Vol. 95

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2019-09-05

Shielding of a Perfectly Conducting Circular Disk: Exact and Static Analytical Solution

By Giampiero Lovat, Paolo Burghignoli, Rodolfo Araneo, Salvatore Celozzi, Amedeo Andreotti, Dario Assante, and Luigi Verolino
Progress In Electromagnetics Research C, Vol. 95, 167-182, 2019
doi:10.2528/PIERC19052908

Abstract

The problem of the shielding evaluation of an infinitesimally thin perfectly conducting circular disk against a vertical magnetic dipole is here addressed. The problem is reduced to a set of dual integral equations and solved in an exact form through the application of the Galerkin method in the Hankel transform domain. It is shown that a second-kind Fredholm infinite matrix-operator equation can be obtained by selecting a complete set of orthogonal eigenfunctions of the static part of the integral operator as expansion basis. A static solution is finally extracted in a closed form which is shown to be accurate up to remarkably high frequencies.

Citation


Giampiero Lovat, Paolo Burghignoli, Rodolfo Araneo, Salvatore Celozzi, Amedeo Andreotti, Dario Assante, and Luigi Verolino, "Shielding of a Perfectly Conducting Circular Disk: Exact and Static Analytical Solution," Progress In Electromagnetics Research C, Vol. 95, 167-182, 2019.
doi:10.2528/PIERC19052908
http://jpier.org/PIERC/pier.php?paper=19052908

References


    1. Bethe, H. A., "Theory of diffraction by small holes," Phys. Rev., Vol. 66, No. 7–8, 163, 1944.
    doi:10.1103/PhysRev.66.163

    2. Bouwkamp, C., "On the diffraction of electromagnetic waves by small circular disks and holes," Philips Research Reports, Vol. 5, 401-422, 1950.

    3. Eggimann, W., "Higher-order evaluation of dipole moments of a small circular disk," IRE Trans. Microw. Theory Techn., Vol. 8, No. 5, 573-573, 1960.
    doi:10.1109/TMTT.1960.1124796

    4. Eggimann, W. H., "Higher-order evaluation of electromagnetic diffraction by circular disks," IRE Trans. Microw. Theory Techn., Vol. 9, No. 5, 408-418, 1961.
    doi:10.1109/TMTT.1961.1125362

    5. Williams, W., "Electromagnetic diffraction by a circular disk," Proc. Cambridge Phil. Soc., Vol. 58, No. 4, 625-630, Cambridge University Press, 1962.
    doi:10.1017/S0305004100040664

    6. Jones, D., "Diffraction at high frequencies by a circular disc," Proc. Cambridge Phil. Soc., Vol. 61, No. 1, 223-245, Cambridge University Press, 1965.
    doi:10.1017/S0305004100038810

    7. Marsland, D., C. Balanis, and S. Brumley, "Higher order diffractions from a circular disk," IEEE Trans. Antennas Propag., Vol. 35, No. 12, 1436-1444, 1987.
    doi:10.1109/TAP.1987.1144034

    8. Duan, D.-W., Y. Rahmat-Samii, and J. Mahon, "Scattering from a circular disk: A comparative study of PTD and GTD techniques," Proc. IEEE, Vol. 79, No. 10, 1472-1480, 1991.
    doi:10.1109/5.104222

    9. Nosich, A. I., "The method of analytical regularization in wave-scattering and eigenvalue problems: Foundations and review of solutions," IEEE Antennas Propag. Mag., Vol. 41, No. 3, 34-49, 1999.
    doi:10.1109/74.775246

    10. Bliznyuk, N. Y., A. I. Nosich, and A. N. Khizhnyak, "Accurate computation of a circular-disk printed antenna axisymmetrically excited by an electric dipole," Microw. Opt. Techn. Lett., Vol. 25, No. 3, 211-216, 2000.
    doi:10.1002/(SICI)1098-2760(20000505)25:3<211::AID-MOP15>3.0.CO;2-D

    11. Hongo, K. and Q. A. Naqvi, "Diffraction of electromagnetic wave by disk and circular hole in a perfectly conducting plane," Progress In Electromagnetics Research, Vol. 68, 113-150, 2007.
    doi:10.2528/PIER06073102

    12. Balaban, M. V., R. Sauleau, T. M. Benson, and A. I. Nosich, "Dual integral equations technique in electromagnetic wave scattering by a thin disk," Progress In Electromagnetics Research, Vol. 16, 107-126, 2009.
    doi:10.2528/PIERB09050701

    13. Hongo, K., A. D. U. Jafri, and Q. A. Naqvi, "Scattering of electromagnetic spherical wave by a perfectly conducting disk," Progress In Electromagnetics Research, Vol. 129, 315-343, 2012.
    doi:10.2528/PIER11102805

    14. Di Murro, F., M. Lucido, G. Panariello, and F. Schettino, "Guaranteed-convergence method of analysis of the scattering by an arbitrarily oriented zero-thickness PEC disk buried in a lossy half-space," IEEE Trans. Antennas Propag., Vol. 63, No. 8, 3610-3620, 2015.
    doi:10.1109/TAP.2015.2438336

    15. Nosich, A. I., "Method of analytical regularization in computational photonics," Radio Sci., Vol. 51, No. 8, 1421-1430, 2016.
    doi:10.1002/2016RS006044

    16. Lucido, M., G. Panariello, and F. Schettino, "Scattering by a zero-thickness PEC disk: A new analytically regularizing procedure based on Helmholtz decomposition and Galerkin method," Radio Sci., Vol. 52, No. 1, 2-14, 2017.
    doi:10.1002/2016RS006140

    17. Chew, W. C., Waves and Fields in Inhomogenous Media, IEEE Press, Piscataway, NJ, 1999.
    doi:10.1109/9780470547052

    18. Tango, W. J., "The circle polynomials of Zernike and their application in optics," Appl. Phys., Vol. 13, No. 4, 327-332, 1977.
    doi:10.1007/BF00882606

    19. Rdzanek, W., "Sound scattering and transmission through a circular cylindrical aperture revisited using the radial polynomials," J. Acoust. Soc. Am., Vol. 143, No. 3, 1259-1282, 2018.
    doi:10.1121/1.5025159

    20. Gradshteyn, I. S. and I. M. Ryzhik, Table of Integrals, Series, and Product, 7th Ed., Academic Press, Burlington, MA, 2014.

    21. Jackson, J. D., "Classical Electrodynamics," Wiley, 1999.

    22. Eason, G., B. Noble, and I. N. Sneddon, "On certain integrals of Lipschitz-Hankel type involving products of Bessel functions," Phil. Trans. R. Soc. Lond. A, Vol. 247, No. 935, 529-551, 1955.
    doi:10.1098/rsta.1955.0005

    23. Reed, M. and B. Simon, Method of Modern Mathematical Physics, Vol. 1: Functional Analysis, Academic Press Inc., San Diego, 1980.