volume | PIER Journals

Abstract

The Electromagnetic (EM) fields of a concentric, mismatched-material, elliptical system are studied when excited by an interior or exterior electric surface current. The interior or exterior surface current is assumed to be proportional to a single, angular Mathieu mode. It is shown that despite the fact that the system is concentric, that a single Mathieu mode surface current excites EM Mathieu-mode fields of all orders. A derivation of the EM fields due a single mode electric surface in an infinite, homogeneous media is given, as well as the matrix formulation from which the EM fields of the mismatched-material, elliptical system may be determined. Validation of numerical results and comparison with other research work is given for both interior and exterior single-mode, current sources. Detailed numerical examples of the EM fields that result for a single-mode, exterior source excitation are given for the first time. Discussion of the EM mode coupling that results by single-mode excitation on a mismatched elliptical system is given.

1. Abramowitz, M., I. StegunHandbook of Mathematical Functions, and Chap. 20, "Mathieu Functions," National Bureau of Standards Applied Mathematics Series 53, 1970. Google Scholar

2. Stratton, J., Electromagnetic Theory, Mcgraw-Hill, 1941.

3. Bowman, J., T. Senior, and P. Uslenghi, Electromagnetic and Acoustic Scattering by Simple Shapes, Chap. 3, "The Elliptic Cylinder," 129-180, 129-180, 1987. Google Scholar

4. Yeh, C., "Backscattering cross section of a dielectric elliptical cylinder," J. Opt. Soc. Amer., Vol. 55, No. 3, 309-314, 1965. Google Scholar

5. Yeh, C., "The diffraction of waves by a penetrable ribbon," J. Math. Phys., Vol. 4, No. 1, 65-71, 1963.
doi:10.1063/1.1703890 Google Scholar

6. Ragheb, H. and L. Shafai, "Electromagnetic scattering from a dielectric-coated elliptic cylinder," Can. J. Physics, Vol. 66, 1115-1122, 1988. Google Scholar

7. Sebak, A., "Scattering from dielectric-coated impedance elliptical cylinder," IEEE Trans. on Antennas and Prop., Vol. 48, No. 10, 1574-1580, 2000.
doi:10.1109/8.899674 Google Scholar

8. Caorsi, S., M. Pastorino, and M. Raffetto, "Electromagnetic scattering by a multilayer elliptic cylinder under transverse-magnetic illumination: Series solution in terms of Mathieu functions," IEEE Trans. on Antennas and Prop., Vol. 45, No. 6, 926-935, 1997.
doi:10.1109/8.585739 Google Scholar

9. Caorsi, S. and M. Pastorino, "Scattering by multilayer isore-fractive elliptic cylinders," IEEE Trans. on Antennas and Prop., Vol. 52 No. 1, No. Vol. 52 1, 189-196, 2004.
doi:10.1109/TAP.2003.822417 Google Scholar

10. Uslenghi, P., "Exact scattering by isorefractive bodies," IEEE Trans. on Antennas and Prop., Vol. 45, No. 9, 1382-1385, 1997.
doi:10.1109/8.623127 Google Scholar

11. Jarem, J., "Rigorous coupled wave analysis of radially and azimuthally-inhomogeneous, elliptical, cylindrical systems," Progress in Electromagnetic Research, Vol. 34, 89-115, 2001. Google Scholar

12. Jarem, J., "Validation and numerical convergence of the Hankel-Bessel and Mathieu rigorous coupled wave analysis algorithms for radially and azimuthally-inhomogeneous, elliptical, cylindrical systems," Progress in Electromagnetic Research, Vol. 36, 153-177, 2002. Google Scholar

13. Balanis, C., Advanced Engineering Mathematics, John Wiley and Sons, 1989.

14. Harrington, R., Field Computations by Moment Methods, MacMillan, 1968.

15. Hill, C. S., "Electromagnetic excitation of dielectric concentric elliptical cylinders," Masters Thesis, 2004. Google Scholar

16. Zhang, S. and J. Jin, "FORTRAN routines for computation of special functions," Programs: MTU12. Google Scholar

17. Jarem, J. and P. Banerjee, "Bioelectromagnetics: A rigorous coupled wave analysis of cylindrical biological tissues," Proceedings of the International Conference on Mathematics and Engineering Techniques in Medicine and Biological Sciences, Vol. II, 26-29, 2000. Google Scholar

18. Hamid, A.-K., "Iterative solution to the TM scattering by two infinitely long lossy dielectric elliptic cylinders," J. of Electromagn. Waves and Appl., Vol. 18, No. 4, 529-546, 2004.
doi:10.1163/156939304774113115 Google Scholar

Dr. Susan Hill

Dr. John Jarem