Vol. 81
Latest Volume
All Volumes
PIER 176 [2023] PIER 175 [2022] PIER 174 [2022] PIER 173 [2022] PIER 172 [2021] PIER 171 [2021] PIER 170 [2021] PIER 169 [2020] PIER 168 [2020] PIER 167 [2020] PIER 166 [2019] PIER 165 [2019] PIER 164 [2019] PIER 163 [2018] PIER 162 [2018] PIER 161 [2018] PIER 160 [2017] PIER 159 [2017] PIER 158 [2017] PIER 157 [2016] PIER 156 [2016] PIER 155 [2016] PIER 154 [2015] PIER 153 [2015] PIER 152 [2015] PIER 151 [2015] PIER 150 [2015] PIER 149 [2014] PIER 148 [2014] PIER 147 [2014] PIER 146 [2014] PIER 145 [2014] PIER 144 [2014] PIER 143 [2013] PIER 142 [2013] PIER 141 [2013] PIER 140 [2013] PIER 139 [2013] PIER 138 [2013] PIER 137 [2013] PIER 136 [2013] PIER 135 [2013] PIER 134 [2013] PIER 133 [2013] PIER 132 [2012] PIER 131 [2012] PIER 130 [2012] PIER 129 [2012] PIER 128 [2012] PIER 127 [2012] PIER 126 [2012] PIER 125 [2012] PIER 124 [2012] PIER 123 [2012] PIER 122 [2012] PIER 121 [2011] PIER 120 [2011] PIER 119 [2011] PIER 118 [2011] PIER 117 [2011] PIER 116 [2011] PIER 115 [2011] PIER 114 [2011] PIER 113 [2011] PIER 112 [2011] PIER 111 [2011] PIER 110 [2010] PIER 109 [2010] PIER 108 [2010] PIER 107 [2010] PIER 106 [2010] PIER 105 [2010] PIER 104 [2010] PIER 103 [2010] PIER 102 [2010] PIER 101 [2010] PIER 100 [2010] PIER 99 [2009] PIER 98 [2009] PIER 97 [2009] PIER 96 [2009] PIER 95 [2009] PIER 94 [2009] PIER 93 [2009] PIER 92 [2009] PIER 91 [2009] PIER 90 [2009] PIER 89 [2009] PIER 88 [2008] PIER 87 [2008] PIER 86 [2008] PIER 85 [2008] PIER 84 [2008] PIER 83 [2008] PIER 82 [2008] PIER 81 [2008] PIER 80 [2008] PIER 79 [2008] PIER 78 [2008] PIER 77 [2007] PIER 76 [2007] PIER 75 [2007] PIER 74 [2007] PIER 73 [2007] PIER 72 [2007] PIER 71 [2007] PIER 70 [2007] PIER 69 [2007] PIER 68 [2007] PIER 67 [2007] PIER 66 [2006] PIER 65 [2006] PIER 64 [2006] PIER 63 [2006] PIER 62 [2006] PIER 61 [2006] PIER 60 [2006] PIER 59 [2006] PIER 58 [2006] PIER 57 [2006] PIER 56 [2006] PIER 55 [2005] PIER 54 [2005] PIER 53 [2005] PIER 52 [2005] PIER 51 [2005] PIER 50 [2005] PIER 49 [2004] PIER 48 [2004] PIER 47 [2004] PIER 46 [2004] PIER 45 [2004] PIER 44 [2004] PIER 43 [2003] PIER 42 [2003] PIER 41 [2003] PIER 40 [2003] PIER 39 [2003] PIER 38 [2002] PIER 37 [2002] PIER 36 [2002] PIER 35 [2002] PIER 34 [2001] PIER 33 [2001] PIER 32 [2001] PIER 31 [2001] PIER 30 [2001] PIER 29 [2000] PIER 28 [2000] PIER 27 [2000] PIER 26 [2000] PIER 25 [2000] PIER 24 [1999] PIER 23 [1999] PIER 22 [1999] PIER 21 [1999] PIER 20 [1998] PIER 19 [1998] PIER 18 [1998] PIER 17 [1997] PIER 16 [1997] PIER 15 [1997] PIER 14 [1996] PIER 13 [1996] PIER 12 [1996] PIER 11 [1995] PIER 10 [1995] PIER 09 [1994] PIER 08 [1994] PIER 07 [1993] PIER 06 [1992] PIER 05 [1991] PIER 04 [1991] PIER 03 [1990] PIER 02 [1990] PIER 01 [1989]
2008-02-05
Electromagnetic Field of a Horizontal Electric Dipole in the Presence of a Four-Layered Region
By
Progress In Electromagnetics Research, Vol. 81, 371-391, 2008
Abstract
In this paper, we study in detail the electromagnetic field excited by a horizontal electric dipole in the presence of a four-layered region, which consists of a perfect conductor, the two dielectric layers, and air above. From the derivations and analysis, it is seen that the electromagnetic field includes four wave modes: Direct wave, ideal reflected wave, trapped surface wave, and lateral wave. The wave numbers of the trapped surface wave, which are determined by the residues of the poles, are between the wave number k0 in the air and k2 in the lower dielectric layer. The lateral waves with the wave number being k0 are determined by the integrations along the branch cuts. It should be pointed out that both the trapped surface wave and lateral wave can be separated into the electric-type terms and magnetic-type terms. Analysis and computations show that the trapped surface waves play major roles at large propagation distance when both the dipole point and the observation point are on or close to the air-dielectric boundary.
Citation
Yi Hui Xu Kai Li Liang 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
http://www.jpier.org/PIER/pier.php?paper=08012303
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 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 edition, Pergamon Press, New York, 1970.

6. Banos, A., Dipole Radiation in the Presence of a Conducting Halfspace, 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. 56, No. 12, 8476-8482, 1984.

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 Sheldon 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. 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

18. 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

19. 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

20. 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

21. 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

22. 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

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 threedielectric- layered substrates rectangular patch microstrip antenna for communication systems," Progress In Electromagnetics Research Letters, Vol. 2, 157-165, 2008.

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.

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, 2002.
doi:10.1029/2000RS002348

30. 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

31. 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.
doi:10.2528/PIER02011801

32. 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

33. 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

34. 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

35. 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

36. Xu, Y. H., K. Li, and L. Liu, "Trapped surface wave and lateral wave in the presence of a four-layered region," submitted to IEEE Trans. Electromag. Compat., 2007.

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