89
Views
2
CrossRef citations to date
0
Altmetric
Articles

Singular integral equations in diffraction problem by an infinite periodic strip grating with one strip removed: E–polarization case

ORCID Icon, & ORCID Icon
Pages 332-346 | Received 18 Feb 2017, Accepted 17 Sep 2017, Published online: 09 Oct 2017

References

  • Kaliberda ME, Lytvynenko LM, Pogarsky SA. Singular integral equations in diffraction problem by an infinite periodic strip grating with one strip removed. J Electromagn Waves Appl. 2016;30:2411–2426.10.1080/09205071.2016.1254071
  • Capolino F, editor. Theory and phenomena of metamaterials (Metamaterials Handbook). Boca Raton (FL): CRC Press; 2009.
  • Silberstein E, Lalanne P, Hugonin J-P, et al. Use of grating theories in integrated optics. J Opt Soc Am A. 2001;18:2865–2875.10.1364/JOSAA.18.002865
  • Barrelet CJ, Bao J, Lončar, et al. Hybrid single-nanowire photonic crystal and microresonator structures. Nano Lett. 2006;6:11–15.10.1021/nl0522983
  • Butler CM, Wilton DRD. General analysis of narrow strips and slots. IEEE Trans Antennas Propag. 1980;28:42–48.10.1109/TAP.1980.1142291
  • Uchida K, Noda T, Matsunaga T. Spectral domain analysis of electromagnetic wave scattering by an infinite plane metallic grating. IEEE Trans Antennas Propag. 1987;35:46–52.10.1109/TAP.1987.1143973
  • Uchida K, Noda T, Matsunaga T. Electromagnetic wave scattering by a conducting strip–spectral domain analysis. Electron Comm Jpn Pt II. 1990;73:49–55.10.1002/(ISSN)1520-6432
  • Vorob’ev SN, Litvinenko LN, Prosvirnin SL. Wave diffraction by a periodic structure consisting of inclined metal tapes. USSR Comput Math Math Phys. 1986;26:159–166.
  • Vorob’ev SN, Litvinenko LN, Prosvirnin SL. Electromagnetic wave diffraction by finite extent structure consisting of nonequidistant strips having different width. Comparison of full-wave spectral and operator method. Radio Phys Radio Astron. 1996;1:110–118. Russian.
  • Lytvynenko LM, Prosvirnin SL. Spectral scattering operators in wave diffraction by plane screens. Kyiv: Naukova Dumka; 1984. Russian.
  • Nishimoto M, Ikuno H. Analysis of electromagnetic wave diffraction by a semi-infinite strip grating and evaluation of end-effects. Prog Electromagn Res. 1999;23:39–58.10.2528/PIER98101602
  • Nishimoto M, Ikuno H. Numerical analysis of plane wave diffraction by a semi-infinite grating. T IEE Jpn. 2001;121-A:905–910.
  • Matsushima A, Itakura T. Singular integral equation approach to plane wave diffraction by an infinite strip grating at oblique incidence. J Electromagn Waves Appl. 1990;4:505–519.
  • Matsushima A, Itakura T. Singular integral equation approach to electromagnetic scattering from a finite periodic array of conducting strips. J Electromagn Waves Appl. 1991;5:545–562.10.1163/156939391X00680
  • Matsushima A, Nakamura Y, Tomino S. Application of integral equation method to metal-plate lens structures. Prog Electromagn Res. 2005;54:245–262.10.2528/PIER05011401
  • Nosich AI. The method of analytical regularization in wave-scattering and eigenvalue problems: foundations and review of solutions. IEEE Antennas Propag Mag. 1999;41:34–49.10.1109/74.775246
  • Nosich AI. Method of analytical regularization based on the static part inversion in wave scattering by imperfect thin screens. J Telecommun Inf Tech. 2001;3:72–79.
  • Zinenko TL. Scattering and absorption of terahertz waves by a free-standing infinite grating of graphene strips: analytical regularization analysis. J Opt. 2015;17:1–8.
  • Sologub VG. Diffraction of a plane wave by an infinite strip grating in the short-wavelength case. USSR J Comput Maths Mathem Phys. 1972;12:159–176.10.1016/0041-5553(72)90121-8
  • Shestopalov VP, Lytvynenko LM, Masalov SA, et al. Waves diffraction by the gratings. Kharkov: Kharkov State University; 1973. Russian.
  • Luneburg E, Westfahl K. Diffraction of plane waves by an infinite strip grating. Ann Phys. 1971;482:257–288.10.1002/(ISSN)1521-3889
  • Baldwin GL, Heins AE. On the diffraction of a plane wave by an infinite plane grating. Math Scand. 1954;2:103–118.
  • Twelsky V. Multiple scattering of radiation by an arbitrary configuration of parallel cylinders. J Acoust Soc Am. 1952;24:42–46.10.1121/1.1906845
  • Twelsky V. On a multiple scattering theory of the finite grating and the wood anomalies. J Appl Phys. 1952;23:1099–1118.10.1063/1.1701993
  • Tsalamengas J. Exponentially converging Nystrom’s methods for systems of SIEs with applications to open/closed strip or slot-loaded 2-D structures. IEEE Trans Antennas Propag. 2006;54:1549–1558.10.1109/TAP.2006.874348
  • Shapoval OV, Sauleau R, Nosich AI. Scattering and absorption of waves by flat material strips analyzed using generalized boundary conditions and Nystrom-type algorithm. IEEE Trans Antennas Propag. 2011;59:3339–3346.10.1109/TAP.2011.2161547
  • Nosich AA, Gandel YV. Numerical analysis of quasioptical multireflector antennas in 2-D with the method of discrete singularities: E-wave case. IEEE Trans Antennas Propag. 2007;55:399–406.10.1109/TAP.2006.889811
  • Kaliberda ME, Pogarsky SA, Lytvynenko LM. Analysis of the E-polarized electromagnetic wave diffraction by an infinite periodical strip grating without one strip. IEEE International Conference on Mathematical Methods in Electromagnetic Theory (MMET); 2016 Jul 5–7; Lviv. p. 248–251.
  • Gandel YV. Method of discrete singularities in electromagnetic problems. Prob Cybernetics. 1986;124:166–183. Russian.
  • Lifanov IK. Singular integral equations and discrete vortices. Utrecht: VSP; 1996.
  • Gandel YuV. Boundary-value problems for the Helmholtz equation and their discrete mathematical models. J Math Sci. 2010;171:74–88.
  • Gandel YV, Bulygin VS. Boundary integral equations of the problem of diffraction by planar screens and their discrete mathematical models. Electromagn Waves Electron Syst. 2010;15:9–21. Russian.
  • Titchmarsh EC. Introduction to the theory of Fourier integrals. Oxford: Oxford University Press Inc.; 1948.
  • Guillemin EA. Communication network. Vol. 1. London: Wiley; 1935.
  • Felsen LB, Marcuvits N. Radiation and scattering of waves. Englewood Cliffs: Prentice-Hall Inc.; 1973.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.