Metamaterials are artificially engineered structures that have properties, such as a negative refractive index1,2,3,4, not attainable with naturally occurring materials. Negative-index metamaterials (NIMs) were first demonstrated for microwave frequencies5,6, but it has been challenging to design NIMs for optical frequencies and they have so far been limited to optically thin samples because of significant fabrication challenges and strong energy dissipation in metals7,8. Such thin structures are analogous to a monolayer of atoms, making it difficult to assign bulk properties such as the index of refraction. Negative refraction of surface plasmons was recently demonstrated but was confined to a two-dimensional waveguide9. Three-dimensional (3D) optical metamaterials have come into focus recently, including the realization of negative refraction by using layered semiconductor metamaterials and a 3D magnetic metamaterial in the infrared frequencies; however, neither of these had a negative index of refraction10,11. Here we report a 3D optical metamaterial having negative refractive index with a very high figure of merit of 3.5 (that is, low loss). This metamaterial is made of cascaded ‘fishnet’ structures, with a negative index existing over a broad spectral range. Moreover, it can readily be probed from free space, making it functional for optical devices. We construct a prism made of this optical NIM to demonstrate negative refractive index at optical frequencies, resulting unambiguously from the negative phase evolution of the wave propagating inside the metamaterial. Bulk optical metamaterials open up prospects for studies of 3D optical effects and applications associated with NIMs and zero-index materials such as reversed Doppler effect, superlenses, optical tunnelling devices12,13, compact resonators and highly directional sources14.
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Veselago, V. G. The electrodynamics of substances with simultaneously negative values of ε and μ . Sov. Phys. Usp. 10, 509–514 (1968)
Smith, D. R., Pendry, J. B. & Wiltshire, M. C. K. Metamaterials and negative refractive index. Science 305, 788–792 (2004)
Pendry, J. B. Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000)
Tsakmakidis, K. L., Boardman, A. D. & Hess, O. ‘Trapped rainbow’ storage of light in metamaterials. Nature 450, 397–401 (2007)
Shelby, R. A., Smith, D. R. & Schultz, S. Experimental verification of a negative index of refraction. Science 292, 77–79 (2001)
Parazzoli, C. G., Greegor, K., Li, K., Koltenbah, B. E. C. & Tanielian, M. Experimental verification of negative index of refraction using Snell’s law. Phys. Rev. Lett. 90, 107401 (2003)
Panoiu, N. C. & Osgood, R. M. Numerical investigations of negative refractive index metamaterials at infrared and optical frequencies. Opt. Commun. 223, 331–337 (2003)
Shalaev, V. M. et al. Optical negative-index metamaterials. Nature Photonics 1, 41–48 (2007)
Lezec, H. J., Dionne, N. A. & Atwater, H. A. Negative refraction at visible frequencies. Science 316, 430–432 (2007)
Liu, N. et al. Three-dimensional photonic metamaterials at optical frequencies. Nature Mater. 7, 31–37 (2008)
Hoffman, A. J. et al. Negative refraction in semiconductor metamaterials. Nature Mater. 6, 946–950 (2007)
Silveirinha, M. & Engheta, N. Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials. Phys. Rev. Lett. 97, 157403 (2006)
Edwards, B. et al. Experimental verification of epsilon-near-zero metamaterial coupling and energy squeezing using a microwave waveguide. Phys. Rev. Lett. 100, 033903 (2008)
Enoch, S. et al. A metamaterial for directive emission. Phys. Rev. Lett. 89, 213902 (2002)
Yen, T. J. et al. Terahertz magnetic response from artificial materials. Science 303, 1494–1496 (2004)
Padilla, W. J. et al. Dynamical electric and magnetic metamaterial response at terahertz frequencies. Phys. Rev. Lett. 96, 107401 (2006)
Chen, H. T. et al. Active terahertz metamaterial devices. Nature 444, 597–600 (2006)
Linden, S. et al. Magnetic response of metamaterials at 100 terahertz. Science 306, 1351–1353 (2004)
Soukoulis, C. M., Linden, S. & Wegener, M. Negative refractive index at optical frequencies. Science 315, 47–49 (2007)
Dolling, G., Wegener, M. & Linden, S. Realization of a three-functional-layer negative-index photonic metamaterial. Opt. Lett. 32, 551–553 (2007)
Alu, A. & Engheta, N. Three-dimensional nanotransmission lines at optical frequencies: A recipe for broad band negative-refraction optical metamaterials. Phys. Rev. B 75, 024304 (2007)
Zhang, S. et al. Optical negative-index bulk metamaterials consisting of 2D perforated metal-dielectric stacks. Opt. Express 14, 6778–6787 (2006)
Li, T. et al. Coupling effect of magnetic polariton in perforated metal/dielectric layered metamaterials and its influence on negative refraction transmission. Opt. Express 14, 11155–11163 (2006)
Eleftheriades, G. V. Analysis of bandwidth and loss in negative-refractive-index transmission-line (NRI–TL) media using coupled resonators. IEEE Microw. Wireless Components Lett. 17, 412–414 (2007)
Grbic, A. & Eleftheriades, G. V. Overcoming the diffraction limit with a planar left-handed transmission-line lens. Phys. Rev. Lett. 92, 117403 (2004)
Lai, A., Carloz, C. & Itoh, T. Composite right-/left-handed composite transmission line metamaterials. IEEE Microw. Mag. 5, 34–50 (2004)
Pendry, J. B., Holdenz, A. J., Robbins, D. J. & Stewartz, W. J. Low frequency plasmons in thin-wire structures. J. Phys. Condens. Matter 10, 4785–4809 (1998)
Fan, X. B. et al. All-angle broadband negative refraction of metal waveguide arrays in the visible range: Theoretical analysis and numerical demonstration. Phys. Rev. Lett. 97, 073901 (2006)
Notomi, M. Theory of light propagation in strongly modulated photonic crystals: Refraction-like behavior in the vicinity of the photonic band gap. Phys. Rev. B 62, 10696 (2000)
Johnson, P. B. & Christy, R. W. Optical constants of the noble metals. Phys. Rev. B 6, 4370–4379 (1972)
We acknowledge funding support from US Army Research Office (ARO) MURI programme 50432-PH-MUR and partly by the NSF Nano-scale Science and Engineering Center DMI-0327077. We thank H. Bechtel and M. C. Martin for assisting in measurements of near-infrared transmission and reflection, and S. R. J. Brueck for discussion. T.Z. acknowledges a fellowship from the Alexander von Humboldt Foundation. Multilayer deposition was performed at the Molecular Foundry, Lawrence Berkeley National Laboratory, which is supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract no. DE-AC02-05CH11231.
This file contains Supplementary Figure S1 with Legend and a more detailed Methods Section. The Supplementary Figure S1 shows the effect of the number of functional layers on the index of refraction and the effect of intrinsic loss in the silver on the index of refraction. The Methods Section contains a more detailed description of the fabrication and experimental measurement procedure. (PDF 309 kb)
The file contains Supplementary Movie 1. This FDTD simulation shows the evolution of the electric and magnetic fields as light passes through the prism, experiencing a negative index of refraction. (MOV 1496 kb)
The file contains Supplementary Movie 2. This FDTD simulation of the magnetic field evolution in a single in-plane unit cell demonstrates that the response of the fishnet is dominated by the cascaded fishnet L-C circuits and not the in-plane periodicity. (MOV 1528 kb)
The file contains Supplementary Movie 3. This FDTD simulation of the electric field evolution in a single in-plane unit cell demonstrates that the response of the fishnet is dominated by the cascaded fishnet L-C circuits and not the in-plane periodicity. (MOV 1507 kb)
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Valentine, J., Zhang, S., Zentgraf, T. et al. Three-dimensional optical metamaterial with a negative refractive index. Nature 455, 376–379 (2008). https://doi.org/10.1038/nature07247
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