volume | PIER Journals

Abstract

In this investigation, scattering from a circular disk with surface impedance has been studied rigorously. The method of analysis is Kobayashi Potential (KP). The mathematical formulation yields the dual integral equations (DIEs). These DIEs are solved by using the discontinuous properties of Weber-Schafheitlin's integral. After applying the boundary conditions and projection, the resulting expressions, finally, reduce to matrix equations for expansion coefficients. The matrix elements are in the form of infinite integrals with single variable. These are then used to compute the values of expansion coefficients. The far field patterns of the scattered wave are computed for different incident angles and surface impedances for both E- and H-polarizations. To verify the results, we have computed the solution based on the physical optics approximation. The agreement between them is fairly good.

1. Senior, T. B. A., "Impedance boundary conditions for imperfectly conducting surfaces," Appl. Sci. Res., Vol. 8(B),418-436, 1960. Google Scholar

2. Lindell, I. V. and A. H. Sihvola, "Realization of impedance boundary," IEEE Transactions on Antennas and Propagation, Vol. 54, No. 12, 3669-3676, Dec. Dec.2006.
doi:/ Google Scholar

3. Shchukin, A. N., Propagation of Radio Waves, Svyazizdat, Moscow, Russia,1940. Google Scholar

4. Leontovich, M. A., "Methods of solution for problems of electromagnetic waves propagation along the Earth surface," Bull.Acad. Sci. USSR, Phys. Ser., Vol. 8, No. 1, 1622, 1944(in Russian).. Google Scholar

5. Pelosi, G. and P. Y. Ufimtsev, "The impedance-boundary condition," IEEE Antennas Propag. Mag., Vol. 38, No. 1, 3135, Feb.1996.
doi:10.1109/74.491289 Google Scholar

6. Miller, R. F., "An approximate theory of the diffraction of an electromagnetic wave by an aperture in a plane screen," Proc. IEE,, Vol. 103C, 177-185, 1956. Google Scholar

7. Miller, R. F., "The diffraction of an electromagnetic wave by a circular aperture," Proc. IEE, Vol. 104C, 87-95, 1957. Google Scholar

8. Mitzner, K. M., "Incremental length diffractions,", Aircraft Division Northrop Corp., Tech. Rep. AFA1-TR-73-296,1974. Google Scholar

9. Shore, R. A. and A. D. Yaghjian, "Comparison of high frequency scattering determined from PO fields enhanced with alternative ILDCs," IEEE Transactions on Antennas and Propagation, Vol. 52, 336-341, 2004.
doi:10.1109/TAP.2003.822452 Google Scholar

10. Keller, J. B., "Geometrical theory of diffraction," J. Opt. Soc.Amer., Vol. 52, No. 2, 116-130, Feb.1962.
doi:10.1364/JOSA.52.000116 Google Scholar

11. McNamara, D. A., C. W. I. Pictorius, and J. A. G. Malherbe, Introduction to the Uniform Geometrical Theory of Diffraction, Artech House, Boston,1990.

12. Li, L. W., P. S. Kooi, Y. L. Qiu, T. S. Yeo, and M. S. Leong, "Analysis of electromagnetic scattering of conducting circular disk using a hybrid method," Progress In Electromagnetics Research, Vol. 20, 101-123, 1998.
doi:10.2528/PIER97111200 Google Scholar

13. Bouwkamp, C. J., "On the diffraction of electromagnetic wave by circular disks and holes," Philips Res. Rep., Vol. 5, 401-422, 1950. Google Scholar

14. Flammer, C., "The vector wave function solution of the diffraction of electromagnetic waves by circular discs and apertures-II, the diffraction problems," J. Appl. Phys., Vol. 24, 1224-1231, 1953.
doi:10.1063/1.1721475 Google Scholar

15. Bjrkberg, J. and G. Kristensson, "Electromagnetic scattering by a perfectly conducting elliptic disk," Can. J. Phys., Vol. 65, 723-734, 1987.
doi:10.1139/p87-106 Google Scholar

16. Kristensson, G., "The current distribution on a circular disc," Can. J. Phys., Vol. 63, 507-516, 1985.
doi:10.1139/p85-080 Google Scholar

17. Kristensson, G. and P. C. Waterman, "The T matrix for acoustic and electromagnetic scattering by circular disks," J. Acoust. Soc.Am., Vol. 72, No. 5, 1612-1625, Nov.1982..
doi:10.1121/1.388497 Google Scholar

18. Kristensson, G. and Natural frequencies of circular disks, IEEE Transactions on Antennas and Propagation, Vol. 32, No. 5, May1984.
doi:10.1109/ Google Scholar

19. 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 Electromagnetic Research B, Vol. 16, 107-126, 2009.
doi:10.2528/PIERB09050701 Google Scholar

20. Nomura, Y. and S. Katsura, "Diffraction of electric wave by circular plate and circular hole," Sci. Rep., Vol. 10, 1-26, Institute of Electrical Communication, Tohoku University,1958. Google Scholar

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

22. Inawashiro, S., "Diffraction of electromagnetic waves from an electric dipole by a conducting circular disk," J. Phys. Soc. Japan, Vol. 18, 273-287, 1963. Google Scholar

23. Bowman, J. J., T. B. A. Senior, and P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering from Simple Shapes, Amsterdam, North-Holland,1969.

24. Balanis, C. A., Antenna Theory Analysis and Design, John Wiley & Sons,1982.

25. Sebak., A. and L. Shafai, "Scattering from arbitrarily-shaped objects with impedance boundary conditions," IEE Proceedings H on Microwaves, Antennas and Propagation, Vol. 136, No. 5, Oct.1989. Google Scholar

26. Harrington, R. F., Field Computation by Moment Methods, Krieger Pub. Co., Florida,1968.

27. Kobayashi, I., "Darstellung eines potentials in zylindrical koordinaten, das sich auf einer ebene unterwirft,", Vol. Science Reports of the Thohoku Imperifal Unversity, Ser. I,XX, No. 2, 197-212, 1931. Google Scholar

28. Sneddon, I. N., Mixed Boundary Value Problems in Potential Theory, North-Hollnd Pub. Co.1966.

Dr. Allah Ditta Ulfat Jafri

Dr. Qaisar Abbas Naqvi

Professor Kohei Hongo