTSE, J. C., 1987. Millimeter-Wave Characteristics of Phase-Correcting Fresnel Zone Plates. IEEE Trans. Microw. Theory Techn. vol. 35, is. 12, pp. 1122–1129. DOI: 10.1109/TMTT.1987.11338262. JI, Y. and FUJITA, M., 1994. Design and Analysis of a Folded Fresnel Zone Plate Antenna. Int. J. Infrared Milli. Waves. vol. 15, is. 8, pp. 1385–1406. DOI: 10.1007/BF02096066.3. SAIDOGLU, N. Y. and NOSICH, A. I., 2020. Method ofanalytical regularization in the analysis of axially symmetricexcitation of imperfect circular disk antennas. Comput. Math. Appl. vol. 79, is. 10, pp. 2872–2884. DOI: 10.1016/j.camwa.2019.12.0204. DIKMEN, F., KARACHUHA, E. and TUCHKIN, Y. A., 2001. Scalar Wave Diffraction by a Perfectly Soft Infi nitely Thin Circular Ring. Turk. J. Elec. Eng. Comp. Sci. vol. 9, no. 2, pp. 199–219.5. AGAFONOVA, M. A., 2013. Methods of Integral Equations in Problems of Diffraction on Strip and Slots. T-comm.no. 11, pp. 21–24. (in Russian).6. DIKMEN, F. and TUCHKIN, Y. A., 2009. Analytical Regularization Method for Electromagnetic Wave Diffraction by Axially Symmetrical Thin Annular Strips. Turk. J. Elec. Eng. Comp. Sci. vol. 17, no. 2, pp. 107–124. DOI: 10.3906/elk-0811-107. KAZ’MIN, I. A., LERER, A. M. and SHEVCHENKO, V. N., 2008. Electromagnetic-Wave Diffraction by a 2D Periodic Grating of Circular and Ring Slots. J. Commun. Technol. Electron. vol. 53, no. 2, pp. 177–183. DOI: 10.1134/S10642269080200718. LI, S. and SCHARSTEIN, R. W., 2005. High Frequency Scattering by a Conducting Ring. IEEE Trans. Antennas Propag. vol. 53, is. 6, pp. 1927–1938. DOI: 10.1109/TAP.2005.8485069. LYTVYNENKO, L. M. and PROSVIRNIN, S. L., 2009. Wave reflection by a periodic layered metamaterial. Eur. Phys. J. Appl. Phys. vol. 46, no. 3, id. 32608. DOI: 10.1051/epjap:200812810. KALIBERDA, M. E., LYTVYNENKO, L. M. and POGARSKY, S. A., 2021. Operator Method in the Problem of the the H-Polarized Wave Diffraction by Two Semi-Infinite Gratings Placed in the Same Plane. Radio Phys. Radio Astron. vol. 26, no. 3, pp. 239–249. (in Ukrainian). DOI: 10.15407/rpra26.03.23911. KALIBERDA, M. E., LYTVYNENKO, L. M. and POGARSKY, S. A., 2018. Operator Method in the Scalar Wave Diffraction by Axially-Symmetric Discontinuities in the Screen. Radio Phys. Radio Astron. vol. 23, no. 1, pp. 36–42. (in Russian). DOI: 10.15407/rpra23.01.03612. KALIBERDA, M. E., POGARSKY, S. A. and LYTVYNENKO, L. M., 2020. Operator Method in Scalar Wave Scatteringby Circular Slot in Screen in Case of Dirichlet Conditions. In: 2020 IEEE Ukrainian Microwave Week (UkrMW) Proceedings. Kharkiv, Ukraine, 21-25 Sept., 2020. pp. 1–4.DOI: 10.1109/UkrMW49653.2020.925263213. NOMURA, Y. and KATSURA, S., 1955. Diffraction of Electromagnetic Waves by Circular Plate and Circular Hole. J. Phys. Soc. Jpn. vol. 10, no. 4, pp. 285–304. DOI: 10.1143/JPSJ.10.28514. LYTVYNENKO, L. M., PROSVIRNIN, S. L. and KHIZHNYAK, A. N., 1988. Semiinversion of the Operator with the Using of Method of Moments in the Scattering Problems by the Structures Consisting of the Thin Disks. Preprint No. 19. Institute of Radio Astronomy, Academy of Sciences of Ukrainian SSR. 31 p. (in Russian). Предмет і мета роботи: Розглядається задача про дифракцію плоскої електромагнітної хвилі на кільцевій щілині відеально провідній нескінченно тонкій площині. Як дуальна до неї розглядається також задача про дифракцію на ідеально провідному плоскому нескінченно тонкому кільці. Мета роботи полягає у розвиненні операторного методу для аксіально-симетричної структури, розташованої у вільному просторі.Методи і методологія: Задача розглядається в спектральній області. Розсіяне поле виражається через невідомі амплітуди Фур’є (спектральні функції). Кільцева щілина надається у вигляді сполучення двох простіших неоднорідностей, а саме круглого диску і круглого отвору в площині, які взаємодіють одна з одною. Амплітуда Фур’є розсіяного поля знаходиться як сума двох амплітуд – амплітуди Фур’є поля струмів, що течуть диском, і амплітуди Фур’є поля струмів, що течуть ідеально провідною площиною з круглим отвором. Для цих амплітуд записано операторні рівняння, які враховують електромагнітний зв’язок диску з отвором в площині. Рівняння використовують оператори відбиття окремого ізольованого диску і окремого отвору в площині. Вони вважаються відомими і можуть бути знайдені, наприклад, методом моментів. Оператори відбиття можуть мати особливості. Після перетворень отримано рівняння, еквівалентні інтегральним рівнянням Фредгольма другого роду, які можуть бути розв’язанні чисельно.Результати: Отримано операторні рівняння відносно амплітуд Фур’є поля, розсіяного розглянутою структурою. Досліджено розсіяні поля в далекій зоні для кільцевої щілини і кільця за різних значень параметрів.Висновки: Отримано строгий розв’язок задачі про дифракцію електромагнітної хвилі на кільцевій щілині в площиніі на кільці. Задачу зведено до інтегральних рівнянь Фредгольма другого роду. Досліджено розподіл поля в далекій зоні за різних параметрів. Розвинений підхід є ефективним інструментом для розв’язання низки задач антенної техніки.Ключові слова: круглий отвір; диск; кільцева щілина; кільце; операторний метод; дифракціяСтаття надійшла до редакції 01.09.2021Radio phys. radio astron. 2021, 26(4): 350-357СПИСОК ЛІТЕРАТУРИ1. Black D. N. and Wiltse J. C. Millimeter-Wave Characteristicsof Phase-Correcting Fresnel Zone Plates. IEEE Trans. Microw. Theory Techn. 1987. Vol. 35, Is. 12. P. 1122–1129. DOI: 10.1109/TMTT.1987.11338262. Ji Y. and Fujita M. Design and Analysis of a Folded Fresnel Zone Plate Antenna. Int. J. Infrared Milli. Waves. 1994.Vol. 15, Is. 8. P. 1385–1406. DOI: 10.1007/BF020960663. Saidoglu N. Y. and Nosich A. I. Method of analytical regularization in the analysis of axially symmetric excitation of imperfect circular disk antennas. Comput. Math. Appl. 2020. Vol. 79, Is. 10. P. 2872–2884. DOI: 10.1016/j.camwa.2019.12.0204. Dikmen F., Karachuha E., and Tuchkin Y. A. Scalar Wave Diffraction by a Perfectly Soft Infinitely Thin Circular Ring. Turk. J. Elec. Eng. Comp. Sci. 2001. Vol. 9, No. 2. P. 199–219.5. Агафонова М. А. Методы интегральных уравнений в задачах дифракции на полосе и щели. T-comm – Телекоммуникации и транспорт. 2013. № 11. С. 21–24.6. Dikmen F. and Tuchkin Y. A. Analytical Regularization Method for Electromagnetic Wave Diffraction by Axially Symmetrical Thin Annular Strips. Turk. J. Elec. Eng. Comp. Sci. 2009. Vol. 17, No. 2. P. 107–124. DOI: 10.3906/elk0811-107. Казьмин И. А., Лерер А. М., Шевченко В. Н. Дифракция электромагнитной волны на двумерно периодической решетке из круглых и кольцевых отверстий. Радиотехника и электроника. 2008. Т. 53, № 2. С. 191–197.8. Li S. and Scharstein R. W. High Frequency Scattering by a Conducting Ring. IEEE Trans. Antennas Propag. 2005. Vol. 53, Is. 6. P. 1927–1938. DOI: 10.1109/TAP.2005.8485069. Lytvynenko L. M. and Prosvirnin S. L. Wave reflection by a periodic layered metamaterial. Eur. Phys. J. Appl. Phys. 2009. Vol. 46, No. 3. id. 32608. DOI: 10.1051/epjap:200812810. Каліберда М. Є., Литвиненко Л. М., Погарський С. О. Операторний метод в задачі про дифракцію H-поляризованої хвилі на двох однакових напівнескінченних решітках, розташованих в одній площині. Радіофізика і радіоастрономія. Т. 26, № 3. С. 239–249. DOI: 10.15407/rpra26.03.23911. Калиберда М. Е., Литвиненко Л. Н., Погарский С. А. Операторний метод в скалярной задаче дифракции на аксиально-симметричных неоднородностях в экране. Радіофізика і радіоастрономія. Т. 23, № 1. С. 36–42. DOI: 10.15407/rpra23.01.03612. Kaliberda M. E., Pogarsky S. A., and Lytvynenko L. M. Operator Method in Scalar Wave Scattering by Circular Slot in Screen in Case of Dirichlet Conditions. In: Proceedings of the 2020 IEEE Ukrainian Microwave Week (UkrMW). (21-25 Sept, 2020. Kharkiv, Ukraine). 2020. P. 1–4. DOI: 10.1109/UkrMW49653.2020.925263213. Nomura Y. and Katsura S. Diffraction of Electromagnetic Waves by Circular Plate and Circular Hole. J. Phys. Soc. Jpn. 1955. Vol. 10, No. 4. P. 285–304. DOI: 10.1143/JPSJ.10.28514. Литвиненко Л. Н., Просвирнин С. Л., Хижняк А. Н. Полуобращение оператора с использованием метода моментов в задачах дифракции волн на структурах изтонких дисков. Препринт № 19. Радиоастрономический институт Академии наук УССР. 1988. 31 с.   Видавничий дім «Академперіодика» 2021-11-18 Article Article application/pdf http://rpra-journal.org.ua/index.php/ra/article/view/1372 10.15407/rpra26.04.350 РАДИОФИЗИКА И РАДИОАСТРОНОМИЯ; Vol 26, No 4 (2021); 350 RADIO PHYSICS AND RADIO ASTRONOMY; Vol 26, No 4 (2021); 350 РАДІОФІЗИКА І РАДІОАСТРОНОМІЯ; Vol 26, No 4 (2021); 350 2415-7007 1027-9636 10.15407/rpra26.04 uk http://rpra-journal.org.ua/index.php/ra/article/view/1372/pdf Copyright (c) 2021 RADIO PHYSICS AND RADIO ASTRONOMY

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