Method of singular integral equations in scattering by double-layer infinite strip grating with several strips removed in every layer

References

• Shestopalov VP, Lytvynenko LM, Masalov SA, et al. Waves diffraction by the gratings. Kharkov: Kharkov State University; 1973.
   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.
   Web of Science ®Google Scholar
• Munk BA. Frequency selective surfaces: theory and design. New York (NY): John Wiley; 2000.
   Google Scholar
• Lamb H. On the reflection and transmission of electric waves by a metallic grating. Proc London Math Soc. 1984;29:523–544.
   Google Scholar
• Miles JW. The diffraction of a plane wave through a grating. Q Appl Math. 1949;7(1):45–64.
   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
• 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.
   Web of Science ®Google Scholar
• Matsushima A, Nakamura Y, Tomino S. Application of integral equation method to metal-plate lens structures. Prog Electromagn Res. 2005;54:245–262.
   Web of Science ®Google Scholar
• Lytvynenko LM, Prosvirnin SL. Spectral scattering operators in wave diffraction by plane screens. Kyiv: Naukova Dumka; 1984; Russian.
   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
• 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.
   Web of Science ®Google Scholar
• Zinenko TL, Matsushima A, Nosich AI. Terahertz range resonances of metasurface based on double grating of microsize graphene strips inside dielectric slab. Proc R Soc A. 2020;476:20200173.
   Google Scholar
• 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.
   Google Scholar
• Luneburg E, Westfahl K. Diffraction of plane waves by an infinite strip grating. Ann Phys. 1971;27:257–288.
   Google Scholar
• Yevtushenko FO, Dukhopelnykov SV, Nosich AI. H-polarized plane-wave scattering by a PEC strip grating on top of a dielectric substrate: analytical regularization based on the Riemann-Hilbert problem solution. J Electromag Waves Appl. 2020;34:483–499.
   Web of Science ®Google Scholar
• Nosich AA, Gandel YV, Magath T, et al. Numerical analysis and synthesis of 2D quasi-optical reflectors and beam waveguides based on an integral-equation approach with Nystrom’s discretization. J Opt Soc Am A. 2007;25:2831–2836.
   Google Scholar
• Koshovy GI. Electromagnetic wave scattering by strip systems with a variable fractal dimension. Telecommun Radio Eng. 2008;67(15):1321–1331.
   Google Scholar
• YuV G. Boundary-value problems for the Helmholtz equation and their discrete mathematical models. J Math Sci. 2010;171:74–88.
   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.
   Web of Science ®Google Scholar
• 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.
   Web of Science ®Google Scholar
• Kaliberda ME, Lytvynenko LM, Pogarsky SA. Singular integral equations in diffraction problem by an infinite periodic strip grating with one strip removed: E-polarization case. J Electromagn Waves Appl. 2018;32:332–346.
   Web of Science ®Google Scholar
• Kaliberda ME, Lytvynenko LM, Pogarsky SA. Method of singular integral equations in diffraction by semi-infinite grating: H -polarization case. Turk J Elec Eng Comp Sci. 2017;25:4496–4509.
   Web of Science ®Google Scholar
• Kaliberda ME, Lytvynenko LM, Pogarsky SA. Method of singular integral equations in diffraction by semi-infinite grating: E -polarization case. Turk J Elec Eng Comp Sci. 2018;26:2406–2416.
   Web of Science ®Google Scholar
• Hall RC, Mittra R, Mitzner KM. Analysis of multilayered periodic structures using generalized scattering matrix theory. IEEE Trans Antennas Propagat. 1988;36:511–517.
   Web of Science ®Google Scholar
• Savin A, Grimberg R, Steigmann R. Scattering matrix analysis of cascaded periodic surfaces. In: Ciuprina G, Ioan D, editors. Scientific computing in electrical engineering. Vol. 11. Mathematics in industry. Berlin: Springer; 2007. p. 115–124.
   Google Scholar
• Lytvynenko LM, Prosvirnin SL. Wave reflection by a periodic layered metamaterial. Eur Phys J: Appl Phys. 2009;46:32608.
   Web of Science ®Google Scholar
• Lytvynenko LM, Prosvirnin SL. Wave diffraction by periodic multilayer structures. Cambridge: Cambridge Scientific Publishers; 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.
   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.
   Google Scholar
• Nishimoto M, Ikuno H. Numerical analysis of plane wave diffraction by a semi-infinite grating. Trans IEE Japan. 2001;121-A:905–910.
   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;44:1–14.
   Web of Science ®Google Scholar
• Kaliberda ME, Lytvynenko LM, Pogarsky SA. Electromagnetic interaction of two semi-infinite coplanar gratings of flat PEC strips with arbitrary gap between them. J Electromag Waves Appl. 2019;33(12):1557–1573.
   Web of Science ®Google Scholar
• Gandel YV. Method of discrete singularities in electromagnetic problems. Problm Cybernet. 1986;124:166–183. Russian.
   Google Scholar
• Titchmarsh EC. Introduction to the theory of Fourier integrals. Oxford: Oxford University Press Inc.; 1948.
   Google Scholar
• Guillemin EA. Communication network. Vol. 1. London: John Wiley and Sons Inc.; 1935.
   Google Scholar
• Lifanov IK. Singular integral equations and discrete vortices. Utrecht: VSP; 1996.
   Google Scholar