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A single-layer wide-angle negative-index metamaterial at visible frequencies

Nature Materials volume 9, pages 407–412 (2010)Cite this article

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Abstract

Metamaterials are materials with artificial electromagnetic properties defined by their sub-wavelength structure rather than their chemical composition. Negative-index materials (NIMs) are a special class of metamaterials characterized by an effective negative index that gives rise to such unusual wave behaviour as backwards phase propagation and negative refraction. These extraordinary properties lead to many interesting functions such as sub-diffraction imaging1,2 and invisibility cloaking3,4,5,6. So far, NIMs have been realized through layering of resonant structures, such as split-ring resonators, and have been demonstrated at microwave7,8 to infrared9,10,11,12,13 frequencies over a narrow range of angles-of-incidence and polarization. However, resonant-element NIM designs suffer from the limitations of not being scalable to operate at visible frequencies because of intrinsic fabrication limitations14, require multiple functional layers to achieve strong scattering13,14 and have refractive indices that are highly dependent on angle of incidence and polarization. Here we report a metamaterial composed of a single layer of coupled plasmonic coaxial waveguides that exhibits an effective refractive index of −2 in the blue spectral region with a figure-of-merit larger than 8. The resulting NIM refractive index is insensitive to both polarization and angle-of-incidence over a ±50∘ angular range, yielding a wide-angle NIM at visible frequencies.

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Figure 1: Negative-index metamaterial geometry.
Figure 2: Coaxial waveguide dispersion relations.
Figure 3: Metamaterial index.
Figure 4: NIM effective parameters.
Figure 5: Wedge refraction.

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References

  1. Pendry, J. B. Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000).

    Article  CAS  Google Scholar 

  2. Fang, N., Lee, H., Sun, C. & Zhang, X. Sub-diffraction-limited optical imaging with a silver superlens. Science 308, 534–537 (2005).

    Article  CAS  Google Scholar 

  3. Alu, A. & Engheta, N. Multifrequency optical invisibility cloak with layered plasmonic shells. Phys. Rev. Lett. 100, 113901 (2008).

    Article  Google Scholar 

  4. Cai, W., Chettiar, U. K., Kildishev, A. V. & Shalaev, V. M. Optical cloaking with metamaterials. Nature Photon. 1, 224–227 (2007).

    Article  CAS  Google Scholar 

  5. Liu, R. et al. Broadband ground-plane cloak. Science 323, 366–369 (2009).

    Article  CAS  Google Scholar 

  6. Pendry, J. B., Schurig, D. & Smith, D. R. Controlling electromagnetic fields. Science 312, 1780–1782 (2006).

    Article  CAS  Google Scholar 

  7. Parazzoli, C. G. et al. Experimental verification and simulation of negative index of refraction using Snell’s law. Phys. Rev. Lett. 90, 107401 (2003).

    Article  CAS  Google Scholar 

  8. Shelby, R. A., Smith, D. R. & Schultz, S. Experimental verification of a negative index of refraction. Science 292, 77–79 (2001).

    Article  CAS  Google Scholar 

  9. Dolling, G. et al. Simultaneous negative phase and group velocity of light in a metamaterial. Science 312, 892–894 (2006).

    Article  CAS  Google Scholar 

  10. Dolling, G., Wegener, M. & Linden, S. Realization of a three-functional-layer negative-index photonic metamaterial. Opt. Lett. 32, 551–553 (2007).

    Article  CAS  Google Scholar 

  11. Shalaev, V. M. et al. Negative index of refraction in optical metamaterials. Opt. Lett. 30, 3356–3358 (2005).

    Article  Google Scholar 

  12. Valentine, J. et al. Three-dimensional optical metamaterial with a negative refractive index. Nature 455, 376–379 (2008).

    Article  CAS  Google Scholar 

  13. Zhang, S. et al. Experimental demonstration of near-infrared negative-index metamaterials. Phys. Rev. Lett. 95, 137404 (2005).

    Article  Google Scholar 

  14. Dolling, G., Wegener, M., Soukoulis, C. M. & Linden, S. Negative-index metamaterial at 780 nm wavelength. Opt. Lett. 32, 53–55 (2007).

    Article  CAS  Google Scholar 

  15. Veselago, V. G. The electrodynamics of substances with simultaneously negative values of ɛ and μ. Sov. Phys. Usp. 10, 509–514 (1968).

    Article  Google Scholar 

  16. Pendry, J. B., Holden, A. J., Robbins, D. J. & Stewart, W. J. Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Microw. Theory 47, 2075–2084 (1999).

    Article  Google Scholar 

  17. Smith, D. R. et al. Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 84, 4184–4187 (2000).

    Article  CAS  Google Scholar 

  18. Dionne, J. A., Verhagen, E., Polman, A. & Atwater, H. A. Are negative index materials achievable with surface plasmon waveguides? A case study of three plasmonic geometries. Opt. Express 16, 19001–19017 (2008).

    Article  CAS  Google Scholar 

  19. Lezec, H. J., Dionne, J. A. & Atwater, H. A. Negative refraction at visible frequencies. Science 316, 430–432 (2007).

    Article  CAS  Google Scholar 

  20. Shvets, G. Photonic approach to making a material with a negative index of refraction. Phys. Rev. B 67, 035109 (2003).

    Article  Google Scholar 

  21. Chettiar, U. K. et al. Dual-band negative index metamaterial: Double negative at 813 nm and single negative at 772 nm. Opt. Lett. 32, 1671–1673 (2007).

    Article  Google Scholar 

  22. Liu, Y., Bartal, G. & Zhang, X. All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region. Opt. Express 16, 15439–15448 (2008).

    Article  CAS  Google Scholar 

  23. Baida, F. I., Belkhir, A., Labeke, D. V. & Lamrous, O. Subwavelength metallic coaxial waveguides in the optical range: Role of the plasmonic modes. Phys. Rev. B 74, 205419 (2006).

    Article  Google Scholar 

  24. Novotny, L. & Hafner, C. Light propagation in a cylindrical waveguide with a complex, metallic, dielectric function. Phys. Rev. E 50, 4094–4106 (1994).

    Article  CAS  Google Scholar 

  25. Johnson, P. B. & Christy, R. W. Optical constants of the noble metals. Phys. Rev. B 6, 4370–4379 (1972).

    Article  CAS  Google Scholar 

  26. Palik, E. D. & Ghosh, G. Handbook of Optical Constants of Solids (Academic, 1985).

    Google Scholar 

  27. Soukoulis, C. M., Linden, S. & Wegener, M. Negative refractive index at optical wavelengths. Science 315, 47–49 (2007).

    Article  CAS  Google Scholar 

  28. Smith, D. R., Vier, D. C., Koschny, T. & Soukoulis, C. M. Electromagnetic parameter retrieval from inhomogeneous metamaterials. Phys. Rev. E 71, 036617 (2005).

    Article  CAS  Google Scholar 

  29. Minowa, Y. et al. Evaluation of effective electric permittivity and magnetic permeability in metamaterial slabs by terahertz time-domain spectroscopy. Opt. Express 16, 4785–4796 (2008).

    Article  Google Scholar 

  30. de Waele, R., Burgos, S. P., Polman, A. & Atwater, H. A. Plasmon dispersion in coaxial waveguides from single-cavity optical transmission measurements. Nano Lett. 9, 2832–2837 (2009).

    Article  CAS  Google Scholar 

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Acknowledgements

We would like to thank J. A. Dionne, H. J. Lezec, E. Verhagen, and A. F. Koenderink for fruitful discussions. This work was supported by the Energy Frontier Research Center program of the Office of Science of the Department of Energy under grant DE-SC0001293, by the National Science Foundation under the Graduate Research Fellowship Program, and made use of facilities supported by the Center for Science and Engineering of Materials, an NSF Materials Research Science and Engineering Center at Caltech. This work is also part of the research program of the ‘Stichting voor Fundamenteel Onderzoek der Materie (FOM)’, which is financially supported by the ‘Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO)’. It was also supported by ‘NanoNed’, a nanotechnology program funded by the Dutch Ministry of Economic Affairs.

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  1. Stanley P. Burgos and Rene de Waele: These authors contributed equally to this work

Authors and Affiliations

  1. Kavli Nanoscience Institute, California Institute of Technology, MS 128-95, Pasadena, California 91125, USA

    Stanley P. Burgos & Harry A. Atwater

  2. Center for Nanophotonics, FOM Institute AMOLF, Science Park 104, 1098 XG Amsterdam, The Netherlands

    Rene de Waele & Albert Polman

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  1. Stanley P. Burgos
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  2. Rene de Waele
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  3. Albert Polman
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  4. Harry A. Atwater
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Contributions

H.A.A. conceived the idea. H.A.A. and A.P. provided guidance throughout the project’s development. S.P.B. took the lead in the FDTD analysis. R.D.W. took the lead in developing the analytic coaxial waveguide theory and code. S.P.B., R.D.W., A.P. and H.A.A. all contributed to the writing and editing of the manuscript.

Corresponding authors

Correspondence to Stanley P. Burgos, Rene de Waele or Harry A. Atwater.

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The authors declare no competing financial interests.

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Burgos, S., de Waele, R., Polman, A. et al. A single-layer wide-angle negative-index metamaterial at visible frequencies. Nature Mater 9, 407–412 (2010). https://doi.org/10.1038/nmat2747

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