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.
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.
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.
5. Williams, W., "Electromagnetic diffraction by a circular disk," Proc. Cambridge Phil. Soc., Vol. 58, No. 4, 625-630, Cambridge University Press, 1962.
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.
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.
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.
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.
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.
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.
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.
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.
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.
15. Nosich, A. I., "Method of analytical regularization in computational photonics," Radio Sci., Vol. 51, No. 8, 1421-1430, 2016.
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.
17. Chew, W. C., Waves and Fields in Inhomogenous Media, IEEE Press, Piscataway, NJ, 1999.
18. Tango, W. J., "The circle polynomials of Zernike and their application in optics," Appl. Phys., Vol. 13, No. 4, 327-332, 1977.
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.
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.
23. Reed, M. and B. Simon, Method of Modern Mathematical Physics, Vol. 1: Functional Analysis, Academic Press Inc., San Diego, 1980.