ДИФРАКЦИЯ Е-ПОЛЯРИЗОВАННОЙ ВОЛНЫ НА БЕСКОНЕЧНОЙ ПЕРИОДИЧЕСКОЙ ЛЕНТОЧНОЙ РЕШЕТКЕ В ОТСУТСТВИЕ ОДНОЙ ЛЕНТЫ

Abstract

PACS number: 41.20.Jb Purpose: The E-polarized wave diffraction by an infinite periodic strip grating without a single strip is considered. Design/methodology/approach: The total field is found as a sum of field of infinite periodical grating and field induced by the removal of a single strip. The problem is reduced to the singular integral equations with additional conditions. Findings: The directional patterns and field distribution in the domain above the grating are represented. Conclusions: The effective algorithm for study of the field which appeared as a result of absence of a single strip is suggested. Key words: infinite periodic grating, integral equation, diffraction Manuscript submitted 30.05.2016 Radio phys. radio astron. 2016, 21(3): 189-197 REFERENCES 1. SHESTOPALOV, V. P., 1971. The method of the Riemann-Hilbert problem in the theory of electromagnetic wave diffraction and propagation . Kharkiv: Kharkiv State University Press (in Russian). 2. SHESTOPALOV, V. P., LYTVYNENKO, L. M., MASALOV, S. A. and SOLOGUB, V. G., 1973. Wave diffraction by gratings . Kharkiv: Kharkiv State University Press,(in Russian). 3. SOLOGUB, V. G., 1975. On some method for studying the problem of diffraction by a finite number of strips in the same plane. Dokl. AN USSR . Ser. A . no. 6, pp. 549–552 (in Russian). 4. LYTVYNENKO, L. M. and PROSVIRNIN, S. L., 2012. Wave diffraction by periodic multilayer structures . Cambridge: Cambridge Scientific Publishers. 5. 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 6. KALIBERDA, M. E., LYTVYNENKO, L. M. and POGARSKY,S. A., 2015. Diffraction of H-polarized electromagnetic waves by a multi-element planar semi-infinitegrating. Telecommunications and Radio Engineering . vol. 74, no. 9, pp. 753–767. DOI: https://doi.org/10.1615/TelecomRadEng.v74.i9.10 7. NEPA, P., MANARA, G. and ARMOGIDA, A., 2005. EM scattering from the edge of a semi-infinite planar strip grating using approximate boundary conditions. IEEE Trans.Antennas Propag . vol. 53, no. 1, pp. 82–90. DOI: https://doi.org/10.1109/TAP.2004.840523 8. GANDEL, YU. V., 1986. The method of discrete singularities in problems of electrodynamics. Voprosy Kibernetiki . no. 124, pp. 166–183 (in Russian) 9. GANDEL, YU. V., 2010. Boundary-value problems for the Helmholtz equation and their discrete mathematical models. J. Math. Sci. vol. 171, no. 1, pp. 74–88. DOI: https://doi.org/10.1007/s10958-010-0127-3 10. ZAGINAYLOV, G. I., GANDEL, Y. V., KAMYSHAN, O. P.,KAMYSHAN, V. V., HIRATA, A., THUMVONGSKUL, T. and SHIOZAWA, T., 2002. Full-wave analysis of the field distribution of natural modes in the rectangular waveguide grating based on singular integral equation method. IEEE Trans. Plasma Sci . vol. 30, no. 3. pp. 1151–1159. DOI: https://doi.org/10.1109/TPS.2002.801613 11. ZAMYATIN, YE. V. and PROSVIRNIN, S. L., 1986. Diffraction of electromagnetic waves by an array with small random fluctuations of the dimensions. Sov. J. Commun. Technol. Electron . vol. 31, no. 3, pp. 43–50. 12. ABRAMOWITZ, M. and STEGUN, I. A., eds., 1964. Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables . Numder 55 in National Bureau of Standards Applied Mathematics Series. U. S. Government Printing Office, Washington, D. C. 13. FELSEN, L. B. and MARCUVITS, N., 1973. Radiation and Scattering of Waves . Englewood Cliffs, N.J.: Prentice-Hall.