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Diffraction of Electromagnetic Wave by Disk and Circular Hole in a Perfectly Conducting Plane

By Kohei Hongo and Qaisar Naqvi
Progress In Electromagnetics Research, Vol. 68, 113-150, 2007


The scattering of electromagnetic plane wave by a perfectly conducting disk is formulated rigorously in a form of the dual integral equations (abbreviated as DIE). 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 Maxwell's equation for the magnetic field on the disk and the required edge condition. At this step we have used the method of the Kobayashi potential and the vector Hankel transform. Applying the pro jection solves the rest of a 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 numerical results are obtained for far field patterns, current densities induced on the disk, transmission coefficient through the circular aperture, and radar cross section. The results are compared with those obtained by other methods when they are available, and agreement among them is fairly well.


 (See works that cites this article)
Kohei Hongo and Qaisar Naqvi, "Diffraction of Electromagnetic Wave by Disk and Circular Hole in a Perfectly Conducting Plane," Progress In Electromagnetics Research, Vol. 68, 113-150, 2007.


    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. Ufimtsev, P. Ya, "Method of edge waves in the physical theory of diffraction," Foreign Technology Division, 1962.

    4. Mitzner, K. M., "Incremental length diffractions," Aircraft Division Northrop Corp., 1-296, 1974.

    5. Michaeli, A., "Equivalent edge currents for arbitrary aspects of observation," IEEE Trans. Antennas Propagat., Vol. AP-32, 252-258, 1984.

    6. Ando, M., "Radiation pattern analysis of reflector antennas," Electron. Commu. in Japan, Vol. 68, No. 4, 93-102, 1985.

    7. Shore, R. A. and A. D. Yaghjian, "Comparison of high-frequency scattering determined from PO fields enhanced with alternative ILDCs," IEEE Trans. Antennas Propagat., Vol. 52, 336-341, 2004.

    8. 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.

    9. Keller, J. B., "Geometrical theory of diffraction," J. Opt. Soc. Amer., Vol. 52, No. 2, 116-130, 1962.

    10. Keller, J. B., "Diffraction by an aperture," J. Appl. Phys., Vol. 28, No. 4, 426-444, 1957.

    11. Kouyoumjian, R. G. and P. H. Pathak, A uniform geometrical theory of diffraction of an edge in a perfectly conducting surface, Proc. IEEE, Vol. 62, No. 11, 1448-1461, 1974.

    12. Ahluwalia, D. S., R. M. Lewis, and J. Boersma, "Uniform asymptotic theory of diffraction by a plane screen," SIAM J. Appl. Math., Vol. 16, 783-807, 1968.

    13. Lee, S. W. and G. A. Deschamps, "A uniform asymptotic theory of electromagnetic diffraction by a curved wedge," IEEE Trans. Antennas Propagat., Vol. 24, No. 1, 25-34, 1976.

    14. 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.

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

    16. Clemmow, P. C., "Edge currents in diffraction theory," Transaction of Inst. Radio Engrs., Vol. AP-4, 282-287, 1956.

    17. Braunbeck, W., "On the diffraction field near a plane screen corner," IEEE Trans. Antennas Propagat., Vol. 4, 219-223, 1956.

    18. Ryan, C. E. and L. Peter, "Evaluation of edge diffracted fields including equivalent currents for the caustic regions," IEEE Trans. Antennas Propagat., Vol. 17, 292-299, 1969.

    19. James, G. L. and V. Kerdemalidis, "Reflector antenna radiation pattern analysis by equivalent edge currents," IEEE Trans. Antennas Propagat., Vol. 21, 19-24, 1973.

    20. Levine, H. and J. Schwinger, "On the theory of electromagnetic wave diffraction by a aperture in an infinite plane conducting screen," Comm. Pure and Appl. Math., Vol. 3, 355-391, 1950.

    21. Hung, C., R. D. Kodis, and H. Levine, "Diffraction by aperture," J. of Appl. Phys., Vol. 26, 151-165, 1953.

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

    23. 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.

    24. Bouwkamp, C. J., "Diffraction theory," Rep. Progr. Phys., Vol. 17, 35-100, 1954.

    25. Bouwkamp, C. J., "On the diffraction of electromagnetic wave by circular disks and holes," Philips Res. Rep., Vol. 5, 401-522, 1950.

    26. 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.

    27. Andrejewski, W., "Die Beugung elektromagnetischen Wellen an der leitende Kreissheibe und an der kreisformigne ̈Offnung im leitenden ebenen Schirm," Z. Angew. Phys., Vol. 5, 178-186, 1950.

    28. Watson, G. N., A Treatise on the Theory of Bessel Functions, Cambridge University Press, 1944.

    29. Nomura, Y. and S. Katsura, "Diffraction of electric wave by circular plate and circular hole," Sci. Rep., Vol. 10, 1-26, 1958.

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

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

    32. Chew, W. C. and J. A. Kong, "Resonance of nonaxial symmetric modes in circular microstrip disk anntena," J. Math. Phys., Vol. 21, No. 3, 2590-2598, 1980.

    33. Seshadri, S. R. and T. T. Wu, "High frequency diffraction of electromagnetic wave by a circular aperture in an infinite plane conducting screen," IRE Trans. Antennas Propagat., Vol. AP-8, 27-36, 1960.

    34. Jones, D. S., Diffraction of a high-frequency plane electromag- netic wave by a perfectly conducting circular disc, Proc. Cam- bridge Phil. Soc., Vol. 61, 247-270, 1965.

    35. Ruck, G. T., D. E. Barrick, W. D. Stuart, and C. K. Krichbaum, Radar Cross Section Handbook, Plenum Press, 1970.

    36. Abramowitz, M. and I. A. Stugun, Handbook of Mathematical Functions, Dover, 1970.