volume | PIER Journals

Abstract

The scattering of an arbitrary electromagnetic wave by a thin disk located in free space is formulated rigorously in terms of coupled dual integral equations (CDIEs) for the unknown images of the jumps and average values of the normal to the disk scattered-field components. Considered are three cases of the disk: (1) zero-thickness perfectly electrically conducting (PEC) disk, (2) thin electrically resistive (ER) disk and (3) dielectric disk. Disk thickness is assumed much smaller than the disk radius and the free space wavelength, in ER and dielectric disk cases, and also much smaller than the skin-layer depth, in the ER disk case. The set of CDIEs are "decoupled" by introduction of the coupling constants. Each set of DIEs are reduced to a Fredholm second kind integral equation by using the semi-inversion of DIE integral operators. The set of "coupling" equations for finding the coupling constants is obtained additionally from the edge behavior condition. Thus, each problem is reduced to a set of coupled Fredholm second kind integral equations. It is shown that each set can be reduced to a block-type three-diagonal matrix equation, which can be effectively solved numerically by iterative inversions of the two diagonal blocks and 2×2 matrix.

1. Chew, W. C. and J. A. Kong, "Resonance of axial symmetric modes in microstrip disk resonators," J. Math. Phys., Vol. 21, No. 3, 582, 1980.
doi:10.1063/1.524457 Google Scholar

2. Chew, W. C. and J. A. Kong, "Analysis of a circular microstrip disk antenna with a thick dielectric substrate," IEEE Trans. Antennas Propag., Vol. 29, 68-76, 2005. Google Scholar

3. Bliznyuk, N. Y. and A. I. Nosich, "Numerical analysis of a lossy circular microstrip antenna," Radio Physics and Electronics, Vol. 4, No. 3, 125-128, Kharkov IRE Press, 1999. Translated to English in Telecommunications and Radio Engineering, Vol. 55, No. 8, 15--23, Begell House Publ., 2001. Google Scholar

4. Ulaby, F. T., K. Sarabandi, K. McDonald, M. Whitt, and M. Craig, "Michigan microwave canopy scattering model," International Journal of Remote Sensing, Vol. 11, 1223-1253, 1990.
doi:10.1080/01431169008955090 Google Scholar

5. Frateschi, N. C. and A. F. J. Levi, "Resonant modes and laser spectrum of microdisk lasers," Appl. Phys. Lett., Vol. 66, No. 22, 2932-2934, 1995.
doi:10.1063/1.114233 Google Scholar

6. Liu, X., W. Fang, Y. Huang, X. H. Wu, S. T. Ho, H. Cao, and R. P. H. Chang, "Optically pumped ultraviolet microdisk laser on a silicon substrate," Appl. Phys. Lett., Vol. 84, No. 14, 2488-2490, 2004.
doi:10.1063/1.1695090 Google Scholar

7. Nosich, A. I., E. I. Smotrova, S. V. Boriskina, T. M. Benson, and P. Sewell, "Trends in microdisk laser research and linear optical modeling," Optical and Quantum Electronics, Vol. 39, No. 15, 1253-1272, 2007.
doi:10.1007/s11082-008-9203-z Google Scholar

8. Boriskin, A. V., A. Rolland, R. Sauleau, and A. I. Nosich, "Assessment of FDTD accuracy in the compact hemielliptic dielectric lens antenna analysis," IEEE Trans. Antennas Propag., Vol. 56, 758-764, 2008.
doi:10.1109/TAP.2008.916950 Google Scholar

9. Tranter, C. J., "A further note on dual integral equations and an application to the diffraction of electromagnetic waves," Quart J. Mech. and Appl. Math., Vol. 7, No. 3, 317-325, 1954.
doi:10.1093/qjmam/7.3.317 Google Scholar

10. Lugovoy, A. V. and V. G. Sologub, "Scattering of electromagnetic waves by a disk placed over lossy dielectric halfspace," URSI-B Symp. Electromagnetic Theory, 198-200, 1974.

11. Nosich, A. I., "The MAR in wave-scattering and eigenvalue problems: Foundations and review of solutions," IEEE Antennas Propagat. Magazine, Vol. 41, No. 3, 25-49, 1999. Google Scholar

12. Nosich, A. I., "Method of analytical regularization based on the static part inversion in wave scattering by imperfect thin screens," J. Telecommunications and Information Technology, No. 3, 72-79, NIT Press, Warsaw, 2001. Google Scholar

13. Panariello, G., F. Schettino, L. Verolino, R. Araneo, and S. Celozzi, "Analysis of microstrip antennas by means of regularization via Neumann series," Review of Radio Science, W. Ross Stone (ed.), 2002. Google Scholar

14. 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.
doi:10.2528/PIER06073102 Google Scholar

15. Bleszynski, E., M. Bleszynski, and T. Jaroszewicz, "Surface-integral equations for electrmagnetic scattering from impenetrable and penetrable sheets," IEEE Antennas Propagat. Magazine, Vol. 35, 14-24, 1993.
doi:10.1109/74.248480 Google Scholar

16. Braver, I., P. Fridberg, K. Garb, and I. Yakover, "The behavior of the electromagnetic field near the edge of a resistive half-plane," IEEE Trans. Antennas Propag., Vol. 36, 1760-1768, 1988.
doi:10.1109/8.14398 Google Scholar

17. Chew, W. C. and T. B. Habashy, "The use of vector transforms in solving some electromagnetic scattering problems," IEEE Trans. Antennas Propag., Vol. 56, No. 1, July 1986. Google Scholar

18. Ali, S. M., W. C. Chew, and J. A. Kong, "Vector Hankel transform analysis of annular-ring microstrip antenna," IEEE Trans. Antennas Propag., Vol. 30, No. 4, 637-644, July 1982.
doi:10.1109/TAP.1982.1142870 Google Scholar

19. Khizhnyak, A. N., "Diffraction of a plane wave by a thin disk," Sov. Physics Acoustics, Vol. 35, No. 5, 539-541, 1989. Google Scholar

20. Bliznyuk, N. Y., A. I. Nosich, and A. N. Khizhnyak, "Accurate computation of a circular-disk printed antenna axysimmetrically excited by an electric dipole," Microwave and Optical Technology Lett., Vol. 25, No. 3, 211-216, 2000.
doi:10.1002/(SICI)1098-2760(20000505)25:3<211::AID-MOP15>3.0.CO;2-D Google Scholar

21. Mandal, B. N. and N. Mandal, "Advances in dual integral equations," Research Notes in Mathematics, Chapman & Hall-CRC, New York, 1999. Google Scholar

22. Cooke, J. C., "A solution of Transfer's dual integral equations problem," Quart J. Mech. and Appl. Math., Vol. 9, No. 1, 103-110, 1956.
doi:10.1093/qjmam/9.1.103 Google Scholar

Mr. Mikhail V. Balaban

Dr. Ronan Sauleau

Professor Trevor Mark Benson

Professor Alexander I. Nosich