Singular integral equations in diffraction problem by an infinite periodic strip grating with one strip removed

References

• Capolino F, editor. Theory and phenomena of metamaterials (metamaterials handbook). Boca Raton (FL): CRC Press; 2009.
   Google Scholar
• 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
   Google Scholar
• Barrelet CJ, Bao J, Loncar M, et al. Hybrid single-nanowire photonic crystal and microresonator structures. Nano Lett. 2006;6:11–15.10.1021/nl0522983
   PubMed Web of Science ®Google Scholar
• Baldwin GL, Heins AE. On the diffraction of a plane wave by an infinite plane grating. Math Scand. 1954;2:103–118.
   Google Scholar
• Sologub VG. Diffraction of a plane wave by an infinite strip grating in the short-wavelength case. USSR Comput Math Math Phys. 1972;12:159–176.10.1016/0041-5553(72)90121-8
   Google Scholar
• Shestopalov VP, Lytvynenko LM, Masalov SA, et al. Waves diffraction by the gratings. Kharkov: Kharkov State University; 1973. Russian.
   Google Scholar
• Twelsky V. On a multiple scattering theory of the finite grating and Wood’s anomalies. J Appl Phys. 1952;23:1099–1118.10.1063/1.1701993
   Web of Science ®Google Scholar
• 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
   Web of Science ®Google Scholar
• Butler CM, Wilton RD. General analysis of narrow strips and slots. IEEE Trans Antennas Propag. 1980;28:42–48.10.1109/TAP.1980.1142291
   Web of Science ®Google Scholar
• Vorob’ev SN, Litvinenko LN, Prosvirnin SL. Wave diffraction by a periodic structure consisting of inclined metal tapes. USSR Comput Math Math Phys 1986;26:159–166.10.1016/0041-5553(86)90129-1
   Web of Science ®Google Scholar
• 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.
   Google Scholar
• Lytvynenko LM, Prosvirnin SL. Spectral scattering operators in wave diffraction by plane screens. Kyiv: Naukova Dumka; 1984. Russian.
   Google Scholar
• 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.
   Web of Science ®Google Scholar
• 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
   Web of Science ®Google Scholar
• Matsushima A, Nakamura Y, Tomino S. Application of integral equation method to metal-plate lens structures. Prog Electromagnet Res. 2005;54:245–262.10.2528/PIER05011401
   Web of Science ®Google Scholar
• Shapoval OV, Gomez-Diaz JS, Perruisseau-Carrier J, et al. Integral equation analysis of plane wave scattering by coplanar graphene-strip gratings in the THz range. IEEE Trans Terahertz Sci Technol. 2013;3:666–674.10.1109/TTHZ.2013.2263805
   Web of Science ®Google Scholar
• Lovat G, Burghignol P, Capolino F, et al. High-gain omnidirectional radiation patterns from a metal strip grating leaky-wave antenna. In: IEEE Antennas Propagation Society International Symposium. Hawaii: Aloha; 2007. p. 9–15.
   Google Scholar
• Baccarelli P, Burghignoli P, Frezza F, et al. Modal properties of surface and leaky waves propagating at arbitrary angles along a metal strip grating on a grounded slab. IEEE Trans Antennas Propag. 2005;53:36–46.10.1109/TAP.2004.840529
   Web of Science ®Google Scholar
• Kaganovsky Y, Shavit R. Analysis of radiation from a line source in a grounded dielectric slab covered by a metal strip grating. IEEE Trans Antennas Propag. 2009;57:135–143.10.1109/TAP.2008.2009667
   Web of Science ®Google Scholar
• 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
   Google Scholar
• Capolino F, Albani M. Truncation effects in a semi-infinite periodic array of thin strips: a discrete Wiener-Hopf formulation. Radio Sci; 2009; 44.
   Google Scholar
• Lytvynenko LM, Prosvirnin SL. Wave diffraction by periodic multilayer structures. Cambridge: Cambridge Scientific; 2012.
   Google Scholar
• Lytvynenko LM, Kaliberda ME, Pogarsky SA. Wave Diffraction by semi-infinite venetian blind type grating. IEEE Trans Antennas Propag. 2013;61:6120–6127.10.1109/TAP.2013.2281510
   Web of Science ®Google Scholar
• Kaliberda ME, Lytvynenko LM, Pogarsky SA. Diffraction of H-polarized electromagnetic waves by a multi-element planar semi-infinite grating. Telecommun Radio Eng. 2015;74:348–357.
   Google Scholar
• Gandel YV. Method of discrete singularities in electromagnetic problems. Prob Cybern. 1986;124:166–183. Russian.
   Google Scholar
• Lifanov IK. Singular integral equations and discrete vortices. Utrecht: VSP; 1996.
   Google Scholar
• 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
   Web of Science ®Google Scholar
• Gandel YV. Boundary-value problems for the Helmholtz equation and their discrete mathematical models. J Math Sci. 2010;171:74–88.
   Google Scholar
• 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.
   Google Scholar
• Tong MS, Chew WC. Nystrom method with edge condition for electromagnetic scattering by 2-D open structures. Prog Electromagnet Res. 2006;62:49–68.10.2528/PIER06021901
   Web of Science ®Google Scholar
• Zygmund A. Trigonometric series I & II. Cambridge: Cambridge University Press; 1959.
   Google Scholar
• Luneburg E, Westfahl K. Diffraction of plane waves by an infinite strip grating. Ann Phys. 1971;27:257–288.10.1002/(ISSN)1521-3889
   Google Scholar
• Titchmarsh EC. Introduction to the theory of Fourier integrals. Oxford: Oxford University Press; 1948.
   Google Scholar
• Guillemin EA. Communication network. Vol. 1. London: Wiley; 1935.
   Google Scholar
• Abramowitz M, Stegun IA, editors. Handbook of mathematical functions with formulas, graphs, and mathematical tables. Washington (DC): National Bureau of Standards (USA); 1964.
   Google Scholar
• Felsen LB, Marcuvits N. Radiation and scattering of waves. Englewood Cliffs (NJ): Prentice-Hall; 1973.
   Google Scholar