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2008-04-02
Trapped Surface Wave and Lateral Wave in the Presence of a Four-Layered Region
By
Progress In Electromagnetics Research, Vol. 82, 271-285, 2008
Abstract
In this paper, propagation model considers the region as a perfect conductor, covered by the two layer dielectrics, and air above. Propagation of the electromagnetic field in the presence of a four-layered region is examined in detail when a vertical electric dipole and observation point are located in the air. Similar to the three-layered case, analytical results are found for the electromagnetic field, which includes four wave modes: a direct wave,an ideal reflected wave, trapped surface waves, and lateral waves. The wave number of the trapped surface wave, which is contributed by the sums of residues of the poles, is between the wave numbers k0 in the air and k2 in the lower dielectric layer. The lateral wave is evaluated by the integrations along the branch cut. Analysis and computations shows that the trapped surface wave play a major role in communication at large distance when both the source point and observation point are on or close to the boundary between the air and the upper dielectric layer.
Citation
Yi Hui Xu, Wang Ren, Liang Liu, and Kai Li, "Trapped Surface Wave and Lateral Wave in the Presence of a Four-Layered Region," Progress In Electromagnetics Research, Vol. 82, 271-285, 2008.
doi:10.2528/PIER08031802
References

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

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

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

4. 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.

5. Wait, J. R., Electromagnetic Waves in Stratified Media, 2nd Ed., Pergamon Press, New York, 1970.

6. Banos, A., Dipole Radiation in the Presence of a Conducting Half-Space, Pergamon Press, Oxford, 1966.

7. Dunn, J. M., "Lateral wave propagation in a three-layered medium," Radio Sci., Vol. 21, 787-796, 1986.
doi:10.1029/RS021i005p00787

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

9. King, R. W. P., "New formulas for the electromagnetic field of a vertical electric dipole in a dielectric or conducting half-space near its horizontal interface," J. Appl. Phys., Vol. 53, 8476-8482, Dec. 1982; erratum, Vol. 56, 3366, Dec. 1984.
doi:10.1063/1.330496

10. 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

11. 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

12. 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

13. 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

14. 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

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

16. 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

17. Li, L.-W., T.-S. Yeo, P .-S. Kooi, and M.-S. Leong, "Radio wave propagation along mixed paths through a four-layered model of rain forest: an analytical approach," IEEE Trans. Antennas and Propagat., Vol. 46, No. 7, 1098-1111, 1998.
doi:10.1109/8.704814

18. Hoh, J. H., L. W. Li, P . S. Kooi, T. S. Yeo, and M. S. Leong, "Dominant lateral waves in the canopy layer of a four-layered forest," Radio Sci., Vol. 34, No. 3, 681-691, 1999.
doi:10.1029/1999RS900007

19. Li, L.-W., C.-K. Lee, T.-S. Yeo, and M.-S. Leong, "Wave mode and path characteristics in four-layered anisotropic forest environment," IEEE Trans. Antennas and Propagat., Vol. 52, No. 9, 2445-2455, 2004.
doi:10.1109/TAP.2004.834021

20. 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

21. 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

22. 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

23. Tang, J. L. and W. Hong, "The electromagnetic field produced by a horizontal electric dipole over a dielectric coated perfect conductor," Progress In Electromagnetics Research, Vol. 36, 139-152, 2005.

24. 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

25. Li, K. 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.2005.856374

26. 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

27. 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

28. 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

29. 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

30. 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

31. 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

32. 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

33. 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

34. 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.

35. 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.

36. 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

37. Gradshteyn, I. S. and I. M. Ryzhik, Table of Integrals, Series, and Products, Academic Press, New York, 1980.