volume | PIER Journals

2007-09-09

Simplified Formulation of Dyadic Green's Functions and Their Duality Relations for General Anisotropic Media

Abdullah Eroglu,

Prof. Abdullah Eroglu

Department of Engineering

Indiana University --- Purdue University

USA

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Jay Kyoon Lee

Dr. Jay Kyoon Lee

Department of Electrical Engineering and Computer Science

Syracuse University

USA

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, Vol. 77, 391-408, 2007

doi:10.2528/PIER07082401

Abstract

A simplified method to obtain the complete set of the dyadic Green's functions (DGFs) for general anisotropic media is presented. The method is based on the k-domain representation of the fields in terms of wave matrices. The Fourier transformed Green's functions are calculated through the inverses of wave matrices. The inverses of the wave matrices, which lead to the final form of DGF, are obtained using dyadic decomposition technique. This facilitates the inverse operation significantly and gives DGFs clear vector representation, which helps their physical interpretation. The dyadic decomposition of the wave matrices has been presented for uniaxially anisotropic, biaxially anisotropic and gyrotropic media. The method of deriving DGF using the technique given in this paper is applied on a uniaxially anisotropic medium and verified with the existing results. It is shown that the knowledge of the inverse of one type of wave matrix is adequate to find the complete set of the dyadic Green's functions for a general anisotropic medium using the method presented. The duality relations of dyadic Green's functions are also developed. It is shown that once the dyadic Green's functions for one of the dual media are obtained, the DGFs for the other dual medium can be found by application of the duality relations shown in this paper.

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Abdullah Eroglu, and Jay Kyoon Lee, "Simplified Formulation of Dyadic Green's Functions and Their Duality Relations for General Anisotropic Media," , Vol. 77, 391-408, 2007.
doi:10.2528/PIER07082401

References

1. Gao, G., C. T. Verdin, and T. M. Habashy, "Analytical techniques to evaluate the integrals of 3D and 2D spatial dyadic Green's functions," Progress In Electromagnetics Research, Vol. 52, 47-80, 2005.
doi:10.2528/PIER04070201

2. Soliman, E. A. and G. A. E. Vandenbosh, "Green's functions of filament sources embedded in stratified dielectric media," Progress In Electromagnetics Research, Vol. 62, 21-40, 2006.
doi:10.2528/PIER06022401

3. Tai, C. T., Dyadic Green's Functions in Electromagnetic Theory, IEEE Press, 1994.

4. Jarem, J. M., "A rapidly-convergent, mixed-partial derivative boundary condition Green's function for an anisotropic half-space: perfect conductor case," Progress In Electromagnetics Research, Vol. 67, 39-112, 2007.
doi:10.2528/PIER06072804

5. Chew, W. C., Waves and Fields in Inhomogeneous Media, IEEE Press, 1995.

6. Yang, R., Y. Xie, P. Wang, and L. Li, "Microstrip antennas with left-handed materials subsrates," J. of Electromagn. Waves and Appl., Vol. 20, No. 9, 1221-1233, 2006.
doi:10.1163/156939306777442908

7. Mudaliar, S. and J. K. Lee, "Dyadic Green's functions for a twolayer biaxially anisotropic medium," J. of Electromagn. Waves and Appl., Vol. 10, No. 7, 909-923, 1996.

8. Barkeshli, S., "Electromagnetic dyadic Green's function for multilayered symmetric gyroelectric media," Radio Science, Vol. 28, No. 1, 23-36, 1993.
doi:10.1029/92RS01926

9. Mudaliar, S., "On the application of the radiative transfer approach to scattering from a random medium layer with a rough boundaries," J. of Electromagn. Waves and Appl., Vol. 20, No. 12, 1739-1749, 2006.
doi:10.1163/156939306779292246

10. Krowne, C. M., "Green's function in spectral domain for biaxial and uniaxial anisotropic planar dielectric structures," IEEE Trans. Antennas Propag., Vol. 32, 1273-1281, 1984.
doi:10.1109/TAP.1984.1143250

11. Li, L.-W., J.-H. Koh, T. S. Yeo, M. S. Leong, and P. S. Kooi, "Cylindrical vector eigenfunction expansion of Green dyadics for multilayered anisotropic media and its application to four layered forest," IEEE Trans., Vol. 52, 466-477, 2004.

12. Tsalamengas, J. L. and N. K. Uzunoglu, "Radiation from a dipole near a general anisotropic layer," IEEE Trans. Antennas Propag., Vol. 38, 9-16, 1990.
doi:10.1109/8.43584

13. Morgan, M. A., D. L. Fisher, and E. A. Milne, "Electromagnetic scattering by stratified inhomogeneous anisotropic media," IEEE Trans. Antennas Propag., Vol. 35, No. 2, 191-197, 1987.
doi:10.1109/TAP.1987.1144069

14. Eroglu, A., "Electromagnetic wave propagation and radiation in gyrotropic medium," Ph.D Dissertation, 2004.

15. 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

16. 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