NATURE Vol 455 18 September 2008 LETTERS and experimental FOM is plotted in Fig. 5. The FOM is 3.5 at 4. Tsakr i=1,775 nm(where Re(n)=-1. 23),which is among the highest metamaterials. Nature 450, 397-401(2007) experimental values so far recorded at optical frequencies. For idea 5. Shelby, R A, Smith, D R& Schultz, S Experimental verification of a negative fabrication conditions, the FOM could rise as high as about 20, as 6. Parazzoli. C G, Greegor, K, Li, K, Koltenbah, B.E.C.&ta determined from theoretical calculations. We emphasize that our erification of negative index of refraction using Snell,s law. Phys. Rev. Lett. 90, results are different from recent reports of negative refraction.2in 107401(2003 anisotropic media with hyperbolic dispersion(equivalent to negative 7. Panoiu, N.C.&Osgood, R. M. Numerical investigations of negative refractive group index but positive phase velocity index metamaterials at infrared and optical frequencies. Opt. Commun. 223, 331-33702003) The fishnet metamaterial has a period about 2/20 in the vertical 8. Shalaev, V M et al. Optical negative-index metamaterials. Nature Photonics 1, direction. The on of light 41-48(2007) ithin some angular range is dominated by this deep sub-wavelength 9. Lezec, H J, Dionne, N A& Atwater, H A Negative refraction at visible period and not by the in-plane period, as long as the wavevector 10. Liu, N et al. Three-dimensional photonic metamaterials at optical frequencies. projection on the in-plane directions is small compared with the Nature Mater. 7. 31-37 (20 in-plane reciprocal lattice vector of the fishnet metamaterial. There 11. Hoffman, A J et al. Negative refraction in semiconductor metamaterials.Nature is only a single propagating mode in the negative-index frequency region, justifying the description of the fishnet metamaterial with an 12. Silveirinha, M. Engheta, N Tunneling of electromagnetic energy through effective index. In contrast, if higher dielectric materials such as sil- hannes and bends using epsilon- near-zero materials. Phys icon (n3.6) are used to serve as the dielectric layer, the ratio 13. Edwards, B et al. Experimental verification of epsilon-near-zero metamaterial between the wavelength and in-plane period can be significantly pling and energy squeezing using a microwave waveguide. Phys. Rev. Lett. 100 increased because of the larger capacitance in the LC circuit. Unlike the negative index obtained from photonic crystals, the 14. Enoch, S et al. A metamaterial for directive emission. Phys.Rev. Lett.89,213902 negative index presented here results from simultaneous negative 15. Yen, T.J. et al. Terahertz magnetic response from artificialmaterials Science 303, 1494-1496(2004 djacent LC resonators. The negative index occurs in the first pro- pagation band and with smooth negative-phase evolution along the 17. Chen, H T et al. Active terahertz metamaterial devices. Nature 444, 597-600 light propagation direction, which differs from the negative refrac tion obtained in photonic crystals. 18. Linden, S et al. Magnetic response of metamaterials at 100 terahertz Science 306, 1351-1353(2004) Here we have experimentally demonstrated the first 3D NIM at 19. Soukoulis, C.M., Linden, S& Wegener, M Negative refractive index at optical optical frequencies and directly measured the refractive index of a equencies Science 315, 47-49(2007) NIM prism in the free space. The 3D optical metamaterials may offer 20. Dolling. G. Wegener, M& Linden, 5. Realization of a the possibility to explore a large variety of optical phenomena assoc- 21. Alu, A Engheta, N. Three-dimensional nanotransm iated with zero and negative refractive index, as well as applications in be for broad band negative-refract f photonics and imaging Phys.Rev.B75.024304(2007) In the numerical studies of the 3D fishnet metamaterial, the intrinsic losses ofthe 23. ui T. ated metal-dielectric stacks. Opt. Express 14,6778-6787(2006) METHODS SUMMARY yered metamaterials and its influence on negative refraction transmission. Opt. metal are included". The multilayer stack was deposited by electron-beam evap- Express 14. 1155-11163(2006) oration of alternating layers of silver(30 nm)and magnesium fluoride(50 nm) 24. Eleftheriades, G. V. Analysis of bandwidth and loss in negative-refractive-index esulting in a total thickness of 830 nm. Two different configurations of the ansmission-line(NRl-TL)media using coupled resonators. IEEE Microw. ples were fabricated on the multilayer stack. Samples of the first Wireless Components Lett 17, 412-414 (2007). configuration consist of 22 X 22 in-plane fishnet unit cells and were used for 25. Grbic, A.& Eleftheriades, G V. Overcoming the diffraction limit with a planar left the characterization of the transmittance. The second configuration(prism handed transmission-line lens. Phys. Rev. Lett. 92, 117403(2004) mple)was formed by etching the film at an angle B to the film surface, using 26. La, A, Carloz, C& Itoh, T Composite right-A nded composite transmission FIB. The exact angle was measured with mic force microscope and was found to vary slightly between samples. A 10 x 10 fishnet pattern was subse- 27. Pendry, J.B., Holdenz, A J,Robbins, D.J.& Stewartz, W.J.Low frequency tures. J Phys. Condens Matter 10, 4785-4809(1998) To obtain the absolute angle of refraction, a window with an area equal to that 28. Fan, X.B. et. All-angle broadband negative refraction of metal waveguide arrays of the prism was etched through the multilayer stack to serve as a reference. The in the visible range: Theoretical analysis and numerical demonstration. phys. Rev Lett97,073901(2006) indow and prism Fourier images were measured for all wavelengths on an 29. Notomi, M Theory of light propagation in strongly modulated photonic crystals indium gallium arsenide infrared camera and the total beam shift d of the spot lefraction-like behavior in the vicinity of the photonic band gap. Phys. Rev. b. centre was calculated. Consequently, the angle of refraction a at the surface of the 10696(2000) prism is given as a=B-arctan(o/f). Snell,'s law (n= sina/sinp)was used to 30. Johnson, P.B.& R W. Optical constants of the noble metals. Phys. Rev. B alculate the real part of the refractive index of the sample. The imaginary part of 6,4370-4379(1972) the refractive index of the sample was obtained from transmittance and reflec tance data acquired with a 21-layer sample of the first configuration (as described supplementary Information is linked to the online version of the paper at Acknowledgements We acknowledge funding support from US Army Research Full Methods and any associated references are available in the online version of office (ARO) MURI programme 50432-PH-MUR and partly by the NSF Nano-scale Science and Engineering Center DMl-0327077. We thank H bech and M. C Martin for assisting in measurements of near-infrared transmission and Received 20 March; accepted 11 July 2008. reflection, and S.R. J. Brueck for discussion. T Z. acknowledges a fellowship from the Molecular Foundry, Lawrence Berkeley National Laboratory, which is 1. Veselago, V.G. The electrodynamics of substances with simultaneously negative supported by the Office of Science, Office of Basic Energy Sciences, of the US 2. Smith, D R, Pendry, J B& Wiltshire, M. C K Metamaterials and negative Department of Energy under contract no DE-AC02-05CH11231 refractive index. Science 305, 788-792(2004). uthor Information Reprints and permissions information is available at 3. Pendry, J. B. Negative refraction makes a perfect lens. Phys. Rev. Lett. www.nature.com/reprints.cOrrespondenceandrequestsformaterialsshouldbe 966-3969(2000) addressed to X.Z. (xiang @berkeley. edu) @2008 Macmillan Publishers Limited All rights reservedand experimental FOM is plotted in Fig. 5. The FOM is 3.5 at l 5 1,775 nm (where Re(n) 5 21.23), which is among the highest experimental values so far recorded at optical frequencies19. For ideal fabrication conditions, the FOM could rise as high as about 20, as determined from theoretical calculations. We emphasize that our results are different from recent reports of negative refraction11,28 in anisotropic media with hyperbolic dispersion (equivalent to negative ‘group index’) but positive phase velocity. The fishnet metamaterial has a period about l/20 in the vertical direction. The propagation of light travelling along this direction or within some angular range is dominated by this deep sub-wavelength period and not by the in-plane period, as long as the wavevector projection on the in-plane directions is small compared with the in-plane reciprocal lattice vector of the fishnet metamaterial. There is only a single propagating mode in the negative-index frequency region, justifying the description of the fishnet metamaterial with an effective index. In contrast, if higher dielectric materials such as sil￾icon (n < 3.6) are used to serve as the dielectric layer, the ratio between the wavelength and in-plane period can be significantly increased because of the larger capacitance in the LC circuit. Unlike the negative index obtained from photonic crystals29, the negative index presented here results from simultaneous negative magnetic and electric responses and shows a resemblance to the left-handed transmission line due to the tight coupling between the adjacent LC resonators. The negative index occurs in the first pro￾pagation band and with smooth negative-phase evolution along the light propagation direction, which differs from the negative refrac￾tion obtained in photonic crystals. Here we have experimentally demonstrated the first 3D NIM at optical frequencies and directly measured the refractive index of a NIM prism in the free space. The 3D optical metamaterials may offer the possibility to explore a large variety of optical phenomena assoc￾iated with zero and negative refractive index, as well as applications in the scaling down of photonics and imaging. METHODS SUMMARY In the numerical studies of the 3D fishnet metamaterial, the intrinsic losses of the metal are included30. The multilayer stack was deposited by electron-beam evap￾oration of alternating layers of silver (30 nm) and magnesium fluoride (50 nm) resulting in a total thickness of 830 nm. Two different configurations of the fishnet samples were fabricated on the multilayer stack. Samples of the first configuration consist of 22 3 22 in-plane fishnet unit cells and were used for the characterization of the transmittance. The second configuration (prism sample) was formed by etching the film at an angle b to the film surface, using FIB. The exact angle was measured with an atomic force microscope and was found to vary slightly between samples. A 10 3 10 fishnet pattern was subse￾quently milled in the prism. To obtain the absolute angle of refraction, a window with an area equal to that of the prism was etched through the multilayer stack to serve as a reference. The window and prism Fourier images were measured for all wavelengths on an indium gallium arsenide infrared camera and the total beam shift d of the spot centre was calculated. Consequently, the angle of refraction a at the surface of the prism is given as a 5 b 2 arctan(d/f2). Snell’s law (n 5 sina/sinb) was used to calculate the real part of the refractive index of the sample. The imaginary part of the refractive index of the sample was obtained from transmittance and reflec￾tance data acquired with a 21-layer sample of the first configuration (as described above). Full Methods and any associated references are available in the online version of the paper at www.nature.com/nature. Received 20 March; accepted 11 July 2008. Published online 11 August 2008. 1. Veselago, V. G. The electrodynamics of substances with simultaneously negative values of e and m. Sov. Phys. Usp. 10, 509–514 (1968). 2. Smith, D. R., Pendry, J. B. & Wiltshire, M. C. K. Metamaterials and negative refractive index. Science 305, 788–792 (2004). 3. Pendry, J. B. Negative refraction makes a perfect lens. Phys. Rev. Lett. 85, 3966–3969 (2000). 4. Tsakmakidis, K. L., Boardman, A. D. & Hess, O. ‘Trapped rainbow’ storage of light in metamaterials. Nature 450, 397–401 (2007). 5. Shelby, R. A., Smith, D. R. & Schultz, S. Experimental verification of a negative index of refraction. Science 292, 77–79 (2001). 6. 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). 7. Panoiu, N. C. & Osgood, R. M. Numerical investigations of negative refractive index metamaterials at infrared and optical frequencies. Opt. Commun. 223, 331–337 (2003). 8. Shalaev, V. M. et al. Optical negative-index metamaterials. Nature Photonics 1, 41–48 (2007). 9. Lezec, H. J., Dionne, N. A. & Atwater, H. A. Negative refraction at visible frequencies. Science 316, 430–432 (2007). 10. Liu, N. et al. Three-dimensional photonic metamaterials at optical frequencies. Nature Mater. 7, 31–37 (2008). 11. Hoffman, A. J. et al. Negative refraction in semiconductor metamaterials. Nature Mater. 6, 946–950 (2007). 12. Silveirinha, M. & Engheta, N. Tunneling of electromagnetic energy through subwavelength channels and bends using epsilon-near-zero materials. Phys. Rev. Lett. 97, 157403 (2006). 13. 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). 14. Enoch, S. et al. A metamaterial for directive emission. Phys. Rev. Lett. 89, 213902 (2002). 15. Yen, T. J. et al. Terahertz magnetic response from artificial materials. Science 303, 1494–1496 (2004). 16. Padilla, W. J. et al. Dynamical electric and magnetic metamaterial response at terahertz frequencies. Phys. Rev. Lett. 96, 107401 (2006). 17. Chen, H. T. et al. Active terahertz metamaterial devices. Nature 444, 597–600 (2006). 18. Linden, S. et al. Magnetic response of metamaterials at 100 terahertz. Science 306, 1351–1353 (2004). 19. Soukoulis, C. M., Linden, S. & Wegener, M. Negative refractive index at optical frequencies. Science 315, 47–49 (2007). 20. Dolling, G., Wegener, M. & Linden, S. Realization of a three-functional-layer negative-index photonic metamaterial. Opt. Lett. 32, 551–553 (2007). 21. 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). 22. Zhang, S. et al. Optical negative-index bulk metamaterials consisting of 2D perforated metal-dielectric stacks. Opt. Express 14, 6778–6787 (2006). 23. 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). 24. 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). 25. Grbic, A. & Eleftheriades, G. V. Overcoming the diffraction limit with a planar left￾handed transmission-line lens. Phys. Rev. Lett. 92, 117403 (2004). 26. Lai, A., Carloz, C. & Itoh, T. Composite right-/left-handed composite transmission line metamaterials. IEEE Microw. Mag. 5, 34–50 (2004). 27. 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). 28. 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). 29. 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). 30. Johnson, P. B. & Christy, R. W. Optical constants of the noble metals. Phys. Rev. B 6, 4370–4379 (1972). Supplementary Information is linked to the online version of the paper at www.nature.com/nature. Acknowledgements 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. Author Information Reprints and permissions information is available at www.nature.com/reprints. Correspondence and requests for materials should be addressed to X.Z. (xiang@berkeley.edu). NATURE| Vol 455| 18 September 2008 LETTERS 379 ©2008 Macmillan Publishers Limited. All rights reserved