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**Asymptotic analysis of transverse magnetic multiple scattering by the diffraction grating of penetrable cylinders at oblique incidence.**
*(English)*
Zbl 1243.78026

The paper presents a rigorous derivation of the asymptotic equations associated with the multiple scattering coefficients of an infinite grating of dielectric circular cylinders for obliquely incident vertically polarized plane electromagnetic waves. The asymptotic behavior is studied when the wavelength of the incident radiation is much larger than the distance between the cylinders. These results are the generalizations of those in the case of non-oblique incidence [V. Twersky, “On scattering of waves by the infinite grating of circular cylinders”, IRE Trans. Antennas and Propag. 10, No. 6, 737–765 (1962; doi:10.1109/TAP.1962.1137940)].

Reviewer: Dmitry Shepelsky (Kharkov)

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\textit{Ö. Kavaklıoğlu} and \textit{R. H. Lang}, J. Appl. Math. 2011, Article ID 715087, 30 p. (2011; Zbl 1243.78026)

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### References:

[1] | Ö. Kavaklıo\uglu, “Scattering of a plane wave by an infinite grating of circular dielectric cylinders at oblique incidence: E-polarization,” International Journal of Electronics, vol. 87, no. 3, pp. 315-336, 2000. |

[2] | Ö. Kavaklıo\uglu, “On diffraction of waves by the infinite grating of circular dielectric cylinders at oblique incidence: floquet representation,” Journal of Modern Optics, vol. 48, no. 1, pp. 125-142, 2001. |

[3] | Ö. Kavaklıo\uglu, “On Schlömilch series representation for the transverse electric multiple scattering by an infinite grating of insulating dielectric circular cylinders at oblique incidence,” Journal of Physics. A. Mathematical and General, vol. 35, no. 9, pp. 2229-2248, 2002. · Zbl 1002.78002 |

[4] | Ö. Kavaklıo\uglu and B. Schneider, “On multiple scattering of radiation by an infinite grating of dielectric circular cylinders at oblique incidence,” International Journal of Infrared and Millimeter Waves, vol. 29, no. 4, pp. 329-352, 2008. |

[5] | Ö. Kavaklıo\uglu and B. Schneider, “On Floquet-Twersky representation for the diffraction of obliquely incident plane H-polarized electromagnetic waves by an infinite grating of insulating dielectric circular cylinders,” Applied Mathematics and Computation, vol. 201, no. 1-2, pp. 1-15, 2008. · Zbl 1144.78311 |

[6] | Ö. Kavaklıo\uglu and B. Schneider, “On the asymptotic solution for the Fourier-Bessel multiple scattering coefficients of an infinite grating of insulating dielectric circular cylinders at oblique incidence,” Applied Mathematics and Computation, vol. 201, no. 1-2, pp. 351-360, 2008. · Zbl 1144.78312 |

[7] | R. H. Lang and Ö. Kavaklıo\uglu, “Mutual coupling effects in needle arrays,” in Proceedings of the URSI Radio Science Meeting and IEEE Antennas and Propagation Society International Symposium, vol. 148, Hyatt Regency, Chicago, Ill, USA, 1992. |

[8] | S. C. Lee, “Dependent scattering of an obliquely incident plane wave by a collection of parallel cylinders,” Journal of Applied Physics, vol. 68, no. 10, pp. 4952-4957, 1990. |

[9] | S. C. Lee, “Scattering by closely-spaced radially-stratified parallel cylinders,” Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 48, no. 2, pp. 119-130, 1992. |

[10] | S. C. Lee, “Scattering of polarized radiation by an arbitrary collection of closely spaced parallel nonhomogeneous tilted cylinders,” Journal of the Optical Society of America A, vol. 13, no. 11, pp. 2256-2265, 1996. |

[11] | S. C. Lee and J. A. Grzesik, “Light scattering by closely spaced parallel cylinders embedded in a semi-infinite dielectric medium,” Journal of the Optical Society of America A, vol. 15, no. 1, pp. 163-173, 1998. |

[12] | S. C. Lee, “Light scattering by closely spaced parallel cylinders embedded in a finite dielectric slab,” Journal of the Optical Society of America A, vol. 16, no. 6, pp. 1350-1361, 1999. |

[13] | S. C. Lee, “Optical extinction by closely spaced parallel cylinders inside a finite dielectric slab,” Journal of the Optical Society of America A, vol. 23, no. 9, pp. 2219-2232, 2006. |

[14] | C. M. Linton, “Schlömilch series that arise in diffraction theory and their efficient computation,” Journal of Physics. A. Mathematical and General, vol. 39, no. 13, pp. 3325-3339, 2006. · Zbl 1099.78004 |

[15] | C. M. Linton and I. Thompson, “Resonant effects in scattering by periodic arrays,” Wave Motion, vol. 44, no. 3, pp. 165-175, 2007. · Zbl 1231.76275 |

[16] | I. Thompson and C. M. Linton, “Euler-maclaurin summation and Schlömilch series,” The Quarterly Journal of Mechanics and Applied Mathematics, vol. 63, no. 1, pp. 39-56, 2010. · Zbl 1200.40001 |

[17] | C. M. Linton, “Lattice sums for the Helmholtz equation,” SIAM Review, vol. 52, no. 4, pp. 630-674, 2010. · Zbl 1208.78016 |

[18] | R. F. Millar, “The scattering of a plane wave by a row of small cylinders,” Canadian Journal of Physics, vol. 38, pp. 272-289, 1960. · Zbl 0098.17802 |

[19] | R. F. Millar, “Plane wave spectra in grating theory. II. Scattering by an infinite grating of identical cylinders,” Canadian Journal of Physics, vol. 41, pp. 2135-2154, 1963. |

[20] | L Rayleigh, “On the electromagnetic theory of light,” Philosophical Magazine, vol. 12, no. 73, pp. 81-101, 1881. |

[21] | L Rayleigh, “Note on the remarkable case of diffraction spectra described by Prof. Wood,” Philosophical Magazine, vol. 14, no. 79, pp. 60-65, 1907. |

[22] | L Rayleigh, “On the dynamical theory of gratings,” Proceedings of the Royal Society A, vol. 79, no. 532, pp. 399-416, 1907. · JFM 38.0842.03 |

[23] | L Rayleigh, “The dispersal of light by a dielectric cylinder,” Philosophical Magazine, vol. 36, no. 215, pp. 365-376, 1918. |

[24] | A. N. Sivov, “Electrodynamic theory of a dense plane grating of parallel conductors,” Radiotekhnika i Elektronika, vol. 6, p. 483, 1961. |

[25] | A. N. Sivov, “Electrodynamic theory of a dense plane grating of parallel conductors,” Radio Engineering and Electronic Physics, vol. 6, no. 4, pp. 429-440, 1961. |

[26] | G. H. Smith, L. C. Botten, R. C. McPhedran, and N. A. Nicorovici, “Cylinder gratings in conical incidence with applications to modes of air-cored photonic crystal fibers,” Physical Review E, vol. 66, no. 5, Article ID 056604, pp. 1-16, 2002. |

[27] | G. H. Smith, L. C. Botten, R. C. McPhedran, and N. A. Nicorovici, “Cylinder gratings in conical incidence with applications to woodpile structures,” Physical Review E, vol. 67, no. 5, Article ID 056620, pp. 1-10, 2003. |

[28] | V. Twersky, “Multiple scattering of radiation by an arbitrary configuration of parallel cylinders,” Journal of the Acoustical Society of America, vol. 24, pp. 42-46, 1952. · Zbl 0046.41604 |

[29] | V. Twersky, “Multiple scattering of radiation by an arbitrary planar configuration of parallel cylinders and by two parallel cylinders,” Journal of Applied Physics, vol. 23, pp. 407-414, 1952. · Zbl 0046.41604 |

[30] | V. Twersky, “On a multiple scattering theory of the finite grating and the Wood anomalies,” Journal of Applied Physics, vol. 23, pp. 1099-1118, 1952. · Zbl 0047.44204 |

[31] | V. Twersky, “On the scattering of waves by an infinite grating,” IRE Transactions on Antennas and Propagation, vol. AP-4, pp. 330-345, 1956. |

[32] | V. Twersky, “Elementary function representations of Schlömilch series,” Archive for Rational Mechanics and Analysis, vol. 8, pp. 323-332, 1961. · Zbl 0107.05804 |

[33] | V. Twersky, “On scattering of waves by the infinite grating of circular cylinders,” IRE Transactions on Antennas and Propagation, vol. AP-10, pp. 737-765, 1962. |

[34] | J. R. Wait, “Reflection from a wire grid parallel to a conducting plane,” Canadian Journal of Physics, vol. 32, pp. 571-579, 1954. · Zbl 0057.42704 |

[35] | J. R. Wait, “Scattering of a plane wave from a circular dielectric cylinder at oblique incidence,” Canadian Journal of Physics, vol. 33, pp. 189-195, 1955. · Zbl 0068.21204 |

[36] | J. R. Wait, “Reflection at arbitrary incidence from a parallel wire grid,” Applied Scientific Research B, vol. 4, no. 6, pp. 393-400, 1955. · Zbl 0068.21302 |

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