NATURAL ELECTROMAGNETIC MODES OF A COMPOSITE OPEN STRUCTURE INVOLVING A PERFECTLY CONDUCTING STRIP GRATING, AN INHOMOGENEOUS FERRITE LAYER, AND A MONOLAYER OF GRAPHENE
Subject and Purpose. Сonsidered are the natural modes and their correspondent eigenfrequencies of a composite structure which is nonuniform along one of the coordinates and consists of a lossy ferromagnetic layer placed in a static magnetic field. The layer involves a perfectly conducting strip grat...
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ferrite layer grapheme stripe grating analytical regularization procedure natural oscillations eigenfrequencies |
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ferrite layer grapheme stripe grating analytical regularization procedure natural oscillations eigenfrequencies Brovenko, A. V. Melezhik, P. N. Poyedinchuk, A. Ye. Senkevych, O. B. Yashina, N. P. NATURAL ELECTROMAGNETIC MODES OF A COMPOSITE OPEN STRUCTURE INVOLVING A PERFECTLY CONDUCTING STRIP GRATING, AN INHOMOGENEOUS FERRITE LAYER, AND A MONOLAYER OF GRAPHENE |
| topic_facet |
ferrite layer grapheme stripe grating analytical regularization procedure natural oscillations eigenfrequencies феритовий шар графен стрічкова ґратка аналітичний метод регуляризації власні коливання власні частоти |
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Article |
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Brovenko, A. V. Melezhik, P. N. Poyedinchuk, A. Ye. Senkevych, O. B. Yashina, N. P. |
| author_facet |
Brovenko, A. V. Melezhik, P. N. Poyedinchuk, A. Ye. Senkevych, O. B. Yashina, N. P. |
| author_sort |
Brovenko, A. V. |
| title |
NATURAL ELECTROMAGNETIC MODES OF A COMPOSITE OPEN STRUCTURE INVOLVING A PERFECTLY CONDUCTING STRIP GRATING, AN INHOMOGENEOUS FERRITE LAYER, AND A MONOLAYER OF GRAPHENE |
| title_short |
NATURAL ELECTROMAGNETIC MODES OF A COMPOSITE OPEN STRUCTURE INVOLVING A PERFECTLY CONDUCTING STRIP GRATING, AN INHOMOGENEOUS FERRITE LAYER, AND A MONOLAYER OF GRAPHENE |
| title_full |
NATURAL ELECTROMAGNETIC MODES OF A COMPOSITE OPEN STRUCTURE INVOLVING A PERFECTLY CONDUCTING STRIP GRATING, AN INHOMOGENEOUS FERRITE LAYER, AND A MONOLAYER OF GRAPHENE |
| title_fullStr |
NATURAL ELECTROMAGNETIC MODES OF A COMPOSITE OPEN STRUCTURE INVOLVING A PERFECTLY CONDUCTING STRIP GRATING, AN INHOMOGENEOUS FERRITE LAYER, AND A MONOLAYER OF GRAPHENE |
| title_full_unstemmed |
NATURAL ELECTROMAGNETIC MODES OF A COMPOSITE OPEN STRUCTURE INVOLVING A PERFECTLY CONDUCTING STRIP GRATING, AN INHOMOGENEOUS FERRITE LAYER, AND A MONOLAYER OF GRAPHENE |
| title_sort |
natural electromagnetic modes of a composite open structure involving a perfectly conducting strip grating, an inhomogeneous ferrite layer, and a monolayer of graphene |
| title_alt |
ВЛАСНІ ЕЛЕКТРОМАГНІТНІ КОЛИВАННЯ ВІДКРИТОЇ КОМПОЗИТНОЇ СТРУКТУРИ, ЩО МІСТИТЬ ЕЛЕКТРОПРОВІДНУ СТРІЧКОВУ ҐРАТКУ, НЕОДНОРІДНИЙ ФЕРИТОВИЙ ШАР І ГРАФЕНОВИЙ МОНОШАР |
| description |
Subject and Purpose. Сonsidered are the natural modes and their correspondent eigenfrequencies of a composite structure which is nonuniform along one of the coordinates and consists of a lossy ferromagnetic layer placed in a static magnetic field. The layer involves a perfectly conducting strip grating at one of its boundaries and a graphene monolayer at the other.Methods and Methodology. The above stated problem can be approached within the analytical regularization procedure developed for dual series equations. The latter concern a broad class of diffraction problems which include, in particular, the diffraction of monochromatic plane waves on strip gratings placed at the boundary of a gyromagnetic medium. The amplitudes of the electromagnetic eigenmodes can be obtained from the infinite set of homogeneous linear algebraic equations solvable within a truncation technique. The roots of the system’s determinant represent complex-valued eigenfrequencies of the system under investigation. The material parameters adopted in our computations for the ferromagnetic layer correspond to such of yttrium iron garnet.Results. A number of numerical programs have been developed which permit analyzing the dependences of wave field eigenfunctions and complex eigenfrequencies upon geometrical parameters of the structure (such as grating slot width and period, and thickness of the lossy layer), as well as on electrodynamic parameters of the ferromagnet and graphene characteristics, specifically the chemical potential and relaxation energy of electrons. A number of behavioral regularities have been established, as well as the effect of non-uniformity of ferrite layer parameters upon the structure’s eigenfrequencies and wave field eigenfunctions.Conclusions. The structure under study has been shown to be is an open oscillatory system with a set of complex-valued natural frequencies demonstrating finite points of accumulation. The real parts of these eigenfrequencies lie in a certain interval determined by characteristic frequencies of the ferrite layer, while the imaginary parts are negative, such that the correspondent natural modes show an exponential decay with time. The grating edges represent the mirrors which the natural surface oscillations are reflected from, being supported at that by the ferromagnetic medium. The results obtained in this paper can be useful for creating the elemental base for microwave devices and the devices themselves.Keywords: ferrite layer; grapheme; stripe grating; analytical regularization procedure; natural oscillations; eigenfrequenciesManuscript submitted 24.02.2024Radio phys. radio astron. 2024, 29(2): 113-126REFERENCES1. Jia, H., Yasumoto, K., and Toyama, H., 2005. Reflection and transmission properties of layered periodic arrays of circular cylinders embedded in magnetized ferrite slab. IEEE Trans. Antennas Propag., 53(3), pp. 1145—1153. DOI: https://doi.org/10.1109/TAP.2004.8426542. Monir, A., Sanada, A., Kubo, H., and Awai, I., 2003. Application of the 2-d finite difference-frequency domain method for the analysis of the dispersion characteristics of ferrite devices. In: Proc. 33rd European Microwave Conference. Munich, Germany, 2–10 Oct. 2003. Munich: IEEE, pp. 1175—1177. DOI: https://doi.org/10.1109/EUMA.2003.3411493. Brovenko, A., Melezhik, P., and Poyedinchuk, A., 2012. Resonance scattering of a plane electromagnetic wave by a ferrite-stripe grating-metamaterial structure. Telecommunications and Radio Engineering, 71(12), pp. 1057—1074. DOI: https://doi.org/10.1615/TelecomRadEng.v71.i12.104. Brovenko, A.V., Melezhik, P.N., Poyedinchuk, A.E., and Troshchilo, A.S., 2020. Diffraction of electromagnetic waves on the com- posite structure "strip grating — ferromagnetic half-space": resonances on surface waves. Radiophys. Elektron., 25(1), pp. 11—20 (in Russian). DOI: https://doi.org/10.15407/rej2020.01.0115. Masalov, S.A., Ryzhak, A.V., Sukharevsky, O.I., and Shkil, V.M., 1999. Physical Foundations of Range Technologies "Stealth". St. Petersburg, Russia: Mozhaisky VIKU Publ. (in Russian).6. Brovenko, A., Vinogradova, E., Melezhik, P., Poyedinchuk, A., and Troschylo, A., 2010. Resonance wave Scattering by strip grating adjusted to ferromagnetic medium. Prog. Electromagn. Res. B, 23, pp. 109—129. DOI: https://doi.org/10.2528/PIERB100122037. Brovenko, A.V., Melezhik, P.N, Poyedinchuk, A.Y., and Yashina, N. P., 2006. Surface resonances of metal stripe grating on the plane boundary of metamaterial. Prog. Electromagn. Res., 63, pp. 209—222. DOI: https://doi.org/10.2528/PIER060524018. Lim, J., Bang, W., Trossman, J., Amanov, D., and Ketterson, J., 2018. Forward volume and surface magnetostatic modes in an yttrium iron garnet film for out-of-plane magnetic fields: Theory and experiment. AIP Advances, 8(5), 056018 DOI: https://doi.org/10.1063/1.50072639. Damon, R.W., and Eshbach, J.R., 1961. Magnetostatic modes on a ferromagnetic slab. J. Phys. Chem. Solids, 19(3—4), pp. 308— 320. DOI: https://doi.org/10.1016/0022-3697(61)90041-510. Gurevich, A.G., and Melkov, G.A., 1994. Magnetic Oscillations and Waves. Moscow: Fizmatgiz (in Russian).11. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Dubonos, S.V., Zhang, Y., Grigorieva, I.V., and Firsov, A.A., 2004. Electric field effect in atomically thin carbon films. Science, 306(5696), pp. 666—669. DOI: https://doi.org/10.1126/science.110289612. Nair, R.R., Blake, P., Grigorenko, A.N., Novoselov, K.S., Booth, T.J., Stauber, T., Peres, N.M.R., and Geim, A.K., 2008. Fine structure constant defines transparency of grapheme. Science, 320, pp. 1308—1308. DOI: https://doi.org/10.1126/science.115696513. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Katsnelson, M.I., Grigorieva, I.V., Dubonos, S.V., and Firsov, A.A., 20025. Two-dimensional gas of massless Dirac fermions in grapheme. Nature, 438, pp. 197—200. DOI: https://doi.org/10.1038/nature0423314. Kaipa, C.S.R., Yakovlev, A.B., Hanson, G.W., Padooru, Y.R., and Medina, F., 2012. Mesa enhanced transmission with a graphene- dielectric microstructure at low-terahertz frequencies. Phys. Rev. B, 85, 245407. DOI: https://doi.org/10.1103/PhysRevB.85.24540715. Padooru, Y.R., Yakovlev, A.B., Kaipa, C.S.R., Hanson, G.W., Medina, F., and Mesa, F., 2013. Dual capacitive-inductive nature of periodic graphene patches: Transmission characteristics at low-terahertz frequencies. Phys. Rev. B, 87, 115401. DOI: https://doi.org/10.1103/PhysRevB.87.11540116. Brovenko, A., Melezhik, P., Poyedinchuk, A., Yashina, N., and Granet, G., 2009. Resonant scattering of electromagnetic wave by stripe grating backed with a layer of metamaterial. Prog. Electromagn. Res. B, 15, p. 423—441. DOI: https://doi.org/10.2528/PIERB0905230217. Hanson, G.W., 2008. Dyadic Green’s functions and guided surface waves for a surface conductivity model of grapheme. J. Appl. Phys., 103(6), 064302. DOI: https://doi.org/10.1063/1.289145218. Brovenko, A.V., Melezhik, P.N., Panin, S.B., and Poyedinchuk A.Ye., 2013. Numerical-analytical method for solving problems of the waves diffraction on layered-inhomogeneous medium. Physical Fundamentals of Instrumentation, 2(1), pp. 34—47 (in Russian).19. Brovenko, A., Melezhik, P., Panin, S., and Poyedinchuk, A., 2013. Wave diffraction on a stripe grating at a boundary of a layered inhomogeneous medium: method of analytic regularization. Radiophysics and Quantum Electronics, 56, pp. 238—248. DOI: https://doi.org/10.1007/s11141-013-9429-x20. Shestopalov, V.P., and Sirenko, Yu.K., 1989. Dynamical lattice theory. Kiev: Naukova Dumka Publ. (in Russian).21. Chandezon, J., Granet, G., Melezhik, P.N., Poyedinchuk, A.Ye., Sirenko (ed.), Yu.K., Sjoberg, D., Strom, S. (ed.), Tuchkin, Yu.A., and Yashina, N.P., 2010. Modern theory of grating. Resonant scattering: analysis techniques and phenomena. New York, Springer Sciens+Business Media, LCC.22. Shestopalov, V.P., Tuchkin, Yu.A., Poyedinchuk, A.Ye., and Sirenko, Yu.K., 1997. New methods for solving direct and inverse problems of diffraction theory. Analytical regularization of boundary value problems of electrodynamics. Kharkov: Osnova Publ. (in Russian).23. Stancil, D.D., 1980. Magnetostatic waves in nonuniform bias fields including exchange effects. IEEE Trans. Magn., 16(5), pp. 1153—1155. DOI: https://doi.org/10.1109/TMAG.1980.106074824. Wilts, C.H., and Prasad, S., 1981. Determination of magnetic profiles in implanted. Garnets using ferromagnetic resonance. IEEE Trans. Magn., 17(5), pp. 2405—2414. DOI: https://doi.org/10.1109/TMAG.1981.1061421 |
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Видавничий дім «Академперіодика» |
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2024 |
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http://rpra-journal.org.ua/index.php/ra/article/view/1441 |
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rpra-journalorgua-article-14412024-07-01T12:16:48Z NATURAL ELECTROMAGNETIC MODES OF A COMPOSITE OPEN STRUCTURE INVOLVING A PERFECTLY CONDUCTING STRIP GRATING, AN INHOMOGENEOUS FERRITE LAYER, AND A MONOLAYER OF GRAPHENE ВЛАСНІ ЕЛЕКТРОМАГНІТНІ КОЛИВАННЯ ВІДКРИТОЇ КОМПОЗИТНОЇ СТРУКТУРИ, ЩО МІСТИТЬ ЕЛЕКТРОПРОВІДНУ СТРІЧКОВУ ҐРАТКУ, НЕОДНОРІДНИЙ ФЕРИТОВИЙ ШАР І ГРАФЕНОВИЙ МОНОШАР Brovenko, A. V. Melezhik, P. N. Poyedinchuk, A. Ye. Senkevych, O. B. Yashina, N. P. ferrite layer; grapheme; stripe grating; analytical regularization procedure; natural oscillations; eigenfrequencies феритовий шар; графен; стрічкова ґратка; аналітичний метод регуляризації; власні коливання; власні частоти Subject and Purpose. Сonsidered are the natural modes and their correspondent eigenfrequencies of a composite structure which is nonuniform along one of the coordinates and consists of a lossy ferromagnetic layer placed in a static magnetic field. The layer involves a perfectly conducting strip grating at one of its boundaries and a graphene monolayer at the other.Methods and Methodology. The above stated problem can be approached within the analytical regularization procedure developed for dual series equations. The latter concern a broad class of diffraction problems which include, in particular, the diffraction of monochromatic plane waves on strip gratings placed at the boundary of a gyromagnetic medium. The amplitudes of the electromagnetic eigenmodes can be obtained from the infinite set of homogeneous linear algebraic equations solvable within a truncation technique. The roots of the system’s determinant represent complex-valued eigenfrequencies of the system under investigation. The material parameters adopted in our computations for the ferromagnetic layer correspond to such of yttrium iron garnet.Results. A number of numerical programs have been developed which permit analyzing the dependences of wave field eigenfunctions and complex eigenfrequencies upon geometrical parameters of the structure (such as grating slot width and period, and thickness of the lossy layer), as well as on electrodynamic parameters of the ferromagnet and graphene characteristics, specifically the chemical potential and relaxation energy of electrons. A number of behavioral regularities have been established, as well as the effect of non-uniformity of ferrite layer parameters upon the structure’s eigenfrequencies and wave field eigenfunctions.Conclusions. The structure under study has been shown to be is an open oscillatory system with a set of complex-valued natural frequencies demonstrating finite points of accumulation. The real parts of these eigenfrequencies lie in a certain interval determined by characteristic frequencies of the ferrite layer, while the imaginary parts are negative, such that the correspondent natural modes show an exponential decay with time. The grating edges represent the mirrors which the natural surface oscillations are reflected from, being supported at that by the ferromagnetic medium. The results obtained in this paper can be useful for creating the elemental base for microwave devices and the devices themselves.Keywords: ferrite layer; grapheme; stripe grating; analytical regularization procedure; natural oscillations; eigenfrequenciesManuscript submitted 24.02.2024Radio phys. radio astron. 2024, 29(2): 113-126REFERENCES1. Jia, H., Yasumoto, K., and Toyama, H., 2005. Reflection and transmission properties of layered periodic arrays of circular cylinders embedded in magnetized ferrite slab. IEEE Trans. Antennas Propag., 53(3), pp. 1145—1153. DOI: https://doi.org/10.1109/TAP.2004.8426542. Monir, A., Sanada, A., Kubo, H., and Awai, I., 2003. Application of the 2-d finite difference-frequency domain method for the analysis of the dispersion characteristics of ferrite devices. In: Proc. 33rd European Microwave Conference. Munich, Germany, 2–10 Oct. 2003. Munich: IEEE, pp. 1175—1177. DOI: https://doi.org/10.1109/EUMA.2003.3411493. Brovenko, A., Melezhik, P., and Poyedinchuk, A., 2012. Resonance scattering of a plane electromagnetic wave by a ferrite-stripe grating-metamaterial structure. Telecommunications and Radio Engineering, 71(12), pp. 1057—1074. DOI: https://doi.org/10.1615/TelecomRadEng.v71.i12.104. Brovenko, A.V., Melezhik, P.N., Poyedinchuk, A.E., and Troshchilo, A.S., 2020. Diffraction of electromagnetic waves on the com- posite structure "strip grating — ferromagnetic half-space": resonances on surface waves. Radiophys. Elektron., 25(1), pp. 11—20 (in Russian). DOI: https://doi.org/10.15407/rej2020.01.0115. Masalov, S.A., Ryzhak, A.V., Sukharevsky, O.I., and Shkil, V.M., 1999. Physical Foundations of Range Technologies "Stealth". St. Petersburg, Russia: Mozhaisky VIKU Publ. (in Russian).6. Brovenko, A., Vinogradova, E., Melezhik, P., Poyedinchuk, A., and Troschylo, A., 2010. Resonance wave Scattering by strip grating adjusted to ferromagnetic medium. Prog. Electromagn. Res. B, 23, pp. 109—129. DOI: https://doi.org/10.2528/PIERB100122037. Brovenko, A.V., Melezhik, P.N, Poyedinchuk, A.Y., and Yashina, N. P., 2006. Surface resonances of metal stripe grating on the plane boundary of metamaterial. Prog. Electromagn. Res., 63, pp. 209—222. DOI: https://doi.org/10.2528/PIER060524018. Lim, J., Bang, W., Trossman, J., Amanov, D., and Ketterson, J., 2018. Forward volume and surface magnetostatic modes in an yttrium iron garnet film for out-of-plane magnetic fields: Theory and experiment. AIP Advances, 8(5), 056018 DOI: https://doi.org/10.1063/1.50072639. Damon, R.W., and Eshbach, J.R., 1961. Magnetostatic modes on a ferromagnetic slab. J. Phys. Chem. Solids, 19(3—4), pp. 308— 320. DOI: https://doi.org/10.1016/0022-3697(61)90041-510. Gurevich, A.G., and Melkov, G.A., 1994. Magnetic Oscillations and Waves. Moscow: Fizmatgiz (in Russian).11. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Dubonos, S.V., Zhang, Y., Grigorieva, I.V., and Firsov, A.A., 2004. Electric field effect in atomically thin carbon films. Science, 306(5696), pp. 666—669. DOI: https://doi.org/10.1126/science.110289612. Nair, R.R., Blake, P., Grigorenko, A.N., Novoselov, K.S., Booth, T.J., Stauber, T., Peres, N.M.R., and Geim, A.K., 2008. Fine structure constant defines transparency of grapheme. Science, 320, pp. 1308—1308. DOI: https://doi.org/10.1126/science.115696513. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Katsnelson, M.I., Grigorieva, I.V., Dubonos, S.V., and Firsov, A.A., 20025. Two-dimensional gas of massless Dirac fermions in grapheme. Nature, 438, pp. 197—200. DOI: https://doi.org/10.1038/nature0423314. Kaipa, C.S.R., Yakovlev, A.B., Hanson, G.W., Padooru, Y.R., and Medina, F., 2012. Mesa enhanced transmission with a graphene- dielectric microstructure at low-terahertz frequencies. Phys. Rev. B, 85, 245407. DOI: https://doi.org/10.1103/PhysRevB.85.24540715. Padooru, Y.R., Yakovlev, A.B., Kaipa, C.S.R., Hanson, G.W., Medina, F., and Mesa, F., 2013. Dual capacitive-inductive nature of periodic graphene patches: Transmission characteristics at low-terahertz frequencies. Phys. Rev. B, 87, 115401. DOI: https://doi.org/10.1103/PhysRevB.87.11540116. Brovenko, A., Melezhik, P., Poyedinchuk, A., Yashina, N., and Granet, G., 2009. Resonant scattering of electromagnetic wave by stripe grating backed with a layer of metamaterial. Prog. Electromagn. Res. B, 15, p. 423—441. DOI: https://doi.org/10.2528/PIERB0905230217. Hanson, G.W., 2008. Dyadic Green’s functions and guided surface waves for a surface conductivity model of grapheme. J. Appl. Phys., 103(6), 064302. DOI: https://doi.org/10.1063/1.289145218. Brovenko, A.V., Melezhik, P.N., Panin, S.B., and Poyedinchuk A.Ye., 2013. Numerical-analytical method for solving problems of the waves diffraction on layered-inhomogeneous medium. Physical Fundamentals of Instrumentation, 2(1), pp. 34—47 (in Russian).19. Brovenko, A., Melezhik, P., Panin, S., and Poyedinchuk, A., 2013. Wave diffraction on a stripe grating at a boundary of a layered inhomogeneous medium: method of analytic regularization. Radiophysics and Quantum Electronics, 56, pp. 238—248. DOI: https://doi.org/10.1007/s11141-013-9429-x20. Shestopalov, V.P., and Sirenko, Yu.K., 1989. Dynamical lattice theory. Kiev: Naukova Dumka Publ. (in Russian).21. Chandezon, J., Granet, G., Melezhik, P.N., Poyedinchuk, A.Ye., Sirenko (ed.), Yu.K., Sjoberg, D., Strom, S. (ed.), Tuchkin, Yu.A., and Yashina, N.P., 2010. Modern theory of grating. Resonant scattering: analysis techniques and phenomena. New York, Springer Sciens+Business Media, LCC.22. Shestopalov, V.P., Tuchkin, Yu.A., Poyedinchuk, A.Ye., and Sirenko, Yu.K., 1997. New methods for solving direct and inverse problems of diffraction theory. Analytical regularization of boundary value problems of electrodynamics. Kharkov: Osnova Publ. (in Russian).23. Stancil, D.D., 1980. Magnetostatic waves in nonuniform bias fields including exchange effects. IEEE Trans. Magn., 16(5), pp. 1153—1155. DOI: https://doi.org/10.1109/TMAG.1980.106074824. Wilts, C.H., and Prasad, S., 1981. Determination of magnetic profiles in implanted. Garnets using ferromagnetic resonance. IEEE Trans. Magn., 17(5), pp. 2405—2414. DOI: https://doi.org/10.1109/TMAG.1981.1061421 Предмет і мета роботи. Розглянуто задачу про власні коливання та відповідні власні частоти композитної структури, що є неоднорідною вздовж однієї з координат і складається з феромагнітного шару з втратами, котрий знаходиться у магнітостатичному полі. На одній з граничних поверхонь розміщено ідеально провідну стрічкову ґратку, а на іншій — графеновий моношар.Методи та методологія. Для розв’язання задачі розроблено метод аналітичної регуляризації парних суматорних рівнянь, до яких зводиться широкий клас задач дифракції. Зокрема, це стосується задач про дифракцію монохроматичних плоских хвиль на стрічкових ґратках, що розташовані на межі гіромагнітного середовища. Для обчислення амплітуд власних електромагнітних полів використано однорідну систему лінійних алгебричних рівнянь, розв’язок якої розшукується методом редукції. Корені детермінанта цієї системи є комплексними власними частотами досліджуваної структури. Матеріальні параметри, котрі було прийнято в розрахунках для феромагнітного шару, відповідають даним залізо-ітрієвого гранату.Результати. Розроблено пакети програм, за допомогою яких чисельно проаналізовано залежності власних полів і комплексних власних частот від геометричних параметрів структури (ширини щілин ґратки, її періоду та товщини феромагнітного шару), а також від електродинамічних параметрів феромагнетика та параметрів графену (хімічного потенціалу та енергії релаксації електронів). Установлено низку закономірностей у динаміці цих залежностей. Також оцінено вплив неоднорідності параметрів феритового шару на власні частоти та власні польові функції структури.Висновки. Показано, що досліджувана структура є відкритою коливальною системою з набором комплекснозначних власних частот із кінцевими точками накопичення. Дійсні частини цих власних частот лежать у певному інтервалі, який визначається характерними частотами феритового шару; уявні частини є негативними, тобто відповідні цим частотам власні коливання згасають експоненціально в часі. Ребра ґраток є «дзеркалами», від яких відбиваються поверхневі власні коливання, а феромагнітне середовище ці коливання підтримує. Отримані результати можуть бути використані при створенні елементної бази і пристроїв НВЧ-діапазону.Ключові слова: феритовий шар; графен; стрічкова ґратка; аналітичний метод регуляризації; власні коливання; власні частотиСтаття надійшла до редакції 24.02.2024Radio phys. radio astron. 2024, 29(2): 113-126БІБЛІОГРАФІЧНИЙ СПИСОК 1. Jia, H., Yasumoto, K., and Toyama, H., 2005. Reflection and transmission properties of layered periodic arrays of circular cylinders embedded in magnetized ferrite slab. IEEE Trans. Antennas Propag., 53(3), pp. 1145—1153. DOI: 10.1109/TAP.2004.842654 2. Monir, A., Sanada, A., Kubo, H., and Awai, I., 2003. Application of the 2-d finite difference-frequency domain method for the analysis of the dispersion characteristics of ferrite devices. In: Proc. 33rd European Microwave Conference. Munich, Germany, 2–10 Oct. 2003. 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Science, 306(5696), pp. 666—669. DOI: 10.1126/science.1102896 12. Nair, R.R., Blake, P., Grigorenko, A.N., Novoselov, K.S., Booth, T.J., Stauber, T., Peres, N.M.R., and Geim, A.K., 2008. Fine structure constant defines transparency of grapheme. Science, 320, pp. 1308—1308. DOI: 10.1126/science.1156965 13. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Katsnelson, M.I., Grigorieva, I.V., Dubonos, S.V., and Firsov, A.A., 20025. Two-dimensional gas of massless Dirac fermions in grapheme. Nature, 438, pp. 197—200. DOI: 10.1038/nature04233 14. Kaipa, C.S.R., Yakovlev, A.B., Hanson, G.W., Padooru, Y.R., and Medina, F., 2012. Mesa enhanced transmission with a graphene- dielectric microstructure at low-terahertz frequencies. Phys. Rev. B, 85, 245407. DOI: 10.1103/PhysRevB.85.245407 15. Padooru, Y.R., Yakovlev, A.B., Kaipa, C.S.R., Hanson, G.W., Medina, F., and Mesa, F., 2013. Dual capacitive-inductive nature of periodic graphene patches: Transmission characteristics at low-terahertz frequencies. Phys. Rev. B, 87, 115401. DOI: 10.1103/ PhysRevB.87.115401 16. Brovenko, A., Melezhik, P., Poyedinchuk, A., Yashina, N., and Granet, G., 2009. Resonant scattering of electromagnetic wave by stripe grating backed with a layer of metamaterial. Prog. Electromagn. Res. B, 15, p. 423—441. DOI: 10.2528/PIERB09052302 17. Hanson, G.W., 2008. Dyadic Green’s functions and guided surface waves for a surface conductivity model of grapheme. J. Appl. Phys., 103(6), 064302. DOI: 10.1063/1.2891452 18. Brovenko, A.V., Melezhik, P.N., Panin, S.B., and Poyedinchuk A.Ye., 2013. Numerical-analytical method for solving problems of the waves diffraction on layered-inhomogeneous medium. Physical Fundamentals of Instrumentation, 2(1), pp. 34—47 (in Russian). 19. Brovenko, A., Melezhik, P., Panin, S., and Poyedinchuk, A., 2013. Wave diffraction on a stripe grating at a boundary of a layered inhomogeneous medium: method of analytic regularization. Radiophysics and Quantum Electronics, 56, pp. 238—248. DOI: 10.1007/s11141-013-9429-x 20. Shestopalov, V.P., and Sirenko, Yu.K., 1989. Dynamical lattice theory. Kiev: Naukova Dumka Publ. (in Russian). 21. Chandezon, J., Granet, G., Melezhik, P.N., Poyedinchuk, A.Ye., Sirenko (ed.), Yu.K., Sjoberg, D., Strom, S. (ed.), Tuchkin, Yu.A., and Yashina, N.P., 2010. Modern theory of grating. Resonant scattering: analysis techniques and phenomena. New York, Springer Sciens+Business Media, LCC. 22. Shestopalov, V.P., Tuchkin, Yu.A., Poyedinchuk, A.Ye., and Sirenko, Yu.K., 1997. New methods for solving direct and inverse problems of diffraction theory. Analytical regularization of boundary value problems of electrodynamics. Kharkov: Osnova Publ. (in Russian). 23. Stancil, D.D., 1980. Magnetostatic waves in nonuniform bias fields including exchange effects. IEEE Trans. Magn., 16(5), pp. 1153—1155. 24. Wilts, C.H., and Prasad, S., 1981. Determination of magnetic profiles in implanted. Garnets using ferromagnetic resonance. IEEE Trans. Magn., 17(5), pp. 2405—2414. Видавничий дім «Академперіодика» 2024-06-24 Article Article application/pdf http://rpra-journal.org.ua/index.php/ra/article/view/1441 10.15407/rpra29.02.113 РАДИОФИЗИКА И РАДИОАСТРОНОМИЯ; Vol 29, No 2 (2024); 113 RADIO PHYSICS AND RADIO ASTRONOMY; Vol 29, No 2 (2024); 113 РАДІОФІЗИКА І РАДІОАСТРОНОМІЯ; Vol 29, No 2 (2024); 113 2415-7007 1027-9636 10.15407/rpra29.02 en http://rpra-journal.org.ua/index.php/ra/article/view/1441/pdf Copyright (c) 2024 RADIO PHYSICS AND RADIO ASTRONOMY |