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


Stadnyk, OM, Silin, OO

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 flat lens conception was considered in the pioneering work of V. G. Veselago, who considered the possibility of electromagnetic waves propagation in media with simultaneously negative permittivity and permeability (according to modern terminology – in the left-handed metamaterials). Later, J. B. Pendry put forward the idea of so-called “superlens”, the resolution of which would exceed the diffraction limit. In view of the prospects for the practical applications it has caused a discussion on the possibility of antiparallelism of phase and group velocities and the actual superresolution implementation for the source in the form of a monopole. However, using the ray theory approximation reduced the generality of the results, neglecting losses radically distorted them, and errors in the theoretical analysis led to the wrong physical interpretation. In this paper, we obtained a rigorous solution to the problem of focusing radiation from elementary electric dipole located perpendicularly to the plane layer of finite thickness made of the left-handed metamaterial with absorption. Spatial distribution of the electromagnetic field in the layer, as well as the incident and reflected fields at various heights of the dipole, layer thickness and losses in each environment are numerically simulated.The analysis of the calculated spatial structure of the electromagnetic field confirmed the focusing ability of the interfaces between ordinary and left-handed media, as well as a flat lens.

Keywords: electric dipole, electromagnetic field, left-handed metamaterial, Pendry lens

Manuscript submitted 07.10.2016
PACS     78.20.Ci; 41.20.Jb; 42.25.Bs; 42.30.Va
Radiofiz. elektron. 2016, 21(4): 40-48
Full text (PDF)

  1. Veselago, V. G., 1967. The electrodynamics 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
  2. 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
  3. 't Hooft, G. W., 2001. Comment on “Negative refraction makes a perfect lens”. Phys. Rev. Lett., 87(24), pp. 249701 (1 p.).
  4. Williams, J. M., 2001. Some problems with negative refraction. Phys. Rev. Lett., 87(24), pp. 249703 (1 p.).
  5. Garcia, N., Nieto-Vesperinas, M., 2002. Left-handed materials do not make a perfect lens. Phys. Rev. Lett., 88(20), pp. 207403 (4 p.).
  6. Shatrov, A. D., 2007. Electrodynamic analysis of a Pendry lens. Radiotekhnika i elektronika, 52(12), pp. 1430–1435 (in Russian). DOI: https://doi.org/10.1134/S1064226907120030
  7. Zhang, X., Forrest, S. R., 2011. Theory of the perfect lens. Phys. Rev. B, 84(4), pp. 045427 (7 р.).
  8. Selina, N. V., Tumayev, E. N., 2016. Propagation of electromagnetic wave in Pendry lens. Nanotechnologies in Russia, 11(5–6), pp. 78–82 (in Russian). DOI: https://doi.org/10.1134/S1995078016030149
  9. Radi, Y., Nikmehr, S., Hosseinzadeh, S., 2016. A novel method for wave focusing investigation in metamaterial half-space and slab lens structures. Int. J. Numer. Model, 29(1), pp. 63–76. DOI: https://doi.org/10.1002/jnm.2046
  10. Wait, J. R., 1970. Electromagnetic waves in stratified media. Oxford: Pergamon Press.
  11. Brekhovskikh, L. M., 1973. Waves in layered media. Мoscow: Nauka Publ. (in Russian).
  12. King, R. W. P., Owens, M., Wu, T. T., 1992. Lateral electromagnetic waves: theory and applications to communications, geophysical exploration, and remote sensing. N. Y.: Springer­Verlag.
  13. King, R. W.  P., Sandler, S. S., 1994. The electromagnetic field of a vertical electric dipole in the presence of a three-layered region. Radio Sci., 29(1), pp. 97–113. DOI: https://doi.org/10.1029/93RS02662
  14. Chew, W. C., 2004. Sommerfeld integrals for left-handed materials. Microw. Opt. Technol. Lett., 42(5), pp. 369–373. DOI: https://doi.org/10.1002/mop.20307
  15. Li, K., 2009. Electromagnetic fields in stratified Media. Berlin: Springer. DOI: https://doi.org/10.1007/978-3-540-95964-9
  16. Novotny, L., Hecht, B., 2012. Principles of nano-optics. Cambridge: Cambridge University Press. DOI: https://doi.org/10.1017/CBO9780511794193
  17. Shreiber, D., Gupta, M., Cravey, R., 2008. Microwave nondestructive evaluation of dielectric materials with a metamaterial lens. Sens. Actuators, A, 144(1), pp. 48–55. DOI: https://doi.org/10.1016/j.sna.2007.12.031
  18. Shreiber, D., Gupta, M., Cravey, R., 2011. Comparative study of 1-D and 2-D metamaterial lens for microwave nondestructive evaluation of dielectric materials. Sens. Actuators, A, 165(2), pp. 256–260. DOI: https://doi.org/10.1016/j.sna.2010.12.004
  19. Ivanov, V. K., Silin, O. O., Stadnyk, O. M., 2013. Focusing of electomagnetic field of the elementary electrical dipole by the interface between ordinary and left-handed media. Radiofizika i elektronika, 4(18)(4), pp. 40–48 (in Russian).
  20. Petrin, A. B., 2008. A point radiator parallel to a plane layer with negative refraction index. Zh. Eksp. Teor. Fiz., 134(3(9)), pp. 436–446 (in Russian).
  21. Petrin, A. B., 2013. On the resolution of lenses made of a negative-index material. Kvantovaya elektronika, 43(9), pp. 814–818 (in Russian).
  22. Stadnyk, O. M., Silin, O. O., 2016. A vertical dipole over metamaterial half-space: distribution of the electromagnetic field and the Poynting vector. Radiofizika i elektronika, 7(21)(3), pp. 88–96 (in Russian).
  23. 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.).
  24. Lagarkov, A. N., Kisel, V. N., 2004. Quality of focusing electromagnetic radiation by a plane-parallel slab with a negative index of refraction. Dokl. Phys., 394(1), pp. 40–45 (in Russian). DOI: https://doi.org/10.1134/1.1648082
  25. Lagarkov, A. N., Kisel, V. N., 2010. Losses in metamaterials: restrictions and benefits. Physica B, 405(14), pp. 2925–2929. DOI: https://doi.org/10.1016/j.physb.2010.01.005
  26. Zemanian, A. H., 1968. Generalized integral transformations. N. Y.: Intersci. Publ.