volume | PIER Journals

Abstract

A complete set of three dimensional multilayered media Green's functions is presentedfor general electric andmagnetic sources. The Green's functions are derived in the mixed potential form, which is identical with the Michalski-Zheng C-formulation. The approach appliedin this paper is basedon the classical Hertz potential representation. A special emphasis is on the formulation of the dyadic Green's functions G^HJ and G^EM. In these functions the derivatives due to the curl operator are taken in the spectral domain. This avoids the needof the numerical differentiation. Furthermore, it is foundthat the Hertzian potentials satisfy several useful duality and reciprocity relations. By these relations the computational efficiency of the Hertz potential approach can be significantly improvedandthe number of requiredSommerfeldin tegrals can be essentially reduced. We show that all spectral domain Green's functions can be obtained from only two spectral domain Hertzian potentials, which correspond to the TE component of a vertical magnetic dipole and the TM component of a vertical electric dipole. The derived formulas are verified by numerical examples.

1. Mosig, J. R., "Arbitrarily shapedmicrostrip structures and their analysis with a mixedp otential integral equation," IEEE Trans. Microwave Theory Tech., Vol. 36, 314-323, 1988.
doi:10.1109/22.3520 Google Scholar

2. Zheng, D. and K. A. Michalski, "Analysis of coaxially fed microstrip antennas of arbitrary shape with thick substrates," Journal of Electromagnetic Waves and Applications, Vol. 5, No. 12, 1303-1327, 1991.
doi:10.1163/156939391X00860 Google Scholar

3. Tsai, M-J., F. De Flaviis, O. Fordham, and N. G. Alexpoulos, "Modelling planar arbitrarily shaped microstrip elements in multilayered media," IEEE Trans. Microwave Theory Tech., Vol. 45, 330-337, 1997.
doi:10.1109/22.563330 Google Scholar

4. Bunger, R. and F. Arngt, "Efficient MPIE approach for the analysis of three-dimensional microstrip structures in layered media," IEEE Trans. Microwave Theory Tech., Vol. 45, 1141-1153, 1997.
doi:10.1109/22.618401 Google Scholar

5. Ling, F., D. Jiao, and andJ. M. Jin, "Efficient electromagnetic modeling of microstrip structures in multilayer media," IEEE Trans. Microwave Theory Tech., Vol. 47, 1810-1818, 1999.
doi:10.1109/22.788516 Google Scholar

6. Michalski, K. A. and D. Zheng, "Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media, Part II: Implementation andresults for contiguous half-spaces," IEEE Trans. Antennas Propagat., Vol. 38, 345-352, 1990.
doi:10.1109/8.52241 Google Scholar

7. Vitebskiy, S., K. Sturgess, and L. Carin, "Short-pulse plane-wave scattering from buried perfectly conducting bodies of revolution," IEEE Trans. Antennas Propag., Vol. 44, 143-151, February 1996.
doi:10.1109/8.481640 Google Scholar

8. Cui, T. J., W. Wiesbeck, and andA. Herschlein, "Electromagnetic scattering by multiple three-dimensional scatterers buried under multilayeredmed ia --- Part I: Theory, Part II: Numerical implementation andresults," IEEE Trans. Geoscience Remote Sensing, Vol. 36, 526-546, March 1998. Google Scholar

9. Cui, T. J. and W. C. Chew, "Fast evaluation of Sommerfeld integrals for EM scattering and radiation by three-dimensional buriedob jects," IEEE Trans. Geoscience Remote Sensing, Vol. 37, 887-900, March 1999. Google Scholar

10. Geng, N. and L. Carin, "Wide-bandelectromagnetic scattering from a dielectric BOR buried in a layered lossy dispersive medium," IEEE Trans. Antennas Propagat., Vol. 47, 610-619, April 1999.
doi:10.1109/8.768799 Google Scholar

11. Mosig, J. R., "Integral equation technique," Numerical Techniques for Microwave and Millimeter-Wave Passive Structures, 133-213, 1989. Google Scholar

12. Chew, W. C., "Waves and Fields in Inhomogeneous Media," IEEE Press, 1990. Google Scholar

13. Michalski, K. A. and J. R. Mosig, "Multilayeredmed ia Green’s functions in integral equation formulations," IEEE Trans. Antennas Propagat., Vol. 45, 508-519, 1997.
doi:10.1109/8.558666 Google Scholar

14. Bernardi, P. and R. Cicchetti, "Dyadic Green’s functions for conductor-bakedla yeredstructures excitedb y arbitrary tridimensional sources," IEEE Trans. Microwave Theory Tech., Vol. 42, 1474-1483, Aug. 1994.
doi:10.1109/22.297809 Google Scholar

15. Chow, Y. L., N. Hojjat, S. Safavi-Naeini, and andR. Faraji-Dana, "Spectral Green’s functions for multilayer media in a convenient computational form," IEE Proc.-Mircow. Antennas Propag., Vol. 145, 85-91, 1998.
doi:10.1049/ip-map:19981598 Google Scholar

16. Sommerfeld, A., "Partial Differential Equations," Academic, 1949. Google Scholar

17. Stoyer, C. H., "Electromagnetic fields of dipoles in stratified media," IEEE Trans. Antennas Propagat., Vol. 25, 547-552, 1977.
doi:10.1109/TAP.1977.1141618 Google Scholar

18. Kong, J. A., "Electromagnetic fields due to dipole antennas over stratifiedanisotropic media," Geophysics, Vol. 37, 985-996, 1972.
doi:10.1190/1.1440321 Google Scholar

19. Tang, C.-M., "Electromagnetic fields due to dipole antennas embedded in stratified anisotropic media," IEEE Trans. Antennas Propagat., Vol. 27, 665-670, 1979.
doi:10.1109/TAP.1979.1142160 Google Scholar

20. Kong, J. A., "Electromagnetic Wave Theory," John Wiley & Sons, 1986. Google Scholar

21. Michalski, K. A. and D. Zheng, "Electromagnetic scattering and radiation by surfaces of arbitrary shape in layered media, Part I: Theory," IEEE Trans. Antennas Propagat., Vol. 38, 335-344, 1990.
doi:10.1109/8.52240 Google Scholar

22. Harrington, R. F., "Boundary integral formulations for homogeneous material bodies," Journal of Electromagnetic Waves and Applications, Vol. 3, No. 1, 1-15, 1989.
doi:10.1163/156939389X00016 Google Scholar

23. Michalski, K. A., The mixed-potential electric field integral equation for objects in layeredmed ia, Vol. 39, 317-322, Arch. Elek. Ubertragung., 1985.

24. Michalski, K. A., "On the scalar potential of a point charge associatedwith a time-harmonic dipole in a layeredmed ium," IEEE Trans. Antennas Propagat., Vol. 35, 1299-1301, 1987.
doi:10.1109/TAP.1987.1144022 Google Scholar

25. Dural, G. and M. I. Aksun, "Closed-form Green’s functions for general sources andstratifiedmed ia," IEEE Trans. Microwave Theory Tech., Vol. 43, 1545-1552, 1995.
doi:10.1109/22.392913 Google Scholar

26. Abramowitz, M. and I. Stegun, Handbook of Mathematical Functions, Dover Publications, 1970.

27. Sarvas, J., M. Taskinen, and andS. Jarvenpaa, "Computing the scattering matrix of a multiport andm ultilayer microstrip patch with the mixedp otential integral equation method," Proceedings of PIERS 1996, Vol. 464, 1996. Google Scholar

28. Hua, Y. and T. K. Sarkar, "On SVD for estimating generalized eigenvalues of singular matrix pencil in noise," IEEE Trans. Signal Processing., Vol. 39, 892-900, 1991.
doi:10.1109/78.80911 Google Scholar

29. Sarkar, T. K. and O. Pereira, "Using the matrix pencil methodto estimate the parameters of a sum of complex exponentials," IEEE Antennas Propag. Magazine., Vol. 37, 49-55, 1995. Google Scholar

30. Ling, F., "Fast electromagnetic modeling of multilayer microstrip antennas andcircuits," h.D. thesis, University of Illinois, 2000. Google Scholar

Dr. Pasi Yla-Oijala

Dr. Matti Taskinen

Dr. Jukka Sarvas