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A terahertz metamaterial with unnaturally high refractive index


Controlling the electromagnetic properties of materials, going beyond the limit that is attainable with naturally existing substances, has become a reality with the advent of metamaterials1,2,3. The range of various structured artificial ‘atoms’ has promised a vast variety of otherwise unexpected physical phenomena3,4,5,6,7,8,9,10,11,12,13,14,15,16,17, among which the experimental realization of a negative refractive index has been one of the main foci thus far. Expanding the refractive index into a high positive regime will complete the spectrum of achievable refractive index and provide more design flexibility for transformation optics9,10,11,12,13,14. Naturally existing transparent materials possess small positive indices of refraction, except for a few semiconductors and insulators, such as lead sulphide or strontium titanate, that exhibit a rather high peak refractive index at mid- and far-infrared frequencies18. Previous approaches using metamaterials were not successful in realizing broadband high refractive indices19,20,21. A broadband high-refractive-index metamaterial structure was theoretically investigated only recently22, but the proposed structure does not lend itself to easy implementation. Here we demonstrate that a broadband, extremely high index of refraction can be realized from large-area, free-standing, flexible terahertz metamaterials composed of strongly coupled unit cells. By drastically increasing the effective permittivity through strong capacitive coupling and decreasing the diamagnetic response with a thin metallic structure in the unit cell, a peak refractive index of 38.6 along with a low-frequency quasi-static value of over 20 were experimentally realized for a single-layer terahertz metamaterial, while maintaining low losses. As a natural extension of these single-layer metamaterials, we fabricated quasi-three-dimensional high-refractive-index metamaterials, and obtained a maximum bulk refractive index of 33.2 along with a value of around 8 at the quasi-static limit.

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Figure 1: Schematic view of the high-index metamaterials and images of the fabricated metamaterials.
Figure 2: Extracted effective permittivity, permeability, refractive index and figure of merit for high-index metamaterials.
Figure 3: Transmission/reflection spectra of multilayer metamaterials and the band structure.
Figure 4: Effective refractive index and peak index frequency as a function of the gap width for a single-layer metamaterial.

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Smith, D. R., Padilla, J. W., Vier, D. C., Nemat-Nasser, S. C. & Schultz, S. Composite medium with simultaneously negative permeability and permittivity. Phys. Rev. Lett. 84, 4184–4187 (2000)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  5. Eleftheriades, G. V., Iyer, A. K. & Kremer, P. C. Planar negative refractive index media using periodically L–C loaded transmission lines. IEEE Trans. Microwave Theory Tech. 50, 2702–2712 (2002)

    Article  ADS  Google Scholar 

  6. Xiao, S. et al. Loss-free and active optical negative-index metamaterials. Nature 466, 735–738 (2010)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  8. Zhang, S. et al. Negative refractive index in chiral metamaterials. Phys. Rev. Lett. 102, 023901 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  CAS  Google Scholar 

  10. Schurig, D. et al. Metamaterial electromagnetic cloak at microwave frequencies. Science 314, 977–980 (2006)

    Article  ADS  MathSciNet  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  13. Valentine, J., Li, J. S., Zentgraf, T., Bartal, G. & Zhang, X. An optical cloak made of dielectrics. Nature Mater. 8, 568–571 (2009)

    Article  ADS  CAS  Google Scholar 

  14. Gabrielli, L. H., Cardenas, J., Poitras, C. B. & Lipson, M. Silicon nanostructure cloak operating at optical frequencies. Nature Photon. 3, 461–463 (2009)

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  16. Liu, Z., Lee, H., Xiong, Y., Sun, C. & Zhang, X. Far-field optical hyperlens magnifying sub-diffraction-limited objects. Science 315, 1686 (2007)

    Article  ADS  CAS  Google Scholar 

  17. Smolyaninov, I. I., Hung, Y. J. & Davis, C. C. Magnifying superlens in the visible frequency range. Science 315, 1699–1701 (2007)

    Article  ADS  CAS  Google Scholar 

  18. Palik, E. D. Handbook of Optical Constants of Solids (Academic, 1998)

    Google Scholar 

  19. Enkrich, C. et al. Magnetic metamaterials at telecommunication and visible frequencies. Phys. Rev. Lett. 95, 203901 (2005)

    Article  ADS  CAS  Google Scholar 

  20. Sievenpiper, D. F. et al. 3D metallo-dielectric photonic crystals with strong capacitive coupling between metallic islands. Phys. Rev. Lett. 80, 2829–2832 (1998)

    Article  ADS  CAS  Google Scholar 

  21. Shen, J. T., Catrysse, P. B. & Fan, S. Mechanism for designing metallic metamaterials with a high index of refraction. Phys. Rev. Lett. 94, 197401 (2005)

    Article  ADS  CAS  Google Scholar 

  22. Shin, J., Shen, J. T. & Fan, S. Three-dimensional metamaterials with an ultrahigh effective refractive index over a broad bandwidth. Phys. Rev. Lett. 102, 093903 (2009)

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  24. Tao, H. et al. Terahertz metamaterials on free-standing highly-flexible polyimide substrates. J. Phys. D Appl. Phys. 41, 232004 (2008)

    Article  ADS  Google Scholar 

  25. Liu, R., Cui, T. J., Huang, D., Zhao, B. & Smith, D. R. Description and explanation of electromagnetic behaviors in artificial metamaterials based on effective medium theory. Phys. Rev. E 76, 026606 (2007)

    Article  ADS  Google Scholar 

  26. Ferguson, B. & Zhang, X. C. Materials for terahertz science and technology. Nature Mater. 1, 26–33 (2002)

    Article  ADS  CAS  Google Scholar 

  27. Duvillaret, L., Garet, F. & Coutaz, J. L. A reliable method for extraction of material parameters in terahertz time-domain spectroscopy. IEEE J. Sel. Top. Quantum Electron. 2, 739–746 (1996)

    Article  ADS  CAS  Google Scholar 

  28. Liu, N. & Giessen, H. Three-dimensional optical metamaterials as model systems for longitudinal and transverse magnetic coupling. Opt. Express 16, 21233–21238 (2008)

    Article  ADS  Google Scholar 

  29. Papasimakis, N. et al. Metamaterial analog of electromagnetically induced transparency. Phys. Rev. Lett. 101, 253903 (2008)

    Article  ADS  CAS  Google Scholar 

  30. Seo, M. A. et al. Terahertz field enhancement by a metallic nano slit operating beyond the skin-depth limit. Nature Photon. 3, 152–156 (2009)

    Article  ADS  CAS  Google Scholar 

  31. Chen, X., Grzegorczyk, T. M., Wu, B.-I., Pacheco, J. & Kong, J. A. Robust method to retrieve the constitutive effective parameters of metamaterials. Phys. Rev. E 70, 016608 (2004)

    Article  ADS  Google Scholar 

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We thank B. Kang for help in the fabrication of micrometre-gap metamaterials, J. S. Chang for proofreading the manuscript before submission, and D. S. Kim for discussions. This work was supported by National Research Foundation of Korea grants funded by the Korean government (numbers 2009-0069459, 2008-0062235 and 2010-0012058). K.-Y.K. acknowledges support by the IT Research and Development programme of MKE/KEIT (number 2006-S-005-04). Y.-H.L. acknowledges support from the National Research Foundation of Korea (number 2007-0093863) and N.P. acknowledges support from National Research Foundation (numbers GRL K20815000003 and 2010-0001859), funded by the Korean government.

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Authors and Affiliations



M.C. and Y.K. performed the numerical simulations. S.H.L. fabricated micro/nano-gap metamaterial samples. S.B.K., M.H.K. and K.-Y.K. conducted THz-TDs experiments. M.C., S.H.L., Y.K., J.S. and B.M. analysed numerical and experimental data. M.C., S.H.L., Y.K., J.S., Y.-H.L., N.P. and B.M. discussed the results. M.C., J.S., Y.-H.L., N.P. and B.M. wrote the manuscript. B.M. led the overall direction of the project.

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Correspondence to Bumki Min.

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Choi, M., Lee, S., Kim, Y. et al. A terahertz metamaterial with unnaturally high refractive index. Nature 470, 369–373 (2011).

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