Progress In Electromagnetics Research
ISSN: 1070-4698, E-ISSN: 1559-8985
Home | Search | Notification | Authors | Submission | PIERS Home | EM Academy
Home > Vol. 167 > pp. 1-10


By G. Lovat, P. Burghignoli, R. Araneo, S. Celozzi, A. Andreotti, D. Assante, and L. Verolino

Full Article PDF (223 KB)

The problem of evaluating the shielding effectiveness of a thin metallic circular disk with finite conductivity against an axially symmetric vertical magnetic dipole is addressed. First, the thin metallic disk is modeled through an appropriate boundary condition, and then, as for the perfectly conducting counterpart, the problem is reduced to a set of dual integral equations which are solved in an exact form through the application of the Galerkin method in the Hankel transform domain. A second-kind Fredholm infinite matrix-operator equation is obtained by selecting a suitable set of basis functions. A low-frequency solution is finally extracted in a closed form. Through a comparison with results obtained from a full-wave commercial software, it is shown that such a simple approximate solution is accurate up to the frequency where the surface-impedance model of the thin disk is valid.

G. Lovat, P. Burghignoli, R. Araneo, S. Celozzi, A. Andreotti, D. Assante, and L. Verolino, "Shielding of an Imperfect Metallic Thin Circular Disk: Exact and Low-Frequency Analytical Solution," Progress In Electromagnetics Research, Vol. 167, 1-10, 2020.

1. Bethe, H. A., "Theory of diffraction by small holes," Physical Review, Vol. 66, No. 7–8, 163, 1944.

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

3. Flammer, C., "The vector wave function solution of the diffraction of electromagnetic waves by circular disks and apertures. I. Oblate spheroidal vector wave functions," J. Appl. Phys., Vol. 24, No. 9, 1218-1223, 1953.

4. Ehrlich, M. J., S. Silver, and G. Held, "Studies of the diffraction of electromagnetic waves by circular apertures and complementary obstacles: The near-zone field," J. Appl. Phys., Vol. 26, No. 3, 336-345, 1955.

5. Millar, R., "The diffraction of an electromagnetic wave by a circular aperture," Proc. IEE-Part C: Monographs, Vol. 104, No. 5, 87-95, 1957.

6. Eggimann, W., "Higher-order evaluation of electromagnetic diffraction by circular disks," IRE Trans. Microw. Theory Techn., Vol. 9, No. 5, 408-418, 1961.

7. Williams, W., "Electromagnetic diffraction by a circular disk," Proc. Cambridge Phil. Soc., Vol. 58, No. 4, 625-630, Cambridge University Press, 1962.

8. 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.

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

10. 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.

11. 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.

12. 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.

13. 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 B, Vol. 16, 107-126, 2009.

14. 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.

15. 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.

16. Nosich, A. I., "Method of analytical regularization in computational photonics," Radio Sci., Vol. 51, No. 8, 1421-1430, 2016.

17. 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.

18. Lovat, G., P. Burghignoli, R. Araneo, S. Celozzi, A. Andreotti, D. Assante, and L. Verolino, "Shielding of a perfectly conducting Circular Disk: Exact and Static analytical solution," Progress In Electromagnetics Research C, Vol. 95, 167-182, 2019.

19. Roberts, A., "Electromagnetic theory of diffraction by a circular aperture in a thick, perfectly conducting screen," J. Opt. Soc. Am. A, Vol. 4, No. 10, 1970-1983, 1987.

20. Lee, H. S. and H. J. Eom, "Electromagnetic scattering from a thick circular aperture," Microw. Opt. Techn. Lett., Vol. 36, No. 3, 228-231, 2003.

21. Balaban, M. V., O. V. Shapoval, and A. I. Nosich, "THz wave scattering by a graphene strip and a disk in the free space: Integral equation analysis and surface plasmon resonances," J. Opt., Vol. 15, No. 11, 114007, 2013.

22. Chew, W. C., Waves and Fields in Inhomogenous Media, IEEE Press, Piscataway, NJ, 1999.

23. Bleszynski, E., M. K. Bleszynski, and T. Jaroszewicz, "Surface-integral equations for electromagnetic scattering from impenetrable and penetrable sheets," IEEE Antennas Propag. Mag., Vol. 35, No. 6, 14-25, 1993.

24. Burghignoli, P., G. Lovat, R. Araneo, and S. Celozzi, "Time-domain shielding of a thin conductive sheet in the presence of vertical dipoles," IEEE Trans. Electromagn. Compat., Vol. 60, No. 1, 157-165, Jan. 2018.

25. Farina, M. and T. Rozzi, "Numerical investigation of the field and current behavior near lossy edges," IEEE Trans. Microw. Theory Tech., Vol. 49, No. 7, 1355-1358, 2001.

26. Bliznyuk, N. Y. and A. I. Nosich, "Numerical analysis of a dielectric disk antenna," Telecommunications and Radio Engineering, Vol. 61, 273-278, 2004.

27. Gradshteyn, I. S. and I. M. Ryzhik, Table of Integrals, Series, and Products, 7th Edition, Academic Press, Burlington, MA, 2014.

28. Rdzanek, W. P., "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.

29. Smith, D. R., Singular-Perturbation Theory: An Introduction with Applications, Cambridge University Press, 1985.

30. 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.

31. Celozzi, S., R. Araneo, and G. Lovat, Electromagnetic Shielding, Wiley-IEEE, Hoboken, 2008.

32. Moser, J. R., "Low-frequency low-impedance electromagnetic shielding," IEEE Trans. Electromagn. Compat., Vol. 30, No. 3, 202-210, 1988.

33. Jin, J.-M., The Finite Element Method in Electromagnetics, Wiley-IEEE Press, 2014.

34. Araneo, R., G. Lovat, S. Celozzi, and P. Burghignoli, "ELF shielding of finite-size finite-thickness screens against magnetic fields," 2018 IEEE International Conference on EEEIC/I&CPS Europe), 1-5, IEEE, 2018.

© Copyright 2014 EMW Publishing. All Rights Reserved