Vol. 129
Latest Volume
All Volumes
PIER 179 [2024] PIER 178 [2023] PIER 177 [2023] PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2012-06-26
Scattering of Electromagnetic Spherical Wave by a Perfectly Conducting Disk
By
Progress In Electromagnetics Research, Vol. 129, 315-343, 2012
Abstract
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.
Citation
Kohei Hongo, Allah Ditta Ulfat Jafri, and Qaisar Naqvi, "Scattering of Electromagnetic Spherical Wave by a Perfectly Conducting Disk," Progress In Electromagnetics Research, Vol. 129, 315-343, 2012.
doi:10.2528/PIER11102805
References

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

20. Bouwkamp, C. J., "Diffraction theory," Rep. Progr. Phys., Vol. 17, 35-100, 1954.
doi:10.1088/0034-4885/17/1/302

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