doi:10.1038/nature07247 LETTERS
Three-dimensional optical metamaterial with a negative refractive index
Jason Valentine1*, Shuang Zhang1*, Thomas Zentgraf1*, Erick Ulin-Avila1, Dentcho A. Genov1, Guy Bartal1 & Xiang Zhang1,2 Metamaterials are artificially engineered structures that have properties, such as a negative refractive index1­4, 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. NIMs, first described by Veselago more than 40 years ago1 and recently discussed in the framework of metamaterials2, arise from the fact that both the permittivity and the permeability of the materials are simultaneously negative. In the past several years, much effort has been dedicated to the engineering and extension of the functionalities of metamaterials at terahertz15­17 and optical frequencies7,8,10,18­21. Metal­dielectric­metal fishnet structures were among the earliest demonstrations of optical NIMs. These structures, however, consist of a single functional layer along the direction of propagation. This is equivalent to an atomic monolayer, making it difficult to explore phenomena in three dimensions and develop device applications. Moreover, as a result of their resonant nature, these systems suffer substantial loss at optical frequencies. On the basis of the above, it is therefore imperative to realize low-loss bulk optical NIMs if we are to demonstrate unambiguously the unique effects associated with negative index of refraction. Recently, it has been suggested theoretically that stacking up multiple fishnet functional layers along the propagation direction constitutes a promising approach for achieving a 3D optical NIM22 (Fig. 1a). This cascading leads to a strong magneto-inductive coupling between neighbouring functional layers23. As demonstrated recently24, the tight coupling between adjacent LC resonators through mutual inductance results in a broadband negative index of refraction with low loss, which is similar to the material response of left-handed transmission lines25,26. In addition, the loss is further reduced owing to the destructive interference of the antisymmetric currents across the metal film, effectively cancelling out the current flow in the centre of the film23. Here we experimentally demonstrate the first 3D optical NIM by directly measuring the angle of refraction from a prism made of cascaded fishnet metamaterial. The experimental results, along with numerical calculations, serve as direct evidence of zero and negative phase index in the metamaterial. The 3D fishnet metamaterial is fabricated on a multilayer metaldielectric stack by using focused ion-beam milling (FIB), which is capable of cutting nanometre-sized features with a high aspect ratio. Figure 1b shows the scanning electron microscopy (SEM) image of the proposed 3D fishnet pattern, which was milled on 21 alternating films of silver and magnesium fluoride, resulting in ten functional layers. To measure the index of refraction of the 3D metamaterial experimentally, a prism was created in the multilayer stack (Fig. 2a, b). Measurements of the refractive index of these structures were performed by observing the refraction angle of light passing through the prism by Snell's law. This provides a direct and unambiguous detera b a
p Ag MgF2 b 1 µm Figure 1 | Diagram and SEM image of fabricated fishnet structure. a, Diagram of the 21-layer fishnet structure with a unit cell of p 5 860 nm, a 5 565 nm and b 5 265 nm. b, SEM image of the 21-layer fishnet structure with the side etched, showing the cross-section. The structure consists of alternating layers of 30 nm silver (Ag) and 50 nm magnesium fluoride (MgF2), and the dimensions of the structure correspond to the diagram in a. The inset shows a cross-section of the pattern taken at a 45u angle. The sidewall angle is 4.3u and was found to have a minor effect on the transmittance curve according to simulation. 1 NSF Nano-scale Science and Engineering Center (NSEC), 3112 Etcheverry Hall, University of California, Berkeley, California 94720, USA. 2Material Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA. *These authors contributed equally to this work. 1
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n=1 f2 d n