Search search
Publication Date
to
Vol. 64
Latest Volume
All Volumes
PIERM 139 PIERM 138 PIERM 137 PIERM 136 PIERM 135 PIERM 134 PIERM 133 PIERM 132 PIERM 131 PIERM 130 PIERM 129 PIERM 128 PIERM 127 PIERM 126 PIERM 125 PIERM 124 PIERM 123 PIERM 122 PIERM 121 PIERM 120 PIERM 119 PIERM 118 PIERM 117 PIERM 116 PIERM 115 PIERM 114 PIERM 113 PIERM 112 PIERM 111 PIERM 110 PIERM 109 PIERM 108 PIERM 107 PIERM 106 PIERM 105 PIERM 104 PIERM 103 PIERM 102 PIERM 101 PIERM 100 PIERM 99 PIERM 98 PIERM 97 PIERM 96 PIERM 95 PIERM 94 PIERM 93 PIERM 92 PIERM 91 PIERM 90 PIERM 89 PIERM 88 PIERM 87 PIERM 86 PIERM 85 PIERM 84 PIERM 83 PIERM 82 PIERM 81 PIERM 80 PIERM 79 PIERM 78 PIERM 77 PIERM 76 PIERM 75 PIERM 74 PIERM 73 PIERM 72 PIERM 71 PIERM 70 PIERM 69 PIERM 68 PIERM 67 PIERM 66 PIERM 65 PIERM 64 PIERM 63 PIERM 62 PIERM 61 PIERM 60 PIERM 59 PIERM 58 PIERM 57 PIERM 56 PIERM 55 PIERM 54 PIERM 53 PIERM 52 PIERM 51 PIERM 50 PIERM 49 PIERM 48 PIERM 47 PIERM 46 PIERM 45 PIERM 44 PIERM 43 PIERM 42 PIERM 41 PIERM 40 PIERM 39 PIERM 38 PIERM 37 PIERM 36 PIERM 35 PIERM 34 PIERM 33 PIERM 32 PIERM 31 PIERM 30 PIERM 29 PIERM 28 PIERM 27 PIERM 26 PIERM 25 PIERM 24 PIERM 23 PIERM 22 PIERM 21 PIERM 20 PIERM 19 PIERM 18 PIERM 17 PIERM 16 PIERM 14 PIERM 13 PIERM 12 PIERM 11 PIERM 10 PIERM 9 PIERM 8 PIERM 7 PIERM 6 PIERM 5 PIERM 4 PIERM 3 PIERM 2 PIERM 1
All Journals
PIER PIER B PIER C PIER M PIER Letters PIER Photonics
2018-01-17
A Novel Asymptotic Solution to the Sommerfeld Radiation Problem: Analytic Field Expressions and the Emergence of the Surface Waves
By
Seil S. Sautbekov,

    Prof. Seil S. Sautbekov

    Al-Farabi Kazakh National University

    Kazakhstan

    Homepage

Sotirios Bourgiotis,

    Dr. Sotirios Bourgiotis

    School of Electrical and Computer Engineering

    National Technical University of Athens

    Greece

    Homepage

Ariadni Chrysostomou,

    Dr. Ariadni Chrysostomou

    School of Electrical and Computer Engineering

    National Technical University of Athens

    Greece

    Homepage

Panayiotis V. Frangos

    Professor Panayiotis V. Frangos

    School of Electrical and Computer Engineering

    National Technical University of Athens

    Greece

    Homepage

Progress In Electromagnetics Research M, Vol. 64, 9-22, 2018
doi:10.2528/PIERM17082806 | Google Scholar

Abstract
The well-known ``Sommerfeld radiation problem" of a small -Hertzian- vertical dipole above flat lossy ground is reconsidered. The problem is examined in the spectral domain, through which it is proved to yield relatively simple integral expressions for the received Electromagnetic (EM) field. Then, using the Saddle Point method, novel analytical expressions for the scattered EM field are obtained, including sliding observation angles. As a result, a closed form solution for the subject matter is provided. Also, the necessary conditions for the emergence of the so-called Surface Wave are discussed as well. A complete mathematical formulation is presented, with detailed derivations where necessary.
Download Full Article (852) View Full Article volume
Citation
Seil S. Sautbekov, Sotirios Bourgiotis, Ariadni Chrysostomou, and Panayiotis V. Frangos, "A Novel Asymptotic Solution to the Sommerfeld Radiation Problem: Analytic Field Expressions and the Emergence of the Surface Waves," Progress In Electromagnetics Research M, Vol. 64, 9-22, 2018.
doi:10.2528/PIERM17082806
References

1. Sommerfeld, A. N., "Propagation of waves in wireless telegraphy," Ann. Phys., Vol. 28, 665-736, Mar. 1909; and Vol. 81, 1135–1153, Dec. 1926.
doi:10.1002/andp.19093330402        Google Scholar

2. Wait, J. R., "The ancient and modern history of EM ground wave propagation," IEEE Antennas and Propagation Magazine, Vol. 40, No. 5, 7-24, Oct. 1998, [online], available: http://dx.doi.org-/10.1109/74.735961.
doi:10.1109/74.735961        Google Scholar

3. King, R. J., "Electromagnetic wave propagation over a constant impedance plane," Electromagnetic wave propagation over a constant impedance plane, Vol. 4, 225-268, 1969, [online], available: http://dx.doi.org/10.1029/RS004i003p00255.        Google Scholar

4. Zenneck, J., "Propagation of plane EM waves along a plane conducting surface," Ann. Phys. (Leipzig), Vol. 23, 846-866, 1907.
doi:10.1002/andp.19073281003        Google Scholar

5. Sarkar, T. K., et al. "Electromagnetic macro modelling of propagation in mobile wireless communication: Theory and experiment," IEEE Antennas and Propagation Magazine, Vol. 54, No. 6, 17-43, Dec. 2012, [online], available: http://dx.doi.org/10.1109/MAP.2012.6387779.
doi:10.1109/MAP.2012.6387779        Google Scholar

6. Bladel, J. G. V., Electromagnetic Fields, Section 9.3: The Sommerfeld Dipole Problem, 448–452, J. Wiley and Sons, Inc., Hoboken, 2007.

7. Banos, A., Jr., Dipole Radiation in the Presence of a Conducting Half-space, Pergamon, 1966.

8. Tyras, G., Radiation and Propagation of Electromagnetic Waves, Academic Press, 1969.

9. Rahmat-Samii, Y., R. Mittra, and P. Parhami, "Evaluation of Sommerfeld integrals for lossy halfspace problems," Electromagn., Vol. 1, 1-28, 1981, [online], available: http://dx.doi.org/10.1080-/02726348108915122.
doi:10.1080/02726348108915122        Google Scholar

10. Collin, R. E., "Hertzian dipole radiating over a lossy earth or sea: Some early and late 20th-century controversies," IEEE Antennas and Propagation Magazine, Vol. 46, No. 2, 64-79, Apr. 2004, [online], available: http://dx.doi.org/10.1109/MAP.2004.1305535.
doi:10.1109/MAP.2004.1305535        Google Scholar

11. Michalski, K. A., "On the efficient evaluation of the integrals arising in the Sommerfeld half-space problem," Inst. Elect. Eng. Proc. Part H — Microwave, Antennas Propagat., Vol. 132, No. 5, 312-318, Aug. 1985, [online], available: http://dx.doi.org/10.1049/ip-h-2.1985.0056.
doi:10.1049/ip-h-2.1985.0056        Google Scholar

12. Pelosi, G. and J. L. Volakis, "The centennial of Sommerfeld’s diffraction problem," Electromagnetics, Vol. 18, No. 2-3, Special Issue, Mar.–Jun. 1998.        Google Scholar

13. Norton, K. A., "The propagation of radio waves over the surface of the Earth," Proceedings of the IRE, Vol. 24, 1367-1387, 1936; and Vol. 25, 1203–1236, 1937, [online], available: http://dx.doi.org-/10.1109/JRPROC.1936.227360.
doi:10.1109/JRPROC.1936.227360        Google Scholar

14. Sautbekov, S., Electromagnetic Waves Propagation in Complex Matter, Chapter: “The Generalized Solutions of a System of Maxwell’s Equations for the Uniaxial Anisotropic Media”, INTECH, 2011, [online], available: http://www.intechopen.com/books/electromagnetic-wavespropagation-in-complex-matter/the-generalized-solutions-of-a-system-of-maxwell-s-equations-forthe-uniaxialanisotropic-media.

15. Christakis, C., K. Ioannidi, S. Sautbekov, P. Frangos, and S. K. Atanov, "The radiation problem from a vertical short dipole antenna above flat and lossy ground: Novel formulation in the spectral domain with closed-form analytical solution in the high frequency regime," Electronics and Electrical Engineering Journal, Vol. 20, No. 9, 35-38, Nov. 2014, [online], available: http://dx.doi.org/10.5755/j01.eee.20.9.8710.        Google Scholar

16. Ioannidi, K., C. Christakis, S. Sautbekov, P. Frangos, and S. K. Atanov, "The radiation problem from a vertical Hertzian dipole antenna above flat and lossy ground: Novel formulation in the spectral domain with closed-form analytical solution in the high frequency regime," International Journal Antennas and Propagation (IJAP), Hindawi Ed. Co., Special Issue Propagation of Electromagnetic (EM) Waves over Terrain (PEWT), Vol. 2014, Article ID 989348, [online], available: http://dx.doi.org/10.1155/2014/989348.        Google Scholar

17. Balanis, C. A., Antenna Theory: Analysis and Design, Appendix VIII:Method of Stationary Phase, 922–927, J. Wiley and Sons Inc., New York, 1997.

18. Moschovitis, C. G., H. Anastassiu, and P. V. Frangos, "Scattering of electromagnetic waves from a rectangular plate using an extended stationary phase method based on fresnel functions (SPM-F)," Progress In Electromagnetic Research, Vol. 107, 63-99, 2010.
doi:10.2528/PIER10040104        Google Scholar

19. Fikioris, J., Introduction to Antenna Theory and Propagation of Electromagnetic Waves, National Technical University of Athens (NTUA), Greek, Athens, Greece, 1982.

20. Arfken, G., Mathematical Methods for Physicists, 3rd Ed., 400-414, Academic Press Inc., Orlando, Florida, USA, 1985.

21. Bourgiotis, S., K. Ioannidi, C. Christakis, S. Sautbekov, and P. Frangos, "The radiation problem from a vertical short dipole antenna above flat and lossy ground: Novel formulation in the spectral domain with numerical solution and closed-form analytical solution in the high frequency regime," CEMA14, 9th International Conference, 12-18, Sofia, Bulgaria, Oct. 2014.        Google Scholar

22. Bourgiotis, S., A. Chrysostomou, K. Ioannidi, S. Sautbekov, and P. Frangos, "Radiation of a vertical dipole over flat and lossy ground using the spectral domain approach: Comparison of stationary phase method analytical solution with numerical integration results," Electronics and Electrical Engineering Journal, Vol. 21, No. 3, 38-41, 2015, [online], available: http://dx.doi.org/10.5755-/j01.eee.21.3.10268.        Google Scholar

23. Chrysostomou, A., S. Bourgiotis, S. Sautbekov, K. Ioannidi, S. Sautbekov, and P. Frangos, "Radiation of a vertical dipole antenna over flat and lossy ground: Accurate electromagnetic field calculation using the spectral domain approach along with redefined integral representations and corresponding novel analytical solution," Electronics and Electrical Engineering Journal, Vol. 22, No. 2, 54-61, 2016.        Google Scholar

24. Weinstein, L. A., The Theory of Diffraction and the Factorization Method, Golem Press, Boulder, Colorado, 1969.

25. Fock, V. A., Diffraction of Radio Waves around the Earth’s Surface, Academy of Sciences, U.S.S.R., 1946.

26. Sautbekov, S. S., "Factorization method for finite fine structures," Progress In Electromagnetic Research B, Vol. 25, 1-21, 2010.
doi:10.2528/PIERB10071801        Google Scholar

Download Full Article (852) View Full Article volume


The EM Academy piers.org jpier.org Who's Who in EM
Copyright © 2022 The Electromagnetics Academy. All Rights Reserved.