volume | PIER Journals

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.

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

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

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.

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

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

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

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

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

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.

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

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.

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.

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

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.

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.

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.

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

Prof. Seil S. Sautbekov

Dr. Sotirios Bourgiotis

Dr. Ariadni Chrysostomou

Professor Panayiotis V. Frangos