volume | PIER Journals

Abstract

To characterize electromagnetic waves in complex media has been an important topic because of its useful applications and scientific significance of its physical mechanism. Dyadic Green's functions, as a mathematical kernel or a dielectric medium response, relate directly the radiated electromagnetic fields and the source distribution. In terms of the vector wave functions in cylindrical coordinates, dyadic Green's functions in a unbounded and a planar, multilayered gyroelectric chiral media are formulated. By use of the scattering superposition principle and taking the multiple reflections into account, a general representation of the Green's dyadics is obtained. Furthermore, the scattering coefficients of the Green's dyadics are determined from the boundary conditions at each interface and are expressed in a greatly compact form of recurrence matrices. In the formulation of the Green's dyadics and their scattering coefficients, three cases are considered, i.e., the current source is impressed in (1) the first, (2) the intermediate, and (3) the last regions, respectively. Although the dyadic Green's functions for a unbounded gyroelectric chiral medium has been reported in the literature, some of the results are incorrect. As compared to the existing results, the current work basically contributes (1) a correct form of dyadic Green's function for a unbounded gyroelectric chiral medium, (2) the general representation of the dyadic Green's functions for a multi-layered gyroelectric chiral medium, and (3) a convincible and direct derivation of the irrotational Green's dyadic.

1. Tai, C. T., Dyadic Green’s Functions in Electromagnetic Theory, 2nd edition, IEEE Press, Piscataway, New Jersey, 1994.

2. Collin, R. E., Field Theory of Guided Waves, 2nd edition, IEEE Press, Piscataway, New Jersey, 1991.

3. Kong, J. A., Electromagnetic Wave Theory, 3rd edition, John Wiley & Sons, New York, 1990.

4. Chew, W. C., Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, New York, 1990.

5. Chew, W. C., "Some observations on the spatial and eigenfunction representations of dyadic Green’s functions," IEEE Trans. Antennas Propagat., Vol. 37, No. 10, 1322-1327, Oct. 1989. Google Scholar

6. Cavalcante, G. P. S., D. A. Rogers, and A. J. Giardola, "Analysis of the electromagnetic wave propagation in multilayered media using dyadic Green’s function," Radio Sci., Vol. 17, 503-508, 1982. Google Scholar

7. Pathak, P. H., "On the eigenfunction expansion of the electric and magnetic field dyadic Green’s functions," IEEE Trans. Antennas Propagat., Vol. 31, 837-846, 1983. Google Scholar

8. Pearson, L. W., "On the spectral expansion of the electric and magnetic dyadic Green’s functions in cylindrical harmonics," Radio Sci., Vol. 18, 166-174, 1983. Google Scholar

9. Li, L. W., "Dyadic Green’s function of inhomogeneous ionospheric waveguide," J. Electromagn. Waves Applic., Vol. 6, No. 1, 53-70, 1992. Google Scholar

10. Li, L. W., P. S. Kooi, M. S. Leong, and T. S. Yeo, "Electromagnetic dyadic Green’s function in spherically multilayered media," IEEE Trans. Microwave Theory Tech., Vol. 42, No. 12, 2302-2310, Part A, December 1994. Google Scholar

11. 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," J. Electromagn. Waves Applic., Vol. 8, No. 6, 663-678, June 1994. Google Scholar

12. Li, L. W., P. S. Kooi, M. S. Leong, and T. S. Yeo, "Alternative formulations of electric dyadic Green functions of the first and second kinds for an infinite rectangular waveguide with a load," Microwave Opt. Technol. Lett., Vol. 8, No. 2, 98-102, February 1995. Google Scholar

13. Li, L. W., P. S. Kooi, M. S. Leong, and T. S. Yeo, "A general expression of dyadic Green’s function in radially multilayered chiral media," IEEE Trans. Antennas Propagat., Vol. 43, No. 3, 232-238, March 1995. Google Scholar

14. Li, L. W., P. S. Kooi, M. S. Leong, and T. S. Yeo, "Analytic representation of scattering dyadic Green’s functions’ coefficients for cylindrically multilayered chiral media," J. Electromagn. Waves Applic., Vol. 9, No. 9, 1207-1221, September 1995. Google Scholar

15. Li, L. W., P. S. Kooi, M. S. Leong, T. S. Yeo, and S. L. Ho, "Input impedance of a probe-excited semi-infinite rectangular waveguide with arbitrary multilayered loads: Part I–Dyadic Green’s functions," IEEE Trans. Microwave Theory Tech., Vol. 43, No. 7, 1559-1566, Part A, July 1995. Google Scholar

16. Li, L. W., P. S. Kooi, M. S. Leong, T. S. Yeo, and S. L. Ho, "On the eigenfunction expansion of dyadic Green’s functions in rectangular cavities and waveguides," IEEE Trans. Microwave Theory Tech., Vol. 43, No. 3, 700-702, March 1995. Google Scholar

17. Kong, J. A., "Electromagnetic field due to dipole antennas over stratified anisotropic medium," Geophysics, Vol. 37, 985-996, 1972. Google Scholar

18. Kong, J. A., "Theorems of bianisotropic media," Proc. IEEE, Vol. 60, 1036-1046, 1972. Google Scholar

19. Ali, S. M. and S. F. Mahmoud, "Electromagnetic fields of buried sources in stratified anisotropic media," IEEE Trans. Antennas Propagat., Vol. 27, 671-678, 1979. Google Scholar

20. Lee, J. K. and J. A. Kong, "Dyadic Green’s functions for layered anisotropic medium," Electromagnetics, Vol. 3, 111-130, 1983. Google Scholar

21. Lee, J. K. and J. A. Kong, "Active microwave remote sensing of an anisotropic random medium layer," IEEE Trans. Geosci. Remote Sensing, Vol. 23, 910-923, 1985. Google Scholar

22. Lee, J. K. and J. A. Kong, "Passive microwave remote sensing of an anisotropic random medium layer," IEEE Trans. Geosci. Remote Sensing, Vol. 23, No. 6, 924-932, Nov. 1985. Google Scholar

23. Krowne, C. M., "Determination of the Green’s function in the spectral domain using a matrix method: Application to radiators immersed in a complex anisotropic layered medium," IEEE Trans. Antennas Propagat., Vol. 34, 247-253, 1986. Google Scholar

24. Krowne, C. M., "Relationships for Green’s function spectral dyadics involving anisotropic imperfect conductors imbedded in layered anisotropic media," IEEE Trans. Antennas Propagat., Vol. 37, No. 9, 1207-1211, Sept. 1989. Google Scholar

25. Monzon, J. C., "Three-dimensional field expansion in the most general rotationally symmetric anisotropic material: Application to scattering by a sphere," IEEE Trans. Antennas Propagat., Vol. 37, No. 6, 728-735, June 1989. Google Scholar

26. Oldano, C., "Electromagnetic-wave propagation in anisotropic stratified media," Physical Review A, Vol. 40, 6014-6020, Nov. 1989. Google Scholar

27. Habashy, T. M., S. M. Ali, J. A. Kong, and M. D. Grossi, "Dyadic Green’s functions in a planar stratified, arbitrarily magnetized linear plasma," Radio Science, Vol. 26, No. 3, 701-715, May–June 1991. Google Scholar

28. Kaklamani, D. I. and N. K. Uzunoglu, "Radiation of a dipole in an infinite triaxial anisotropic medium," Electromagnetics, Vol. 12, 231-245, 1992. Google Scholar

29. Ren, W., "Contributions to the electromagnetic wave theory of bounded homogeneous anisotropic media," Physical Rev. E, Vol. 47, No. 1, 664-673, Jan. 1993. Google Scholar

30. Weiglhofer, W. S. and I. V. Lindell, "Analytic solution for the dyadic Green’s function of a nonreciprocal uniaxial bianisotropic medium," Archiv f¨ur Elektronik und ¨ Ubertragungstechnik., Vol. 48, No. 2, 116-119, 1994. Google Scholar

31. Lindell, I. V., "Decomposition of electromagnetic sources in axially chiral uniaxial anisotropic media," Journal of Electromagnetic Waves and Applications, Vol. 10, No. 1, 51-59, 1996. Google Scholar

32. Cheng, D. and W. Ren, "Green dyadics in reciprocal uniaxial bianisotropic media by by cylindrical vector wave functions," Physics Review E, Vol. 54, No. 3, 2917-2924, Sept. 1994. Google Scholar

33. Uzunoglu, N. K., P. G. Cottis, and J. G. Fikioris, "Excitation of electromagnetic waves in a gyroelectric cylinder," IEEE Trans. Antenna and Propagat., Vol. 33, 90-99, 1987. Google Scholar

34. Barkeshli, S., "Eigenvalues and eigenvectors of gyroelectric media," IEEE Trans. Antennas Propagat., Vol. 40, 340-344, 1992. Google Scholar

35. Barkeshli, S., "Electromagnetic dyadic Green’s function for multilayered symmetric gyroelectric media," Radio Science, Vol. 28, No. 1, 23-36, Jan.–Feb. 1993. Google Scholar

36. Weiglhofer, W. S., "Dyadic Green’s function representation in electrically gyrotropic media," AEU, Archiv f¨ur Elektronik und ¨ Ubertragungstechnik: Electronics and Communication, Vol. 47, No. 3, 125-130, May 1993. Google Scholar

37. Cheng, D., "Field representation in a gyroelectric chiral media by cylindrical vector wave functions," Journal of Physics D, Vol. 28, 246-251, 1995. Google Scholar

38. Cheng, D., "Eigenfunction expansion of the dyadic Green’s function in a gyroelectric chiral medium by cylindrical vector wave functions," Physics Review E, Vol. 55, No. 2, 1950-1958, Feb. 1997. Google Scholar

39. Yin, W., P. Li, and W. Wang, "The theory of dyadic Green’s function and the radiation characteristics of sources in stratified bi-isotropic media," Progress In Electromagnetics Research (Series), J. A. Kong (Ed.), Vol. 9, 117–136, EMW Publishing, Boston, 1994. Google Scholar

40. Li, L. W., M. S. Leong, T. S. Yeo, and P. S. Kooi, "Comments on ‘eigenfunction expansion of the dyadic Green’s function in a gyroelectric chiral medium by cylindrical vector wave functions’," Accepted by Physical Review E, April, 1998 and to appear in March 1999. Google Scholar

41. Cheng, D., Y.-Q. Jin, and W. Ren, "Green dyadics in gyroelectric chiral medium by cylindrical vector wave functions," Int. J. Appl. Electromagn. Mechanics, Vol. 7, 213-226, 1996. Google Scholar

42. Cheng, D. and Y. M. M. Antar, "Cylindrical vector wave functions and applications in a source-free uniaxial chiral medium," Physics Review E, Vol. 56, No. 6, 7273-7287. Google Scholar

43. Cheng, D., "Vector-wave-function theory of uniaxial bianisotropic semiconductor material," Physics Review E, Vol. 56, No. 2, 2321-2324, August 1997. Google Scholar

44. Cheng, D., "Transient electromagnetic field of dipole source in chiral medium," Int. J. Appl. Electromagn. Mechanics, Vol. 8, 179-183, 1997. Google Scholar

45. Cheng, D., W. Ren, and Y.-Q. Jin, "Green dyadics in uniaxial bianisotropic-ferrite medium by cylindrical vector wavefunctions," J. Phys. A: Math. Gen., Vol. 30, 573-585, 1997. Google Scholar

46. Ren, W., "Dyadic Green’s functions and dipole radiations in layered chiral media," J. Appl. Phys., Vol. 75, No. 1, 30-35, Jan. 1994. Google Scholar

Dr. L.-W. Li

Dr. S. B. Yeap

Dr. M.-S. Leong

Professor Tat Yeo

Dr. P.-S. Kooi