volume | PIER Journals

Abstract

In this paper, we study in detail both the trapped surface wave and lateral wave excited by a dipole antenna parallel to the plane boundaries of a three-layered region in spherical coordinate. An approximate formula is obtained for the solution of the electrictype pole equation when a condition is satisfied by √k²₁-k²₀l≤0.6. Similarly, an approximate formula is obtained for the solution of the magnetic-type pole equation when a condition is satisfied by √ k²₁-k²₀l-π/2≤1. Furthermore, because of its useful applications in microstrip antenna, the radiation patterns of a patch antenna with specific current distributions are treated specifically. Analysis and computations are carried out in several typical cases. It is seen that, for the component E_0Θ, the total field is determined primarily by the trapped surface wave of electric type, and, for the component E_0Φ, the total field is determined primarily by the trapped surface wave of magnetic type.

1. Sommerfeld, A., "Propagation of waves in wireless telegraphy," Ann. Phys., Vol. 28, 665-736, Mar. 1909.
doi:10.1002/andp.19093330402

2. Sommerfeld, A., "Propagation of waves in wireless telegraphy," Ann. Phys., Vol. 81, 1135-1153, Dec. 1926.
doi:10.1002/andp.19263862516

3. Wait, J. R., "Radiation from a vertical electric dipole over a stratified ground," IRE Trans. Antennas Propagat., Vol. 1, 9-12, 1953; Vol. 2, 144-146, 1954.

4. Wait, J. R., "Radiation from a vertical electric dipole over a curved stratified ground ground," Journal of Res. Nat. Bur. Standards, Vol. 56, 232-239, 1956.

5. Wait, J. R., "Excitation of surface waves on conducting dielectric clad and corrugated surfaces," Journal of Res. Nat. Bur. Standards, Vol. 59, No. 6, 365-377, 1957.

6. Wait, J. R., "Electromagnetic surface waves," Advances in Radio Research, 157-219, Academic Press, New York, 1964.

7. Wait, J. R., Electromagnetic Waves in Stratified Media, 2nd edition, 1970.

8. Wait, J. R., "Radiation from a vertical electric dipole located over laterally anisotropic groundplane," Electronics Letters, Vol. 26, No. 1, 74-76, 1990.
doi:10.1049/el:19900049

9. Wait, J. R., "Electromagnetic fields of a vertical electric dipole over a laterally anisotropic surface," IEEE Trans. Antennas and Propagat., Vol. 38, No. 10, 1719-1723, 1990.
doi:10.1109/8.59789

10. Mahmoud, S. F., "Remarks on `The electromagnetic field of a vertical electric dipole over the earth or sea'," IEEE Trans. Antennas Propagat., Vol. 46, No. 12, 1745-1946, 1999.
doi:10.1109/8.814958

11. Collin, R. E., "Some observations about the near zone electric field of a hertzian dipole above a lossy earth," IEEE Trans. Antennas Propagat., Vol. 52, No. 11, 3133-3137, 2004.
doi:10.1109/TAP.2004.835270

12. King, R. W. P., M. Owens, and T. T. Wu, Lateral Electromagnetic Waves: Theory and Applications to Communications, Geophysical Exploration, and Remoting Sensing, 1992.

13. King, R. W. P., G. J. Fikioris, and R. B. Mack, Cylindrical Antennas and Array, University Press, 2002.

14. King, R. W. P. and S. S. Sandler, "The electromagnetic field of a vertical electric dipole over the earth or sea," IEEE Trans. Antennas Propagat., Vol. 42, No. 3, 382-389, 1994.
doi:10.1109/8.280725

15. King, R. W. P., "The electromagnetic field of a horizontal electric dipole in the presence of a three-layered region," J. Appl. Phys., Vol. 69, No. 12, 7987-7995, 1991.
doi:10.1063/1.347494

16. King, R. W. P., "The electromagnetic field of a horizontal electric dipole in the presence of a three-layered region: Supplement ," J. Appl. Phys., Vol. 74, No. 8, 4845-4548, 1993.
doi:10.1063/1.354313

17. King, R. W. P. and S. S. Sandler, "The electromagnetic field of a vertical electric dipole in the presence of a three-layered region," Radio Sci., Vol. 29, No. 1, 97-113, 1994.
doi:10.1029/93RS02662

18. Wait, J. R., "Comment on 'The electromagnetic field of a vertical electric dipole in the presence of a three-layered region' by Ronold, W. P. King and S. S. Sandler," Radio Sci., Vol. 33, No. 2, 251-253, 1998.
doi:10.1029/97RS02696

19. King, R. W. P. and S. S. Sandler, "Reply," Radio Sci., Vol. 33, No. 2, 255-256, 1998.
doi:10.1029/97RS02695

20. Collin, R. E., "Hertzian dipole radiation over a lossy earth or sea: Some early and late 20th century controversies," IEEE Antennas and Propagation Magazine, Vol. 46, No. 2, 64-79, 2004.
doi:10.1109/MAP.2004.1305535

21. Koledintseva, M. Y., V. V. Bodrov, I. V. Sourkova, M. M. Sabirov, and V. I. Sourkov, "Unified spectral technique application for study of radiator behavior near planar layered composites," Progress In Electromagnetics Research, Vol. 66, 317-357, 2006.
doi:10.2528/PIER06111701

22. Xu, X.-B. and Y. Huang, "An efficient analysis of vertical dipole antennas above a lossy half-space," Progress In Electromagnetics Research, Vol. 74, 353-377, 2007.
doi:10.2528/PIER07052202

23. Abo-Seida, O. M., "Far-field due to a vertical magnetic dipole in sea," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 6, 707-715, 2006.
doi:10.1163/156939306776143406

24. Zheng, Q.-R., Y.-Q. Fu, and N.-C. Yuan, "Characteristics of planar PBG structures with a cover layer," Journal of Electromagnetic Waves and Applications, Vol. 20, No. 11, 1439-1453, 2006.
doi:10.1163/156939306779274264

25. Chen, H. T., J.-X. Luo, and D.-K. Zhang, "An analytic formula of the current distribution for the VLF horizontal wire antenna above lossy half-space," Progress In Electromagnetics Research Letters, Vol. 1, 149-158, 2008.
doi:10.2528/PIERL07112904

26. Sharma, A. and G. Singh, "Design of single Pin shorted three-dielectric-layered substrates rectangular patch microstrip antenna for communication systems," Progress In Electromagnetics Research Letters, Vol. 2, 157-165, 2008.
doi:10.2528/PIERL08010703

27. Attiya, A. M., "Dyadic Green's function of an elementary point source above a periodically-defected-grounded dielectric slab," Progress In Electromagnetics Research B, Vol. 4, 127-145, 2008.
doi:10.2528/PIERB08011001

28. Zhang, L., Y. H. Zhang, W. Hu, W. Yu, and G.-Q. Zhu, "Automatic incorporation of surface wave poles in discrete complex image method," Progress In Electromagnetics Research, Vol. 80, 161-178, 2008.
doi:10.2528/PIER07110105

29. Zhang, H. Q. and W. Y. Pan, "Electromagnetic field of a vertical electric dipole on a perfect conductor coated with a dielectric layer," Radio Science, Vol. 37, No. 4, 13-1-13-7, 2002.
doi:10.1029/2000RS002348

30. Zhang, H.-Q., K. Li, and W.-Y. Pan, "The electromagnetic field of a vertical dipole on the dielectric-coated imperfect conductor," Journal of Electromagnetic Waves and Applications, Vol. 18, No. 10, 1305-1320, 2004.
doi:10.1163/1569393042955009

31. Zhang, H.-Q., W.-Y. Pan, K. Li, and K.-X. Shen, "Electromagnetic field for a horizontal electric dipole buried inside a dielectric layer coated high Lossy half space," Progress In Electromagnetics Research, Vol. 50, 163-186, 2005.
doi:10.2528/PIER04052301

32. K., Li and Y. Lu, "Electromagnetic field generated by a horizontal electric dipole near the surface of a planar perfect conductor coated with a uniaxial layer," IEEE Trans. Antennas and Propagat., Vol. 53, No. 10, 3191-3200, 2005.
doi:10.1109/TAP.2005.856305

33. Mei, J. P. and K. Li, "Electromagnetic field from a horizontal electric dipole on the surface of a high lossy medium coated with a uniaxial layer," Progress In Electromagnetics Research, Vol. 73, 71-91, 2007.
doi:10.2528/PIER07032604

34. Xu, Y. H., W. Ren, L. Liu, and K. Li, "Electromagnetic field of a horizontal electric dipole in the presence of a four-layered region," Progress In Electromagnetics Research, Vol. 81, 371-391, 2008.
doi:10.2528/PIER08012303

35. Xu, Y. H., K. Li, and L. Liu, "Electromagnetic field of a horizontal electric dipole in the presence of a four-layered region," Progress In Electromagnetics Research, Vol. 81, 371-391, 2008.
doi:10.2528/PIER08012303

36. Xu, Y. H., W. Ren, L. Liu, and K. Li, "Electromagnetic field of a horizontal electric dipole in the presence of a four-layered region," Progress In Electromagnetics Research, Vol. 81, 371-391, 2008.
doi:10.2528/PIER08012303

37. Liu, L. and K. Li, "Radiation from a vertical electric dipole in the presence of a three-layered region," IEEE Trans. Antennas and Propagat., Vol. 55, No. 12, 3469-3475, 2007.
doi:10.1109/TAP.2007.910355

38. Hoffman, R. K., Handbook of Microwave Integrated Circuits, 1987.

39. Gradshteyn, I. S. and I. M. Ryzhik, Table of Integrals, Series, and Products, 1980.

Dr. Liang Liu

Prof. Kai Li

Dr. Yi Hui Xu