volume | PIER Journals

Abstract

The dyadic Green's functions (DGFs) for unbounded and layered general anisotropic media are considered in this paper. First, the DGF for unbounded problem is derived using the eigen-decomposition method. Two different approaches are proposed to obtain the DGF for layered problem when the source is located inside the anisotropic region. The first approach is to apply the modified symmetrical property of DGF to obtain the DGF for the field in the isotropic region when the source is located inside the anisotropic region, from the DGF for the field in anisotropic region when the source is in the isotropic region. This modified symmetrical property can be applied for the layered geometry with bounded anisotropic region being either reciprocal or non-reciprocal medium. However, this method can not give the DGF for the field inside the anisotropic region. Thus, the second approach is presented to obtain the complete set of DGFs for all the regions including the anisotropic region, by applying the direct construction method through eigen-decomposition together with matrix method.

1. Bunkin, F. V., "On radiation in anisotropic media," JETP Lett., Vol. 5, No. 2, 338-346, Sep. 1957. Google Scholar

2. Arbel, E. and L. B. Felsen, "Theory of radiation from sources in anisotropic media. Part I: General sources in stratified media. Part II: Point source in infinite homogeneous medium," Electromagnetic Waves, 391-459, 1963. Google Scholar

3. Wu, C. P., "Radiation from dipoles in a magneto-ionic medium," IEEE Trans. Antennas Propagation, Vol. 11, 681-689, 1963. Google Scholar

4. Tsalamengas, J. L., "Electromagnetic fields of elementary dipole antennas embedded in strati¯ed general anisotropic media," IEEE Trans. Antennas Propagation, Vol. 37, No. 3, 399-403, 1989.
doi:10.1109/8.18739 Google Scholar

5. Hsia, I. Y. and N. G. Alexopoulos, "Radiation characteristics of Hertzian dipole antennas in a nonreciprocal superstrate-substrate structure ," IEEE Trans. Antennas Propagation, Vol. 40, No. 7, 782-790, Jul. 1992.
doi:10.1109/8.155743 Google Scholar

6. Lee, J. K. and J. A. Kong, "Dyadic Green's functions for layered anisotropic medium," Electromagnetics, Vol. 3, 111-130, 1983.
doi:10.1080/02726348308915180 Google Scholar

7. Mudaliar, S. and J. K. Lee, "Dyadic Green's function for two layered biaxially anisotropic medium," Journal of Electromagnetic Waves and Applications, Vol. 10, No. 7, 909-923, 1996.
doi:10.1163/156939396X00027 Google Scholar

8. Eroglu, A. and J. K. Lee, "Dyadic Green's functions for an electrically gyrotropic medium," Progress In Electromagnetics Research, Vol. 58, 223-241, 2006.
doi:10.2528/PIER05070203 Google Scholar

9. Tsang, L., E. Njoku, and J. A. Kong, "Microwave thermal emission from a stratified medium with nonuniforn temperature distribution," Journal of Applied Physics, Vol. 46, No. 12, Dec. 1975.
doi:10.1063/1.321571 Google Scholar

10. Pettis, G. and J. K. Lee, "Radiation of Hertzian dipoles embedded in planarly layered biaxial media," The Second IASTED International Conference on Antennas, Radar, and Wave Propagation, Jul. 2005. Google Scholar

11. Krowne, C. M., "Green's function in the spectral domain for biaxial and uniaxial anisotropic planar dielectric structures," IEEE Trans. Antennas and Propagation , Vol. 32, No. 12, Dec. 1984.
doi:10.1109/TAP.1984.1143250 Google Scholar

12. Mesa, F.L., R. Marques, and M. Horno, "A general algorithm for computing the bidimensional spectral Green's dyad in multilayered complex bianisotropic media: The equivalent boundary method," IEEE Trans. Microwave Theory and Techniques, Vol. 39, No. 9, Sep. 1991.
doi:10.1109/22.83841 Google Scholar

13. Li, L. W., P. S. Kooi, M. S. Leong, and T. S. Yeo, "on the eigenfunction expansion of dyadic Green's function in planarly stratified media," Journal of Electromagnetic Waves and Applications, Vol. 8, No. 6, 663-678, 1994. Google Scholar

14. Li, L. W., N. H. Lim, W.-Y. Yin, and J.-A. Kong, "Eigen functional expansion of dyadic Green's functions in gyrotropic media using cylindrical vector wave functions," Progress In Electromagnetics Research, Vol. 43, 101-121, 2003.
doi:10.2528/PIER03020201 Google Scholar

15. Vegni, L., R. Cicchetti, and P. Capece, "Spectral dyadic Green's function formulation for planar integrated structures," IEEE Trans. Antennas and Propagation, Vol. 36, No. 8, 1057-1065, Aug. 1988.
doi:10.1109/8.7217 Google Scholar

16. Lee, J. K. and J. A. Kong, "Active microwave remote sensing of an anisotropic random medium layer," IEEE. Trans. Geoscience and Remote Sensing, Vol. 23, No. 6, 910-923, 1985.
doi:10.1109/TGRS.1985.289478 Google Scholar

17. Chen, H., Theory of Electromagnetic Wave: A Coordinate Free Approach, McGraw-Hill, 1983.

18. Zhuck, N. P. and A. S. Omar, "Radiation and low-frequency scattering of EM waves in a general anisotropic homogeneous medium," IEEE Trans. Antennas and Propagation, Vol. 47, No. 8, 1364-1373, Aug. 1999.
doi:10.1109/8.791956 Google Scholar

19. Trefethen, L. N. and D. Bau, Numerical Linear Algebra, Society for Industrial and Applied Mathematics, 1997.
doi:10.1137/1.9780898719574

20. Tai, C. T., "Dyadic Green's Functions in Electromagnetic Theory," IEEE Press, 1994. Google Scholar

21. Huang, Y. and J. K. Lee, The modified symmetrical property of the dyadic Green's functions for the non-reciprocal medium, EECS Dept. Technical Report, Syracuse University, Jun. 2010.

Dr. Ying Huang

Dr. Jay Kyoon Lee