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ISSN 2415-3400 (Online)
ISSN 1028-821X (Print)


Stadnyk, OM, Silin, OO

O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine

O. Ya. Usikov Institute for Radiophysics and Electronics of the National Academy of Sciences of Ukraine
12, Proskura st., Kharkov, 61085, Ukraine
E-mail: ostadnyk@ire.kharkov.ua

Language: Russian

The problem of generalization of the classical results on the electric dipole radiation over the Earth's surface in the case of the left-handed metamaterial half-space is important for many practical applications related to the focusing of wave fields. It is desirable to do without undue simplifications: geometrical optics approximation, neglecting losses, restrictions on the wave packet associated with the introduction of the group velocity, neglecting the type (only monopole) of source. In the paper, the model problem of radiation of elementary electric dipole situated normally to the plane boundary between dissipative left-handed and ordinary media has been rigorously solved. The numerical simulation revealed the expected radar pattern-like structure of the reflected field in the first medium and complex (on average tapered) interference field structure with a pronounced maximum in the region of the left-handed metamaterial half-space. The spatial distribution of the electromagnetic field in two media, depending on the height of the dipole and the magnitude of losses in the left-handed metamaterial is presented. The analysis of the Poynting vector streamlines confirmed the hypothesis, previously put forward by the authors, that the change in sign of the tangential component at the interface, that is common for electromagnetic surface waves, is the cause of the focusing ability of the boundary between the normal and the left-handed media, rather than each of them individually.

Keywords: boundary, electric dipole, electromagnetic field, left-handed metamaterial, Poynting vector

Manuscript submitted 02.09.2016
PACS 42.25.Bs; 78.20.Ci; 41.20.Jb; 42.30.Va
Radiofiz. elektron. 2016, 21(3): 88-96

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  1. Sommerfeld, A., 1909. Propagation of waves in wireless telegraphy. Annalen der Physik, 28, pp. 665–736. DOI: https://doi.org/10.1002/andp.19093330402
  2. Sommerfeld, A., 1926. Propagation of waves in wireless telegraphy. Annalen der Physik, 81, pp. 1135–1153. DOI: https://doi.org/10.1002/andp.19263862516
  3. Wait, J. R., 1970. Electromagnetic waves in stratified media. Oxford: Pergamon Press.
  4. Brekhovskikh, L. M., 1973. Waves in stratified media. Moscow: Nauka Publ. (in Russian).
  5. King, R. W. P., Owens, M. and Wu, T. T., 1992. Lateral electromagnetic waves: theory and applications to communications, geophysical exploration, and remote sensing. N. Y.: Springer­Verlag.
  6. Collin, R. E., 2004. Hertzian dipole radiation over a lossy earth or sea: some early and late 20th century controversies. IEEE Antennas Propag. Mag., 46(2), pp. 64–79. DOI: https://doi.org/10.1109/MAP.2004.1305535
  7. Collin, R. E., 2004. Some observations about the near zone electric field of a hertzian dipole above a lossy earth. IEEE Trans. Antennas Propag., 52(11), pp. 3133–3137. DOI: https://doi.org/10.1109/TAP.2004.835270
  8. Fei, T., Li, L.-W., Yeo, T.-S., Wang, H.-L., Wu, Q., 2007. A comparative study of radio wave propagation over the earth due to a vertical electric dipole. IEEE Trans. Antennas Propag., 55(10), pp. 2723–2732. DOI: https://doi.org/10.1109/TAP.2007.905869
  9. Michalski, K. A. and Mosig, J. R., 2016. The Sommerfeld half-space problem revisited: from radio frequencies and Zenneck waves to visible light and Fano modes. J. Electromagn. Waves Appl., 30(1), pp. 1–42. DOI: https://doi.org/10.1080/09205071.2015.1093964
  10. Veselago, V. G., 1967. Electrodynamivs of substances with simultaneously negative values of e and m. Usp. Fiz. Nauk, 92(3), pp. 517–526 (in Russian). DOI: https://doi.org/10.3367/UFNr.0092.196707d.0517
  11. Ivanov, V. K., Silin, A. O., and Stadnik, A. M., 2011. Measurement of complex permittivity of liquids using open-ended coaxial-line and metamaterial substrates. Radiofizika i elektronika, 2(16)(1), pp. 92–99 (in Russian).
  12. Petrin, A. B., 2008. On electromagnetic wave distribution in the medium with negative refraction from the point source situated in air. Pis'ma Zh. Eksp. Teor. Fiz., 87(9), pp. 550–555 (in Russian).
  13. Ivanov, V. K., Silin, А. О. and Stadnik, А. М., 2013. Focusing of electromagnetic field of the elementary electric dipole by the interface between ordinary and left-handed media. Radiofizika i elektronika, 4(18)(4), pp. 40–48 (in Russian).
  14. Stockman, M. I., 2007. Criterion for negative refraction with low optical losses from a fundamental principle of causality. Phys. Rev. Lett., 98(17), pp. 177404 (4 р.).
  15. Zemanian, A. H., 1968. Generalized integral transformations. N. Y.: Intersci. Publ.
  16. Arfken, G. B., Weber, H. J. and Harris, F. E., 2013. Mathematical methods for physicists: a comprehensive guide. Amsterdam: Elsevier.
  17. Bliokh, K. Yu. and Bliokh, Yu. P., 2004. Localization of a stationary electromagnetic field by means of the metamaterial plane interface. Usp. Fiz. Nauk, 174(4), pp. 339–447 (in Russian).
  18. Shevchenko, V. V., 2011. Localization of a stationary electromagnetic field by means of the metamaterial plane interface. Usp. Fiz. Nauk, 181(11), pp. 1171–1181 (in Russian). DOI: https://doi.org/10.3367/UFNr.0181.201111c.1171
  19. Shevchenko, V.V., 2016. On localization of a convergent spherical wave passing through the plane interface. Radiotekhnika i elektronika, 61(5), pp. 442–446 (in Russian).
  20. Pendry, J. B., 2000. Negative refraction makes a perfect lens. Phys. Rev. Lett., 85(18), pp. 3966–3969. DOI: https://doi.org/10.1103/PhysRevLett.85.3966