THE H-POLARIZED ELECTROMAGNETIC WAVE DIFFRACTION BY MULTI-ELEMENT PLANE SEMI-INFINITE GRATING
The H-polarized wave diffraction by multi-element plane semiinfinite periodic strip grating is considered. The problem is reduced to a nonlinear operator equation with respect to the unknown reflection operator of a structure. The equation is obtained as a result of solution of the auxiliary problem...
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plane semi-infinite grating Venetian blind type semi-infinite grating operator method relaxation method |
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plane semi-infinite grating Venetian blind type semi-infinite grating operator method relaxation method Kaliberda, M. E. Lytvynenko, L. M. Pogarsky, S. A. THE H-POLARIZED ELECTROMAGNETIC WAVE DIFFRACTION BY MULTI-ELEMENT PLANE SEMI-INFINITE GRATING |
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plane semi-infinite grating Venetian blind type semi-infinite grating operator method relaxation method плоская полубесконечная решетка полубесконечная решетка типа жалюзи операторный метод метод релаксации плоска напівнескінченна решітка напівнескінченна решітка типа жалюзі операторний метод метод релаксації |
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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 |
THE H-POLARIZED ELECTROMAGNETIC WAVE DIFFRACTION BY MULTI-ELEMENT PLANE SEMI-INFINITE GRATING |
| title_short |
THE H-POLARIZED ELECTROMAGNETIC WAVE DIFFRACTION BY MULTI-ELEMENT PLANE SEMI-INFINITE GRATING |
| title_full |
THE H-POLARIZED ELECTROMAGNETIC WAVE DIFFRACTION BY MULTI-ELEMENT PLANE SEMI-INFINITE GRATING |
| title_fullStr |
THE H-POLARIZED ELECTROMAGNETIC WAVE DIFFRACTION BY MULTI-ELEMENT PLANE SEMI-INFINITE GRATING |
| title_full_unstemmed |
THE H-POLARIZED ELECTROMAGNETIC WAVE DIFFRACTION BY MULTI-ELEMENT PLANE SEMI-INFINITE GRATING |
| title_sort |
h-polarized electromagnetic wave diffraction by multi-element plane semi-infinite grating |
| title_alt |
ДИФРАКЦИЯ H-ПОЛЯРИЗОВАННОЙ ЭЛЕКТРОМАГНИТНОЙ ВОЛНЫ НА МНОГОЭЛЕМЕНТНОЙ ПЛОСКОЙ ПОЛУБЕСКОНЕЧНОЙ РЕШЕТКЕ ДИФРАКЦІЯ H-ПОЛЯРИЗОВАНОЇ ЕЛЕКТРОМАГНІТНОЇ ХВИЛІ НА БАГАТОЕЛЕМЕНТНІЙ ПЛОСКІЙ НАПІВНЕСКІНЧЕННІЙ РЕШІТЦІ |
| description |
The H-polarized wave diffraction by multi-element plane semiinfinite periodic strip grating is considered. The problem is reduced to a nonlinear operator equation with respect to the unknown reflection operator of a structure. The equation is obtained as a result of solution of the auxiliary problem – wave diffraction by semi-infinite periodic venetian blind-type grating with the strips placed in parallel planes. The dependences of the reflection coefficient of plane waves are presented for one, two, three and four strips per period and for the near and far fields are calculated.Key words:plane semi-infinite grating, Venetian blind type semi-infinite grating, operator method, relaxation methodManuscript submitted 02.07.2014Radio phys. radio astron. 2014, 19(4): 348-357 REFERENCES1. FEL'D, Y. N., 1958. Electromagnetic wave diffractionby semi-infinite grating. Radiotekhnika i Elektronika, vol.13, no. 7, pp. 882–889 (in Russian). 2. FEL'D, Y. N., 1955. On infinite systems of linear algebraicequations connected with problems on semi-infinite periodicstructures. Doklady AN USSR, vol. 102, no. 2, pp. 257–260 (in Russian). 3. HILLS, N. L. and KARP, S. N., 1965. Semi-infinite diffractiongratings. I. Commun. Pure Appl. Math., vol. 18, no. 1/2, pp. 203–233. 4. HILLS, N. L., 1965. Semi-infinite diffraction gratings. II. Inward resonance. Commun. Pure Appl. Math., vol. 18, no. 3, pp. 385–395. 5. WASYLKIWSKYJ, W., 1973. Mutual coupling effects insemi-infinite arrays. IEEE Trans. Antennas Propag., vol. 21,no. 3, pp. 277–285. DOI: https://doi.org/10.1109/TAP.1973.1140507 6. LINTON, C. M. and MARTIN, P. A., 2004. Semi-infinitearrays of isotropic point-scatterers. A unified approach.SIAM J. Appl. Math., vol. 64, pp. 1035–1056. DOI: https://doi.org/10.1137/S0036139903427891 7. LINTON, C. M., PORTER, R. and THOMPSON, I., 2007. Scattering by a semi-infinite periodic array and theexcitation of surface waves. SIAM J. Appl. Math., vol. 67, no. 5, pp. 1233–1258. DOI: https://doi.org/10.1137/060672662 8. CAPOLINO, F. and ALBANI, M., 2009. Truncation effectsin a semi-infinite periodic array of thin strips: A discreteWiener-Hopf formulation. Radio Sci., vol. 44, pp. 1223–1234. DOI: https://doi.org/10.1029/2007RS003821 9. NISHIMOTO, M. and IKUNO, H., 1999. Analysis ofelectromagnetic wave diffraction by a semi-infinite stripgrating and evaluation of end-effects. Progr. Electromagn. Res. (PIER), vol. 23, pp. 39–58. DOI: https://doi.org/10.1163/156939399X01177 10. CAMINITA, F., NANNETTI, M. and MACI, S., 2008. An efficient approach to the solution of a semi-infinitestrip grating printed on infinite grounded slab excited by asurface wave. In: XXIX URSI General Assembly. Chicago, IL, August 7-13, 2008, BPS 2.5. 11. NEPA, P., MANARA, G. and ARMOGIDA, A., 2005. EM scattering from the edge of a semi-infinite planar stripgrating using approximate boundary conditions. IEEE Trans. Antennas Propag. vol. 53, no. 1, pp. 82–90. DOI: https://doi.org/10.1109/TAP.2004.840523 12. LYTVYNENKO, L. M., REZNIK, I. I. and LYTVYNENKO, D. L., 1991. Wave scattering by semi-infinite periodic structure. Doklady AN Ukr. SSR. no. 6, pp. 62–67 (in Russian). 13. LYTVYNENKO, L. M. and PROSVIRNIN, S. L., 2012. Wave Diffraction by Periodic Multilayer Structures. Cambridge: Cambridge Scientific Publishers. 14. KALIBERDA, M. E., LITVINENKO, L. N. and POGARSKII, S. A., 2009. Operator method in the analysis ofelectromagnetic wave diffraction by planar screens. J. Commun. Technol. Electron., vol. 54, no. 9, pp. 975–981.DOI: https://doi.org/10.1134/S1064226909090010 15. KALIBERDA, M. E., LYTVYNENKO, L. N. and POGARSKY, S. A., 2011. Electrodynamic characteristics ofmultilayered system of plane screens with a slot. Radio Phys. Radio Astron. vol. 2, no. 4. pp. 339–344. 16. LYTVYNENKO, L. M., KALIBERDA, M. E. and POGARSKY,S. A., 2012. Solution of waves transformation problem in axially symmetric structures. Frequenz., vol. 66, no. 1-2, pp. 17–25. DOI: https://doi.org/10.1515/freq.2012.012 17. LYTVYNENKO, L. M., KALIBERDA, M. E. and POGARSKY, S. A., 2013. Wave diffraction by semi-infinite venetian blind type grating. IEEE Trans. Antennas Propag., vol. 61, no. 12, pp. 6120–6127. DOI: https://doi.org/10.1109/TAP.2013.2281510 18. VOROBYOV, S. N. and LYTVYNENKO, L. M., 2011. Electromagnetic wave diffraction by semi-infinite stripgrating. IEEE Trans. Antennas Propag., vol. 59, no. 6,pp. 2169–2177. DOI: https://doi.org/10.1109/TAP.2011.2143655 19. FELSEN, L. B. and MARCUVITZ, N., 1973. Radiationand Scattering of Waves. Englewood Cliffs, NJ: Prentice-Hall. 20. MESZMER, P., 2010. Hierarchical quadrature for multidimen sionalsingular integrals. J. Numer. Math. vol. 18, no. 2, pp. 91–117. 21. MESZMER, P., 2014. Hierarchical quadrature for multidimensional singular integrals – Part II. J. Numer. Math, vol. 22, no. 1, pp. 33–60. DOI: https://doi.org/10.1515/jnum-2014-0002 22. LIFANOV, I. K., 1995. The method of singular integral equations and numerical experiment (in mathematical physics, aerodynamics, theory of elasticity and diffraction of waves). Moscow: Yanus Publ. 23. NOSICH, A. A. and GANDEL, Y. V., 2007. Numerical Analysis of Quasioptical Multireflector Antennas in 2-D with the Method of Discrete Singularities: E-Wave Case. IEEE Trans. Antennas Propag. vol. 55, no. 2, pp. 399–406. DOI: https://doi.org/10.1109/TAP.2006.889811 24. MITTRA, R. and S. W. LEE, 1974. Analytical Techniques in the Theory of Guided Waves. Moscow: Myr Publ. (in Russian). 25. ORTEGA, J. M. and RHEINBOLDT, W. C., 1970. Iterative Solution of Nonlinear Equations in Several Variables. New York: Academic Press. DOI: https://doi.org/10.1137/1.9780898719468 26. SHESTOPALOVOV, V. P., LYTVYNENKO, L. N., MASALOV, P. and SOLOGUB, V. G., 1973. Diffraction of waves on gratings. Kharkiv: Univer. Publ. (in Russian). |
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Видавничий дім «Академперіодика» |
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2015 |
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http://rpra-journal.org.ua/index.php/ra/article/view/1193 |
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rpra-journalorgua-article-11932017-06-27T10:07:24Z THE H-POLARIZED ELECTROMAGNETIC WAVE DIFFRACTION BY MULTI-ELEMENT PLANE SEMI-INFINITE GRATING ДИФРАКЦИЯ H-ПОЛЯРИЗОВАННОЙ ЭЛЕКТРОМАГНИТНОЙ ВОЛНЫ НА МНОГОЭЛЕМЕНТНОЙ ПЛОСКОЙ ПОЛУБЕСКОНЕЧНОЙ РЕШЕТКЕ ДИФРАКЦІЯ H-ПОЛЯРИЗОВАНОЇ ЕЛЕКТРОМАГНІТНОЇ ХВИЛІ НА БАГАТОЕЛЕМЕНТНІЙ ПЛОСКІЙ НАПІВНЕСКІНЧЕННІЙ РЕШІТЦІ Kaliberda, M. E. Lytvynenko, L. M. Pogarsky, S. A. plane semi-infinite grating; Venetian blind type semi-infinite grating; operator method; relaxation method плоская полубесконечная решетка; полубесконечная решетка типа жалюзи; операторный метод; метод релаксации плоска напівнескінченна решітка; напівнескінченна решітка типа жалюзі; операторний метод; метод релаксації The H-polarized wave diffraction by multi-element plane semiinfinite periodic strip grating is considered. The problem is reduced to a nonlinear operator equation with respect to the unknown reflection operator of a structure. The equation is obtained as a result of solution of the auxiliary problem – wave diffraction by semi-infinite periodic venetian blind-type grating with the strips placed in parallel planes. The dependences of the reflection coefficient of plane waves are presented for one, two, three and four strips per period and for the near and far fields are calculated.Key words:plane semi-infinite grating, Venetian blind type semi-infinite grating, operator method, relaxation methodManuscript submitted 02.07.2014Radio phys. radio astron. 2014, 19(4): 348-357 REFERENCES1. FEL'D, Y. N., 1958. Electromagnetic wave diffractionby semi-infinite grating. Radiotekhnika i Elektronika, vol.13, no. 7, pp. 882–889 (in Russian). 2. FEL'D, Y. N., 1955. On infinite systems of linear algebraicequations connected with problems on semi-infinite periodicstructures. Doklady AN USSR, vol. 102, no. 2, pp. 257–260 (in Russian). 3. HILLS, N. L. and KARP, S. N., 1965. Semi-infinite diffractiongratings. I. Commun. Pure Appl. Math., vol. 18, no. 1/2, pp. 203–233. 4. HILLS, N. L., 1965. Semi-infinite diffraction gratings. II. Inward resonance. Commun. Pure Appl. Math., vol. 18, no. 3, pp. 385–395. 5. WASYLKIWSKYJ, W., 1973. Mutual coupling effects insemi-infinite arrays. IEEE Trans. Antennas Propag., vol. 21,no. 3, pp. 277–285. DOI: https://doi.org/10.1109/TAP.1973.1140507 6. LINTON, C. M. and MARTIN, P. A., 2004. Semi-infinitearrays of isotropic point-scatterers. A unified approach.SIAM J. Appl. Math., vol. 64, pp. 1035–1056. DOI: https://doi.org/10.1137/S0036139903427891 7. LINTON, C. M., PORTER, R. and THOMPSON, I., 2007. Scattering by a semi-infinite periodic array and theexcitation of surface waves. SIAM J. Appl. Math., vol. 67, no. 5, pp. 1233–1258. DOI: https://doi.org/10.1137/060672662 8. CAPOLINO, F. and ALBANI, M., 2009. Truncation effectsin a semi-infinite periodic array of thin strips: A discreteWiener-Hopf formulation. Radio Sci., vol. 44, pp. 1223–1234. DOI: https://doi.org/10.1029/2007RS003821 9. NISHIMOTO, M. and IKUNO, H., 1999. Analysis ofelectromagnetic wave diffraction by a semi-infinite stripgrating and evaluation of end-effects. Progr. Electromagn. Res. (PIER), vol. 23, pp. 39–58. DOI: https://doi.org/10.1163/156939399X01177 10. CAMINITA, F., NANNETTI, M. and MACI, S., 2008. An efficient approach to the solution of a semi-infinitestrip grating printed on infinite grounded slab excited by asurface wave. In: XXIX URSI General Assembly. Chicago, IL, August 7-13, 2008, BPS 2.5. 11. NEPA, P., MANARA, G. and ARMOGIDA, A., 2005. EM scattering from the edge of a semi-infinite planar stripgrating using approximate boundary conditions. IEEE Trans. Antennas Propag. vol. 53, no. 1, pp. 82–90. DOI: https://doi.org/10.1109/TAP.2004.840523 12. LYTVYNENKO, L. M., REZNIK, I. I. and LYTVYNENKO, D. L., 1991. Wave scattering by semi-infinite periodic structure. Doklady AN Ukr. SSR. no. 6, pp. 62–67 (in Russian). 13. LYTVYNENKO, L. M. and PROSVIRNIN, S. L., 2012. Wave Diffraction by Periodic Multilayer Structures. Cambridge: Cambridge Scientific Publishers. 14. KALIBERDA, M. E., LITVINENKO, L. N. and POGARSKII, S. A., 2009. Operator method in the analysis ofelectromagnetic wave diffraction by planar screens. J. Commun. Technol. Electron., vol. 54, no. 9, pp. 975–981.DOI: https://doi.org/10.1134/S1064226909090010 15. KALIBERDA, M. E., LYTVYNENKO, L. N. and POGARSKY, S. A., 2011. Electrodynamic characteristics ofmultilayered system of plane screens with a slot. Radio Phys. Radio Astron. vol. 2, no. 4. pp. 339–344. 16. LYTVYNENKO, L. M., KALIBERDA, M. E. and POGARSKY,S. A., 2012. Solution of waves transformation problem in axially symmetric structures. Frequenz., vol. 66, no. 1-2, pp. 17–25. DOI: https://doi.org/10.1515/freq.2012.012 17. LYTVYNENKO, L. M., KALIBERDA, M. E. and POGARSKY, S. A., 2013. Wave diffraction by semi-infinite venetian blind type grating. IEEE Trans. Antennas Propag., vol. 61, no. 12, pp. 6120–6127. DOI: https://doi.org/10.1109/TAP.2013.2281510 18. VOROBYOV, S. N. and LYTVYNENKO, L. M., 2011. Electromagnetic wave diffraction by semi-infinite stripgrating. IEEE Trans. Antennas Propag., vol. 59, no. 6,pp. 2169–2177. DOI: https://doi.org/10.1109/TAP.2011.2143655 19. FELSEN, L. B. and MARCUVITZ, N., 1973. Radiationand Scattering of Waves. Englewood Cliffs, NJ: Prentice-Hall. 20. MESZMER, P., 2010. Hierarchical quadrature for multidimen sionalsingular integrals. J. Numer. Math. vol. 18, no. 2, pp. 91–117. 21. MESZMER, P., 2014. Hierarchical quadrature for multidimensional singular integrals – Part II. J. Numer. Math, vol. 22, no. 1, pp. 33–60. DOI: https://doi.org/10.1515/jnum-2014-0002 22. LIFANOV, I. K., 1995. The method of singular integral equations and numerical experiment (in mathematical physics, aerodynamics, theory of elasticity and diffraction of waves). Moscow: Yanus Publ. 23. NOSICH, A. A. and GANDEL, Y. V., 2007. Numerical Analysis of Quasioptical Multireflector Antennas in 2-D with the Method of Discrete Singularities: E-Wave Case. IEEE Trans. Antennas Propag. vol. 55, no. 2, pp. 399–406. DOI: https://doi.org/10.1109/TAP.2006.889811 24. MITTRA, R. and S. W. LEE, 1974. Analytical Techniques in the Theory of Guided Waves. Moscow: Myr Publ. (in Russian). 25. ORTEGA, J. M. and RHEINBOLDT, W. C., 1970. Iterative Solution of Nonlinear Equations in Several Variables. New York: Academic Press. DOI: https://doi.org/10.1137/1.9780898719468 26. SHESTOPALOVOV, V. P., LYTVYNENKO, L. N., MASALOV, P. and SOLOGUB, V. G., 1973. Diffraction of waves on gratings. Kharkiv: Univer. Publ. (in Russian). УДК 537.874.6 Рассматривается задача о дифракции H-поляризованной волны на многоэлементной плоской полубесконечной периодической ленточной решетке. Задача сводится к нелинейному операторному уравнению относительно неизвестного оператора отражения решетки. Уравнение получено в результате решения вспомогательной задачи – задачи о дифракции волны на полубесконечной периодической ленточной решетке типа жалюзи, ленты которой расположены в параллельных плоскостях. Представлены зависимости коэффициента отражения плоских волн для одной, двух, трех и четырех лент на периоде и распределение поля в ближней и дальней зонах.Ключевые слова: плоская полубесконечная решетка, полубесконечная решетка типа жалюзи, операторный метод, метод релаксацииСтатья поступила в редакцию 02.07.2014Radio phys. radio astron. 2014, 19(4): 348-357 СПИСОК ЛИТЕРАТУРЫ1. Фельд Я. Н. Дифракция электромагнитной волны наполубесконечной решетке // Радиотехника и электроника. – 1958. – Т. 13, № 7. – С. 882–889.2. Фельд Я. Н. О бесконечных системах линейных алгебраических уравнений, связанных с задачами о полубесконечных периодических структурах // ДокладыАН СССР. – 1955. – Т. 102, № 2. – С. 257–260.3. Hills N. L. and Karp S. N. Semi-Infinite DiffractionGratings – I // Commun. Pure Appl. Math. – 1965. –Vol. 18, No. 1/2. – P. 203–233.4. Hills N. L. Semi-Infinite Diffraction Gratings. II. InwardResonance // Commun. Pure Appl. Math. – 1965. –Vol. 18, No. 3. – P. 385–395.5. Wasylkiwskyj W. Mutual coupling effects in semi-infinitearrays // IEEE Trans. Antennas Propag. – 1973. – Vol. 21,No. 3. – P. 277–285.6. Linton C. M. and Martin P. A. Semi-infinite arrays of isotropicpoint-scatterers. A unified approach // SIAM J. Appl. Math. – 2004. – Vol. 64, No. 3. – P. 1035–1056.7. Linton C. M., Porter R., and Thompson I. Scattering bya Semi-Infinite Periodic Array and the Excitation of SurfaceWaves // SIAM J. Appl. Math. – 2007. – Vol. 67,No. 5. – P. 1233–1258.8. Capolino F. and Albani M. Truncation effects in a semiinfiniteperiodic array of thin strips: A discrete Wiener-Hopf formulation // Radio Sci. – 2009. – Vol. 44, Is. 2. –id. RS2S91.9. Nishimoto M. and Ikuno H. Analysis of electromagneticwave diffraction by a semi-infinite strip grating and evaluationof end-effects // Prog. Electromagn. Res. (PIER) –1999. – Vol. 23. – P. 39–58.10. Caminita F., Nannetti M., and Maci S. An efficient approachto the solution of a semi-infinite strip grating printedon infinite grounded slab excited by a surface wave //XXIX URSI General Assembly. – Chicago, Illinois (USA). –2008. – BPS 2.5.11. Nepa P., Manara G., and Armogida A. EM scattering fromthe edge of a semi-infinite planar strip grating using approximateboundary conditions // IEEE Trans. AntennasPropag. – 2005. – Vol. 53, No. 1. – P. 82–90.12. Литвиненко Л. М., Резник І. І., Литвиненко Д. Л. Дифракція хвиль на напівнескінченних періодичних структурах // Доповіді АН Української РСР. – 1991. – № 6. –С. 62–66.13. Lytvynenko L. M. and Prosvirnin S. L. Wave Diffractionby Periodic Multilayer Structures. – Cottenham, UK:Cambridge Scientific Publishers, 2012. – 158 p.14. Kaliberda M. E., Litvinenko L. N., and Pogarskii S. A.Operator Method in the Analysis of Electromagnetic WaveDiffraction by Planar Screens // J. Commun. Technol. Electron.– 2009. – Vol. 54, No. 9. – P. 975–981.15. Kaliberda M. E., Lytvynenko L. N., and Pogarsky S. A.Electrodynamic characteristics of multilayered system ofplane screens with a slot // Radio Physics and Radio Astronomy.– 2011. – Vol. 2, Is. 4. – P. 339–344.16. Lytvynenko L. M., Kaliberda M. E., and Pogarsky S. A.Solution of Waves Transformation Problem in Axially SymmetricStructures // Frequenz. – 2012. – Vol. 66,No. 1–2. – P. 17–25.17. Lytvynenko L. M., Kaliberda M. E., and Pogarsky S. A.Wave diffraction by semi-infinite venetian blind typegrating // IEEE Trans. Antennas Propag. – 2013. – Vol. 61,No. 12. – P. 6120–6127.18. Vorobyov S. N. and Lytvynenko L. M. Electromagnetic wavediffraction by semi-infinite strip grating // IEEE Trans. AntennasPropag. – 2011. – Vol. 59, No. 6. – P. 2169–2177.19. Felsen L. B. and Marcuvits N. Radiation and Scatteringof Waves. – Englewood Cliffs, NJ: Prentice-Hall, 1973. –ch. 4.20. Meszmer P. Hierarchical quadrature for multidimensionalsingular integrals // J. Numer. Math. – 2010. – Vol. 18,No. 2. – P. 91–117.21. Meszmer P. Hierarchical quadrature for multidimensionalsingular integrals – Part II // J. Numer. Math. – 2014. –Vol. 22, No. 1. – P. 33–60.22. Лифанов И. К. Метод сингулярных интегральных уравнений и численный эксперимент (в математическойфизике, аэродинамике, теории упругости и дифракцииволн). – М: ТОО “Янус”, 1995. – 520 с.23. Nosich A. A. and Gandel Y. V. Numerical Analysis of QuasiopticalMultireflector Antennas in 2-D With the Methodof Discrete Singularities: E-Wave Case // IEEE Trans. AntennasPropag. – 2007. – Vol. 55, No. 2. – P. 399–406.24. Миттра Р., Ли С. Аналитические методы теории волноводов. – М.: Мир, 1974. – 325 с.25. Ortega J. M. and Rheinboldt W. C. Iterative Solutionof Nonlinear Equations in Several Variables. – New York:Academic Press, 1970. – 566 p.26. Шестопалов В. П., Литвиненко Л. Н., Масалов С. А.,Сологуб В. Г. Дифракция волн на решетках. – Харьков: Издательство ХГУ, 1973. – 287 с. УДК 537.874.6 Розглядається задача дифракції H-поляризованої хвилі на багатоелементній плоскій напівнескінченній періодичній стрічковій решітці. Задачу зведено до нелінійного операторного рівняння відносно невідомого оператора відбиття решітки. Рівняння отримане в результаті розв’язання допоміжної задачі – задачі дифракції хвилі на напівнескінченній періодичній стрічковій решітці типу жалюзі, стрічки якої лежать у паралельних площинах. Надаються залежності коефіцієнта відбиття плоских хвиль для однієї, двох та чотирьох стрічок на періоді та розподіл поля у ближній та дальній зонах. Ключові слова: плоска напівнескінченна решітка, напівнескінченна решітка типа жалюзі, операторний метод, метод релаксаціїСтаття надійшла до редакції 02.07.2014Radio phys. radio astron. 2014, 19(4): 348-357 СПИСОК ЛІТЕРАТУРИ 1. Фельд Я. Н. Дифракция электромагнитной волны наполубесконечной решетке // Радиотехника и электроника. – 1958. – Т. 13, № 7. – С. 882–889. 2. Фельд Я. Н. О бесконечных системах линейных алгебраических уравнений, связанных с задачами о полубесконечных периодических структурах // ДокладыАН СССР. – 1955. – Т. 102, № 2. – С. 257–260. 3. Hills N. L. and Karp S. N. Semi-Infinite DiffractionGratings – I // Commun. Pure Appl. Math. – 1965. –Vol. 18, No. 1/2. – P. 203–233. 4. Hills N. L. Semi-Infinite Diffraction Gratings. II. InwardResonance // Commun. Pure Appl. Math. – 1965. –Vol. 18, No. 3. – P. 385–395. 5. Wasylkiwskyj W. Mutual coupling effects in semi-infinitearrays // IEEE Trans. Antennas Propag. – 1973. – Vol. 21,No. 3. – P. 277–285. 6. Linton C. M. and Martin P. A. Semi-infinite arrays of isotropicpoint-scatterers. A unified approach // SIAM J. Appl. Math. – 2004. – Vol. 64, No. 3. – P. 1035–1056. 7. Linton C. M., Porter R., and Thompson I. Scattering bya Semi-Infinite Periodic Array and the Excitation of SurfaceWaves // SIAM J. Appl. Math. – 2007. – Vol. 67,No. 5. – P. 1233–1258. 8. Capolino F. and Albani M. Truncation effects in a semiinfiniteperiodic array of thin strips: A discrete Wiener-Hopf formulation // Radio Sci. – 2009. – Vol. 44, Is. 2. –id. RS2S91. 9. Nishimoto M. and Ikuno H. Analysis of electromagneticwave diffraction by a semi-infinite strip grating and evaluationof end-effects // Prog. Electromagn. Res. (PIER) –1999. – Vol. 23. – P. 39–58. 10. Caminita F., Nannetti M., and Maci S. An efficient approachto the solution of a semi-infinite strip grating printedon infinite grounded slab excited by a surface wave //XXIX URSI General Assembly. – Chicago, Illinois (USA). –2008. – BPS 2.5. 11. Nepa P., Manara G., and Armogida A. EM scattering fromthe edge of a semi-infinite planar strip grating using approximateboundary conditions // IEEE Trans. AntennasPropag. – 2005. – Vol. 53, No. 1. – P. 82–90. 12. Литвиненко Л. М., Резник І. І., Литвиненко Д. Л. Дифракція хвиль на напівнескінченних періодичних структурах // Доповіді АН Української РСР. – 1991. – № 6. –С. 62–66. 13. Lytvynenko L. M. and Prosvirnin S. L. Wave Diffractionby Periodic Multilayer Structures. – Cottenham, UK:Cambridge Scientific Publishers, 2012. – 158 p. 14. Kaliberda M. E., Litvinenko L. N., and Pogarskii S. A.Operator Method in the Analysis of Electromagnetic WaveDiffraction by Planar Screens // J. Commun. Technol. Electron.– 2009. – Vol. 54, No. 9. – P. 975–981. 15. Kaliberda M. E., Lytvynenko L. N., and Pogarsky S. A.Electrodynamic characteristics of multilayered system ofplane screens with a slot // Radio Physics and Radio Astronomy.– 2011. – Vol. 2, Is. 4. – P. 339–344. 16. Lytvynenko L. M., Kaliberda M. E., and Pogarsky S. A.Solution of Waves Transformation Problem in Axially SymmetricStructures // Frequenz. – 2012. – Vol. 66,No. 1–2. – P. 17–25. 17. Lytvynenko L. M., Kaliberda M. E., and Pogarsky S. A.Wave diffraction by semi-infinite venetian blind typegrating // IEEE Trans. Antennas Propag. – 2013. – Vol. 61,No. 12. – P. 6120–6127. 18. Vorobyov S. N. and Lytvynenko L. M. Electromagnetic wavediffraction by semi-infinite strip grating // IEEE Trans. AntennasPropag. – 2011. – Vol. 59, No. 6. – P. 2169–2177. 19. Felsen L. B. and Marcuvits N. Radiation and Scatteringof Waves. – Englewood Cliffs, NJ: Prentice-Hall, 1973. –ch. 4. 20. Meszmer P. Hierarchical quadrature for multidimensionalsingular integrals // J. Numer. Math. – 2010. – Vol. 18,No. 2. – P. 91–117. 21. Meszmer P. Hierarchical quadrature for multidimensionalsingular integrals – Part II // J. Numer. Math. – 2014. –Vol. 22, No. 1. – P. 33–60. 22. Лифанов И. К. Метод сингулярных интегральных уравнений и численный эксперимент (в математическойфизике, аэродинамике, теории упругости и дифракцииволн). – М: ТОО “Янус”, 1995. – 520 с. 23. Nosich A. A. and Gandel Y. V. Numerical Analysis of QuasiopticalMultireflector Antennas in 2-D With the Methodof Discrete Singularities: E-Wave Case // IEEE Trans. AntennasPropag. – 2007. – Vol. 55, No. 2. – P. 399–406. 24. Миттра Р., Ли С. Аналитические методы теории волноводов. – М.: Мир, 1974. – 325 с. 25. Ortega J. M. and Rheinboldt W. C. Iterative Solutionof Nonlinear Equations in Several Variables. – New York:Academic Press, 1970. – 566 p. 26. Шестопалов В. П., Литвиненко Л. Н., Масалов С. А.,Сологуб В. Г. Дифракция волн на решетках. – Харьков: Издательство ХГУ, 1973. – 287 с. Видавничий дім «Академперіодика» 2015-01-13 Article Article application/pdf http://rpra-journal.org.ua/index.php/ra/article/view/1193 10.15407/rpra19.04.348 РАДИОФИЗИКА И РАДИОАСТРОНОМИЯ; Vol 19, No 4 (2014); 348 RADIO PHYSICS AND RADIO ASTRONOMY; Vol 19, No 4 (2014); 348 РАДІОФІЗИКА І РАДІОАСТРОНОМІЯ; Vol 19, No 4 (2014); 348 2415-7007 1027-9636 10.15407/rpra19.04 ru http://rpra-journal.org.ua/index.php/ra/article/view/1193/829 Copyright (c) 2014 RADIO PHYSICS AND RADIO ASTRONOMY |