volume | PIER Journals

Abstract

We investigate radiation of a dipole at or below the interface of (an)isotropic Epsilon Near Zero (ENZ) media, akin to the classic problem of a dipole above a dielectric half-space. To this end, the radiation patterns of dipoles at the interface of air and a general anisotropic medium (or immersed inside the medium) are derived using the Lorentz reciprocity method. By using an ENZ halfspace, air takes on the role of the denser medium. Thus we obtain shaped radiation patterns in air which were only previously attainable inside the dielectric half-space. We then follow the early work of Collin on anisotropic artificial dielectrics which readily enables the implementation of practical anisotropic ENZs by simply stacking sub-wavelength periodic bi-layers of metal and dielectric at optical frequencies. We show that when such a realistic anisotropic ENZ has a low longitudinal permittivity, the desired shaped radiation patterns are achieved in air. In such cases the radiation is also much stronger in air than in the ENZ media, as air is the denser medium. Moreover, we investigate the subtle differences of the dipolar patterns when the anisotropic ENZ dispersion is either elliptic or hyperbolic.

1. Sommerfeld, A., "Uber die ausbreitung der wellen in der drahtlosen telegraphie," Annalen der Physik, Vol. 333, No. 4, 665-736, 1909.

2. Norton, K., "The propagation of radio waves over the surface of the earth and in the upper atmosphere," Proceedings of the Institute of Radio Engineers, Vol. 24, No. 10, 1367-1387, 1936.

3. Felsen, L., "Radiation from a uniaxially anisotropic plasma half space," IEEE Transactions on Antennas and Propagation, Vol. 11, No. 4, 469-484, 1963.

4. Kong, J., "Electromagnetic fields due to dipole antennas over stratified anisotropic media," Geophysics, Vol. 37, No. 6, 985-996, 1972.

5. Lukosz, W. and R. E. Kunz, "Light emission by magnetic and electric dipoles close to a plane interface. I. Total radiated power," J. Opt. Soc. Am., Vol. 67, No. 12, 1607-1615, 1977.

6. Lukosz, W. and R. E. Kunz, "Light emission by magnetic and electric dipoles close to a plane dielectric interface. II. Radiation patterns of perpendicular oriented dipoles," J. Opt. Soc. Am., Vol. 67, No. 12, 1615-1619, 1977.

7. Lukosz, W., "Light emission by magnetic and electric dipoles close to a plane dielectric interface. III. Radiation patterns of dipoles with arbitrary orientation," J. Opt. Soc. Am., Vol. 69, No. 11, 1495-1503, 1979.

8. King, R. and G. Smith, Antennas in Matter: Fundamentals, Theory and Applications, MIT Press, Cambridge, MA, 1981.

9. Brewitt-Taylor, C., D. Gunton, and H. Rees, "Planar antennas on a dielectric surface," Electronics Letters, Vol. 17, No. 20, 729-731, 1981.

10. Rahmat-Samii, Y., R. Mittra, and P. Parhami, "Evaluation of sommerfeld integrals for lossy half-space problems," Electromagnetics, Vol. 1, No. 1, 1-28, 1981.

11. Engheta, N., C. H. Papas, and C. Elachi, "Radiation patterns of interfacial dipole antennas," Radio Science, Vol. 17, No. 6, 1557-1566, 1982.

12. Rutledge, D. and M. Muha, "Imaging antenna arrays," IEEE Transactions on Antennas and Propagation, Vol. 30, No. 4, 535-540, 1982.

13. Smith, G., "Directive properties of antennas for transmission into a material half-space," IEEE Transactions on Antennas and Propagation, Vol. 32, No. 3, 232-246, 1984.

14. Engheta, N., C. Papas, and C. Elachi, "Interface extinction and subsurface peaking of the radiation pattern of a line source," Applied Physics B, Vol. 26, No. 4, 231-238, 1981.

15. Valle, S., L. Zanzi, M. Sgheiz, G. Lenzi, and J. Friborg, "Ground penetrating radar antennas: Theoretical and experimental directivity functions," IEEE Transactions on Geoscience and Remote Sensing, Vol. 39, No. 4, 749-759, 2001.

16. Radzevicius, S. J., C.-C. Chen, L. Peters, Jr., and J. J. Daniels, "Nearfield dipole radiation dynamics through FDTD modeling," Journal of Applied Geophysics, Vol. 52, No. 23, 75-91, 2003.

17. Sarabandi, K., M. D. Casciato, and I.-S. Koh, "Efficient calculation of the fields of a dipole radiating above an impedance surface," IEEE Transactions on Antennas and Propagation, Vol. 50, No. 9, 1222-1235, 2002.

18. 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.

19. Firouzeh, Z. H., G. A. Vandenbosch, R. Moini, S. H. H. Sadeghi, and R. Faraji-Dana, "Efficient evaluation of Green's functions for lossy half-space problems," Progress In Electromagnetics Research, Vol. 109, 139-157, 2010.

20. Parise, M., "Exact electromagnetic field excited by a vertical magnetic dipole on the surface of a lossy half-space," Progress In Electromagnetics Research B, Vol. 23, 69-82, 2010.

21. Luan, L., P. R. Sievert, and J. B. Ketterson, "Near-field and farfield electric dipole radiation in the vicinity of a planar dielectric half space," New Journal of Physics, Vol. 8, No. 11, 264, 2006.

22. Felsen, L., "Lateral waves on an anisotropic plasma interface," IRE Transactions on Antennas and Propagation, Vol. 10, No. 3, 347-349, 1962.

23. Shavit, R. and E. Rosen, "Lateral wave contribution to the radiation from a dielectric half medium," IEEE Transactions on Antennas and Propagation, Vol. 43, No. 7, 751-755, 1995.

24. Rafi, G. Z., R. Moini-Mazandaran, and R. Faraji-Dana, "A new time domain approach for analysis of vertical magnetic dipole radiation in front of lossy half-space," Progress In Electromagnetics Research, Vol. 29, 57-68, 2000.

25. Tsalamengas, J. and N. Uzunoglu, "Radiation from a dipole near a general anisotropic layer," IEEE Transactions on Antennas and Propagation, Vol. 38, No. 1, 9-16, 1990.

26. Saarinen, J. J. and J. E. Sipe, "A Green function approach to surface optics in anisotropic media," Journal of Modern Optics, Vol. 55, No. 1, 13-32, 2008.

27. Alù, A., M. G. Silveirinha, A. Salandrino, and N. Engheta, "Epsilon-near-zero metamaterials and electromagnetic sources: Tailoring the radiation phase pattern," Phys. Rev. B, Vol. 75, 155410, 2007.

28. Memarian, M. and G. V. Eleftheriades, "Radiation of dipoles at the interface of low permittivity media," Proc. IEEE International Symp. on Antennas and Propagation, 2013.

29. Collin, R. E., "A simple artificial anisotropic dielectric medium," IRE Transactions on Microwave Theory and Techniques, Vol. 6, No. 2, 206-209, 1958.

30. Collin, R. E., Field Theory of Guided Waves, IEEE Press Series on Electromagnetic Wave Theory, Wiley, 1990.

31. Enoch, S., G. Tayeb, P. Sabouroux, N. Guérin, and P. Vincent, "A metamaterial for directive emission," Physical Review Letters, Vol. 89, No. 21, 213902, 2002.

32. Salandrino, A. and N. Engheta, "Far-field subdiffraction optical microscopy using metamaterial crystals: Theory and simulations," Phys. Rev. B, Vol. 74, 075103, 2006.

33. Jacob, Z., L. V. Alekseyev, and E. Narimanov, "Optical hyperlens: Far-field imaging beyond the diffraction limit," Opt. Express, Vol. 14, No. 18, 8247-8256, 2006.

34. Liu, Z., H. Lee, Y. Xiong, C. Sun, and X. Zhang, "Far-field optical hyperlens magnifying sub-diffraction-limited objects," Science, Vol. 315, No. 5819, 1686, 2007.

35. Fang, A., T. Koschny, and C. M. Soukoulis, "Optical anisotropic metamaterials: Negative refraction and focusing," Phys. Rev. B, Vol. 79, 245127, 2009.

36. Engheta, N., "Pursuing near-zero response," Science, Vol. 340, No. 6130, 286-287, 2013.

37. Elser, J., V. A. Podolskiy, I. Salakhutdinov, and I. Avrutsky, "Nonlocal effects in effective-medium response of nanolayered metamaterials," Applied Physics Letters, Vol. 90, No. 19, 191109, 2007.

38. Orlov, A. A., P. M. Voroshilov, P. A. Belov, and Y. S. Kivshar, "Engineered optical nonlocality in nanostructured metamaterials," Phys. Rev. B, Vol. 84, 045424, 2011.

39. Chebykin, A. V., A. A. Orlov, A. V. Vozianova, S. I. Maslovski, Y. S. Kivshar, and P. A. Belov, "Nonlocal effective medium model for multilayered metal-dielectric metamaterials," Phys. Rev. B, Vol. 84, 115438, 2011.

40. Chebykin, A. V., A. A. Orlov, C. R. Simovski, Y. S. Kivshar, and P. A. Belov, "Nonlocal effective parameters of multilayered metaldielectric metamaterials," Phys. Rev. B, Vol. 86, 115420, 2012.

41. Naik, G. V., J. Liu, A. V. Kildishev, V. M. Shalaev, and A. Boltasseva, "Demonstration of Al : ZnO as a plasmonic component for near-infrared metamaterials," Proceedings of the National Academy of Sciences, Vol. 109, No. 23, 8834-8838, 2012.

42. Chern, R.-L., "Spatial dispersion and nonlocal effective permittivity for periodic layered metamaterials," Opt. Express, Vol. 21, No. 14, 16514-16527, 2013.

43. Alù, A. and N. Engheta, "Extremely anisotropic boundary conditions and their optical applications," Radio Science, Vol. 46, No. 5, 1-8, 2011.

Mr. Mohammad Memarian

Dr. George Eleftheriades