volume | PIER Journals

Abstract

The image produced by metamaterial slabs is discussed in a number of papers in terms of the electromagnetic field distribution. In this paper a procedure is proposed to efficiently calculate the image of an extended object placed behind a metamaterial slab as it will be seen by an observer - which can greatly differ from the image formed by the intensity maxima. The first step of the procedure retrieves the dispersion relation of a periodic metamaterial slab from the S parameters calculated with full wave electromagnetic simulation of the unit cell. The second step of the procedure utilizes the retrieved dispersion relation in the transfer matrix method to calculate the image of a point source placed behind the metamaterial slab as a function of the observation angle. Knowing the image distance of the point source for all observation angles, the image of an extended object can be efficiently calculated. The procedure is demonstrated with a Fishnet type metamaterial.

1. Solymar, L. and E. Shamonina, Waves in Metamaterials, Oxford University Press, 2009.

2. Pendry, J. B., "Negative refraction makes a perfect lens," Physical Review Letters, Vol. 85, 3966-3969, 2000.
doi:10.1103/PhysRevLett.85.3966

3. Shelby, R. A., D. R. Smith, and S. Schultz, "Experimental verification of a negative index of refraction," Science, Vol. 292, No. 5514, 77-79, 2001.
doi:10.1126/science.1058847

4. Smith, D. R., J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science, Vol. 305, No. 5685, 788-792, 2004.
doi:10.1126/science.1096796

5. Shalaev, V. M., "Optical negative-index metamaterials," Nature Photonics, Vol. 1, 41-48, 2007.
doi:10.1038/nphoton.2006.49

6. Moitra, P., Y. Yang, Z. Anderson, I. I. Kravchenko, D. P. Briggs, and J. Valentine, "Realization of an all-dielectric zero-index optical metamaterial," Nature Photonics, Vol. 7, 791-795, 2013.
doi:10.1038/nphoton.2013.214

7. Choi, M., S. H. Lee, Y. Kim, S. B. Kang, J. Shin, M. H. Kwak, K.-Y. Kang, Y.-H. Lee, N. Park, and B. Min, "A terahertz metamaterial with unnaturally high refractive index," Nature, Vol. 470, No. 7334, 369-373, 2011.
doi:10.1038/nature09776

8. Ziolkowski, R. W., "Design, fabrication, and testing of double negative metamaterials," IEEE Transactions on Antennas and Propagation, Vol. 51, 1516-1529, 2003.
doi:10.1109/TAP.2003.813622

9. Shalaev, V. M., W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Optics Letters, Vol. 30, No. 24, 3356-3358, 2005.
doi:10.1364/OL.30.003356

10. Cai, W. and V. M. Shalaev, Optical Metamaterials, Springer, 2010.
doi:10.1007/978-1-4419-1151-3

11. Kildishev, A. V., A. Boltasseva, and V. M. Shalaev, "Planar photonics with metasurfaces," Science, Vol. 339, 1232009, 2013.
doi:10.1126/science.1232009

12. Fang, N. and X. Zhang, "Imaging properties of a metamaterial superlens," Applied Physics Letters, Vol. 82, 161-163, 2003.
doi:10.1063/1.1536712

13. Belov, P. and Y. Hao, "Subwavelength imaging at optical frequencies using a transmission device formed by a periodic layered metal-dielectric structure operating in the canalization regime," Physical Review B - Condensed Matter and Materials Physics, Vol. 73, No. 11, 113110, 2006.
doi:10.1103/PhysRevB.73.113110

14. Hegde, R. S., Z. Szabó, Y. L. Hor, Y. Kiasat, E. P. Li, and W. J. R. Hoefer, "The dynamics of nanoscale superresolution imaging with the superlens," IEEE Transactions on Microwave Theory and Techniques, Vol. 59, 2612-2623, 2011.
doi:10.1109/TMTT.2011.2160084

15. Lu, D. and Z. Liu, "Hyperlenses and metalenses for far-field super-resolution imaging," Nature Communications, Vol. 3, 1205, 2012.

16. Szabó, Z., Y. Kiasat, and E. P. Li, "Subwavelength imaging with composite metamaterials," Journal of the Optical Society of America B - Optical Physics, Vol. 31, No. 6, 1298-1307, 2014.
doi:10.1364/JOSAB.31.001298

17. Aieta, F., P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gahurro, F. Capasso, Z. Gaburro, and F. Capasso, "Aberration-free ultrathin at lenses and axicons at telecom wavelengths based on plasmonic metasurfaces," Nano Letters, Vol. 12, No. 9, 4932-4936, 2012.
doi:10.1021/nl302516v

18. Aieta, F., P. Genevet, M. Kats, and F. Capasso, "Aberrations of at lenses and aplanatic metasurfaces," Optics Express, Vol. 21, 31530-31539, 2013.
doi:10.1364/OE.21.031530

19. Luo, C., S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, "All-angle negative refraction without negative effective index," Physical Review B, Vol. 65, No. 20, 201104, 2002.
doi:10.1103/PhysRevB.65.201104

20. Lu, W. T. and S. Sridhar, "Flat lens without optical axis: Theory of imaging," Optics Express, Vol. 13, No. 26, 10673-10680, 2005.
doi:10.1364/OPEX.13.010673

21. Fan, X., G. P. Wang, J. C. W. Lee, and C. T. Chan, "All-angle broadband negative refraction of metal waveguide arrays in the visible range: Theoretical analysis and numerical demonstration," Physical Review Letters, Vol. 97, No. 7, 1-4, 2006.
doi:10.1103/PhysRevLett.97.073901

22. Lu, W. T. and S. Sridhar, "Superlens imaging theory for anisotropic nanostructured metamaterials with broadband all-angle negative refraction," Physical Review B - Condensed Matter and Materials Physics, Vol. 77, No. 23, 1-4, 2008.

23. Yao, J., K.-T. Tsai, Y. Wang, Z. Liu, G. Bartal, Y.-L. Wang, and X. Zhang, "Imaging visible light using anisotropic metamaterial slab lens," Optics Express, Vol. 17, 22380-22385, 2009.
doi:10.1364/OE.17.022380

24. Silin, R., "On the history of backward electromagnetic waves in metamaterials," Metamaterials, Vol. 6, No. 1-2, 1-7, 2012.
doi:10.1016/j.metmat.2012.09.004

25. Menzel, C., C. Rockstuhl, T. Paul, F. Lederer, and T. Pertsch, "Retrieving effective parameters for metamaterials at oblique incidence," Physical Review B, Vol. 77, 195328, 2008.
doi:10.1103/PhysRevB.77.195328

26. Paul, T., C. Rockstuhl, C. Menzel, and F. Lederer, "Anomalous refraction, diffraction, and imaging in metamaterials," Physical Review B, Vol. 79, No. 11, 115430, 2009.
doi:10.1103/PhysRevB.79.115430

27. Szabó, Z., G.-H. H. Park, R. Hedge, and E. P. Li, "A unique extraction of metamaterial parameters based on Kramers-Kronig relationship," IEEE Transactions on Microwave Theory and Techniques, Vol. 58, No. 10, 2646-2653, 2010.
doi:10.1109/TMTT.2010.2065310

28. Szabó, Z. and J. Füzi, "Equivalence of magnetic metamaterials and composites in the view of effective medium theories," IEEE Transactions on Magnetics, Vol. 50, No. 4, 1-4, 2014.
doi:10.1109/TMAG.2013.2288297

29. Chen, X. D., T. M. Grzegorczyk, B. I. Wu, J. Pacheco, and J. A. Kong, "Robust method to retrieve the constitutive effective parameters of metamaterials," Physical Review E, Vol. 70, No. 1, 016608, 2004.
doi:10.1103/PhysRevE.70.016608

30. Brillouin, L., Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices, Courier Corporation, 2003.

31. Bohren, C. F. and D. R. Huffman, Absorption and Scattering of Light by Small Particles, John Wiley & Sons, 2008.

32. Dolling, G., C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Low-loss negative-index metamaterial at telecommunication wavelengths," Optics Letters, Vol. 31, 1800-1802, 2006.
doi:10.1364/OL.31.001800

33. Taflove, A. and S. C. Hagness, Computational Electrodynamics, Artech House Publishers, 2000.

34. Born, M. and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, CUP Archive, 2000.

Mr. Arnold Kalvach

Dr. Zsolt Szabo