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Bistatic Scattering and Backscattering of Electromagnetic Waves by Conducting and Coated Dielectric Spheroids: A New Analysis Using Mathematica Package

L.-W. Li,

Dr. L.-W. Li

Department of Electrical and Computer Engineering

The National University of Singapore

Singapore

Homepage

T. S. Yeo,

Dr. T. S. Yeo

Department of Electrical Engineering

The National University of Singapore

Singapore

Homepage

M.-S. Leong

Dr. M.-S. Leong

Department of Electrical and Computer Engineering

The National University of Singapore

Singapore

Homepage

, Vol. 31, 225-245, 2001

doi:10.2528/PIER00071706 | Google Scholar

Abstract

Solutions to electromagnetic scattering at any angle of incidence by a perfectly conducting spheroid and a homogeneous dielectric spheroid coated with a dielectric layer are obtained by solving Maxwell's equations together with boundary conditions. The method used is that of expanding electric and magnetic fields in the spheroidal coordinates in terms of the spheroidal vector wave functions and matching their respective boundary conditions at spheroidal interfaces. In this formulation, the column vector of the series expansion coefficients of the scattered field is obtained from that of the incident field by means of a matrix transformation, which is in turn obtained from a system of equations derived from boundary conditions. The matrix depends only on the scatterer's properties; hence the scattered field at a different direction of incidence is obtained without repeatedly solving a new set of simultaneous equations. Different from the previous work, the present work developed an accurate and efficient Mathematica source code for more accurate solution to the problem. Normalized bistatic and backscattering cross sections are obtained for conducting (for verification purpose), homogeneous dielectric (for verification purpose), and coated dielectric prolate (for some new results) spheroids, with real and complex permittivities. Numerically exact results for the coated dielectric prolate spheroids are newly obtained and are not found in existing literature.

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L.-W. Li, T. S. Yeo, and M.-S. Leong, "Bistatic Scattering and Backscattering of Electromagnetic Waves by Conducting and Coated Dielectric Spheroids: A New Analysis Using Mathematica Package," , Vol. 31, 225-245, 2001.
doi:10.2528/PIER00071706

References

1. Stratton, J. A., Electromagnetic Theory, McGraw-Will, New York, 1941.

2. Van de Hulst, H. C., Light Scattering by Small Particles, John Wiley & Sons, New York, 1957.
doi:10.1063/1.3060205

3. Rheinstein, J., "Scattering of electromagnetic waves from dielectric coated conducting spheres," IEEE Trans. Antennas Propagat., Vol. 12, No. 3, 334-340, March 1964.
doi:10.1109/TAP.1964.1138223 Google Scholar

4. Adey, A. W., "Scattering of electromagnetic waves by long cylinder," Electron. Radio Eng., Vol. 35, 149-158, 1958. Google Scholar

5. Uslenghi, P. L. E., "High frequency scattering from a coated cylinder," Canadian Journal of Physics, Vol. 42, 2121-2128, 1964.
doi:10.1139/p64-195 Google Scholar

6. Siegel, K. M., F. V. Schultz, B. H. Gere, and F. B. Sleator, "The theory and numerical determination of the radar cross section of a prolate spheroid," IRE Trans. Antennas Propagat., Vol. 4, 266-275, 1956.
doi:10.1109/TAP.1956.1144425 Google Scholar

7. Sinha, B. P. and R. H. MacPhie, "Electromagnetic scattering from prolate spheroids for axial incidence," IEEE Trans. Antennas Propagat., Vol. 23, No. 5, 676-679, May 1975.
doi:10.1109/TAP.1975.1141161 Google Scholar

8. Sinha, B. P. and R. H. MacPhie, "Electromagnetic scattering by prolate spheroids for plane waves with arbitrary polarization and angle of incidence," Radio Sci., Vol. 12, 171-184, 1977.
doi:10.1029/RS012i002p00171 Google Scholar

9. Flammer, C., Spheroidal Wave Functions, Stanford Univ. Press, California, 1957.

10. Asano, S. and G. Yamamoto, "Light scattering by a spheroidal particle," Appl. Opt., Vol. 14, 29-49, 1975.
doi:10.1364/AO.14.000029 Google Scholar

11. Cooray, M. F. R. and I. R. Ciric, "Scattering of electromagnetic waves by a coated dielectric spheroid," J. Electromagn. Waves Applic., Vol. 6, 1491-1507, 1992.
doi:10.1163/156939392X00021 Google Scholar

12. Perterson, B. and S. Strom, "T-matrix formulation of electromagnetic scattering from multilayered scatterers," Phys. Review D, Vol. 10(8), 2670-2684, Oct. 1974. Google Scholar

13. Wang, D. S. and P. W. Barber, "Scattering by inhomogeneous nonspherical objects," Appl. Opts., Vol. 18(8), 1190-1197, April 1979. Google Scholar

14. Li, L.-W., M.-S. Leong, T.-S. Yeo, P.-S. Kooi, and K. Y. Tan, "Computations of spheroidal harmonics with complex argument: A review with an algorithm," Physical Review E, Vol. 58, No. 5, 6792-6806, November 1998.
doi:10.1103/PhysRevE.58.6792 Google Scholar

15. Stratton, J. A., P. M. Morse, L. J. Chu, J. D. C. Little, and F. J. Corbato, Spheroidal Wave Functions, John Wiley & Sons, New York, 1956.

16. Sinha, B. P. and A. R. Sebak, "Scattering by a conducting spheroidal object with dielectric coating at axial incidence," IEEE Trans. Antennas Propagat., Vol. 40, No. 3, 268-274, 1992.
doi:10.1109/8.135468 Google Scholar

17. Sebak, A. and L. Shafai, "Electromagnetic scattering by spheroidal objects with impedance boundary conditions at axial incidence," Radio Sci., Vol. 23, No. 6, 1048-1060, 1988.
doi:10.1029/RS023i006p01048 Google Scholar

18. Bohren, C. F. and D. R. Huffman, Absorption and Scattering of Light by Small Particles, John Wiley & Sons, New York, 1983.

19. Born, M. and E. Wolf, Principles of Optics, Pergamon Press, Oxford, 1970.