The scattering of electromagnetic spherical wave by a perfectly conducting circular disk is studied by using the method of Kobayashi Potential (abbreviated as KP method). The formulation of the problem yields the dual integral equations (DIE). The spherical wave is produced by an arbitrarily oriented dipole. The unknowns are the induced surface current (or magnetic field) and the tangential components of the electric field on the disk. The solution for the surface current is expanded in terms of a set of functions which satisfy one of a pair (equations for the magnetic field) of Maxwell equations and the required edge condition on the surface of the disk. At this stage we have used the vector Hankel transform. Applying the projection solves the rest of the pair of equations. Thus the problem reduces to the matrix equations for the expansion coefficients. The matrix elements are given in terms of the infinite integrals with a single variable and these may be transformed into infinite series that are convenient for numerical computation. The far field patterns of the scattered wave are computed and compared with those computed based on the physical optics approximation. The agreement between them is fairly good.
1. Silver, S., Microwave Antenna Theory and Design, McGraw-Hill Book Co., 1949.
2. Balanis, C. A., Antenna Theory Analysis and Design, John Wiley & Sons, 1982.
3. Miller, R. F., "An approximate theory of the diffraction of an electromagnetic wave by an aperture in a plane screen," Proc. of the IEE, Vol. 103C, 177-185, 1956.
4. Miller, R. F., "The diffraction of an electromagnetic wave by a circular aperture," Proc. of the IEE, Vol. 104C, 87-95, 1957.
5. Ya Ufimtesev, P., "Method of edge waves in the physical theory of diffraction," Foreign Technology Division, Wright-Patterson, AFB, Ohio, 1962.
6. Mitzner, K. M., Incremental Length Diffractions, Aircraft Division Northrop Corp., Technical Report AFA1-TR-73-296, 1974.
7. Michaeli, A., "Equivalent edge currents for arbitrary aspects of observation," IEEE Trans. on Antennas and Propagat., Vol. 32, 252-258, 1984. doi:10.1109/TAP.1984.1143303
8. Shore, R. A. and A. D. Yaghjian, "Comparison of high frequency scattering determined from PO fields enhanced with alternative ILDCs," IEEE Trans. on Antennas and Propagat., Vol. 52, 336-341, 2004. doi:10.1109/TAP.2003.822452
9. 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
10. Keller, J. B., "Diffraction by an aperture," J. of Appl. Phys., Vol. 28, 426-444, Apr. 1957. doi:10.1063/1.1722767
11. Kouyoumjian, R. G. and P. H. Pathak, "A uniform geormterical theory of diffraction of an edge in a perfectly conducting surface," Proc. of the IEEE, Vol. 62, 1448-1461, Nov. 1974.
12. McNamara, D. A., C. W. I. Pictorius, and J. A. G. Malherbe, Introduction to the Uniform Geometrical Theory of Diffraction, Artech House, Boston, 1990.
13. Ross, R. A., "Radar cross section of rectangular flat plates as a function of aspect angles," IEEE Trans. on Antennas and Propagat., Vol. 14, No. 3, 329-335, May 1966. doi:10.1109/TAP.1966.1138696
14. Clemmow, P. C., "Edge currents in diffraction theory," Transaction of Inst. Radio Engrs., Vol. 4, 282-287, 1956.
15. Ryan, C. E. and L. Peter, "Evaluation of edge diffracted fields including equivalent currents for the caustic regions," IEEE Trans. on Antennas and Propagat., Vol. 17, 292-299, 1969. doi:10.1109/TAP.1969.1139445
16. Harrington, R. F., Field Computation by Moment Methods, Krieger Pub. Co., Florida, 1968.
17. Kim, T. J. and G. A. Thiele, "A hybrid diffraction technique - General theory and applications," IEEE Trans. Antennas and Propagat., Vol. AP-30, 888-897, Sept. 1982. doi:10.1109/TAP.1982.1142918
18. Murthy, P. K., K. C. Hill, and G. A. Thiele, "A hybrid-iterative method for solving scattering problems," IEEE Trans. Antennas Propagat., Vol. AP-34, No. 10, 1173-1180, 1986. doi:10.1109/TAP.1986.1143738
19. 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
21. Bouwkamp, C. J., "On the diffraction of electromagnetic wave by circular disks and holes," Philips Res. Rep., Vol. 5, 401-522, 1950.
22. Meixner, J. and W. Andrejewski, "Strenge theorie der beugung ebener elektromagnetischen wellen an der vollkommen leitende kreissheibe und an der kreisformigne Offnung im vollkommen leitenden ebenen schirm," Ann. Physik, Vol. 7, 157-158, 1950. doi:10.1002/andp.19504420305
23. Andrejewski, W., "Die beugung elektromagnetischen wellen an der leitende kreissheibe und an der lreisformigne Offnung im leitenden ebenen schirm," Z. Angew. Phys., Vol. 5, 178-186, 1950.
24. Flammer, C., "The vector wave function solution of the diffraction of electromagnetic waves by circular discs and Apertures-II, the diffraction problems," J. of Appl. Phys., Vol. 24, 1224-1231, 1953. doi:10.1063/1.1721475
25. Bjrkberg, J. and G. Kristensson, "Electromagnetic scattering by a perfectly conducting elliptic disk," Can. J. of Phys., Vol. 65, 723-734, 1987. doi:10.1139/p87-106
26. Kristensson, G., "The current distribution on a circular disc," Can. J. of Phys., Vol. 63, 507-516, 1985. doi:10.1139/p85-080
27. 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
28. Kristensson, G., "Natural frequencies of circular disks," IEEE Trans. on Antennas and Propagat., Vol. 32, No. 5, May 1984. doi:10.1109/TAP.1984.1143356
29. Balaban, M. V., R. Sauleau, T. M. Benson, and A. I. Nosich, "Dual itegral equations technique in electromagnetic wave scattering by a thin disk," Progress In Electromagnetic Research B, Vol. 16, 107-126, 2009. doi:10.2528/PIERB09050701
30. Kobayashi, I., "Darstellung eines potentials in zylindrical koordinaten, das sich auf einer ebene unterwirft,", Science Reports of the Thohoku Imperifal Unversity, Ser. I, Vol. XX, No. 2, 1931.
31. Sneddon, I. N., Mixed Boundary Value Problems in Potential Theory, North-Hollnd Pub. Co., 1966.
32. Nomura, Y. and S. Katsura, "Diffraction of electric wave by circular plate and circular hole," Sci. Rep., Inst., Electr. Comm., Vol. 10, 1-26, Tohoku University, 1958.
33. Hongo, K. and H. Serizawa, "Diffraction of electromagnetic plane wave by a rectangular plate and a rectangular hole in the conducting plate," IEEE Trans. on Antennas and Propagat., Vol. 47, No. 6, 1029-10041, Jun. 1999. doi:10.1109/8.777128
34. 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
35. Inawashiro, S., "Diffraction of electromagnetic waves from an electric dipole by a conducting circular disk," J. Phys. Soc., Vol. 18, 273-287, Japan, 1963. doi:10.1143/JPSJ.18.273
36. Bowman, J. J., T. B. A. Senior, and P. L. E. Uslenghi, Electromagnetic and Acoustic Scattering from Simple Shapes, Amsterdam, North-Holland, 1969.
37. Chew, W. C. and J. A. Kong, "Resonance of non-axial symmetric modes in circular microstrip disk antenna," J. Math. Phys., Vol. 21, No. 3, 2590-2598, 1980. doi:10.1063/1.524366
38. Watson, G. N., A Treatise on the Theory of Bessel Functions, Cambridge at the University Press, 1944.
39. Magunus, W., F. Oberhettinger, and R. P. Soni, Formulas and Theorems for the Spherical Functions of Mathematical Physics, Springer Verlag, 1966.
40. Gradshteyn, I. S. and I. W. Ryzhik, Table of Integrals, Series and Products, Academic Press Inc., 1965.
41. Hongo, K. and G. Ishii, "Diffraction of electromagnetic plane wave by a slit," IEEE Trans. on Antennas and Propagat., Vol. 26, 494-499, 1978. doi:10.1109/TAP.1978.1141870
42. Felsen, L. B. and N. Marcuvitz, Radiation and Scattering of Waves, Prentice Hall International Inc., 1972.
43. Van Bladel, J., Electromagnetic Fields, 2nd Edition, IEEE Press, Series on Electromagnetic Wave Theory, 2007. doi:10.1002/047012458X
44. Tai, C. T., Dyadic Greens Functions in Electromagnetic Theory, Intext Educational Publisher, 1971.
45. Illahi, A. and Q. A. Naqvi, "Scattering of an arbitrarily oriented dipole field by an infinite and finite length PEMC circular cylinder," Central European Journal of Physics, 829-853, 2009. doi:10.2478/s11534-008-0162-6