Realization of an all-dielectric zero-index optical metamaterial

Metamaterials offer unprecedented flexibility for manipulating the optical properties of matter, including the ability to access negative index1–4, ultrahigh index5 and chiral optical properties6–8. Recently, metamaterials with near-zero refractive index have attracted much attention9–13. Light inside such materials experiences no spatial phase change and extremely large phase velocity, properties that can be applied for realizing directional emission14–16, tunnelling waveguides17, large-area single-mode devices18 and electromagnetic cloaks19. However, at optical frequencies, the previously demonstrated zeroor negative-refractive-index metamaterials have required the use of metallic inclusions, leading to large ohmic loss, a serious impediment to device applications20,21. Here, we experimentally demonstrate an impedance-matched zero-index metamaterial at optical frequencies based on purely dielectric constituents. Formed from stacked silicon-rod unit cells, the metamaterial has a nearly isotropic low-index response for transversemagnetic polarized light, leading to angular selectivity of transmission and directive emission from quantum dots placed within the material. Over the past several years, most work aimed at achieving zero index has been focused on epsilon-near-zero metamaterials (ENZs), which can be realized using diluted metals or metal waveguides operating below cutoff. These studies have included experimental demonstrations in the microwave9,14, mid-infrared13 and visible regimes12. ENZ metamaterials have a permittivity 1 near zero and a permeability m of unity, resulting in a near-zero refractive index (n = m1 √ ). However, because the permeability remains finite, the relative optical impedance (Z = m/1 √ ) is inevitably mismatched from free space, resulting in large reflections from the interface. Impedance-matched zero-index metamaterials (ZIMs), in which both the permittivity and permeability are set to zero, eliminate these strong reflections and have recently been demonstrated at optical frequencies using metal-based fishnet structures11. However, fishnet metamaterials do not have isotropic optical properties, and the use of metals inevitably introduces ohmic loss that will limit the thickness of the material. Resonant all-dielectric metamaterials offer one potential solution to these issues22–24. Formed from high-refractive-index resonators, dielectric metamaterial unit cells support an electric and magnetic dipole response due to Mie resonances. Proper control of the lattice arrangement, resonator geometry, and composition allows control over the effective permittivity and permeability of the metamaterial. Because of the absence of ohmic loss, dielectric metamaterials can be much less absorptive than their metallic counterparts, and their simple unit-cell geometries offer the possibility to achieve three-dimensional isotropic metamaterials25, a task that has proven challenging when utilizing more complicated metal-based unit cells21. However, while magnetic modes in high-index particles have recently been characterized experimentally at optical frequencies26,27, implementations of dielectric metamaterials have so far been limited to the microwave25,28,29 and mid-infrared regimes30. Here, we report the first experimental demonstration of an alldielectric ZIM operating at infrared frequencies. The design of the metamaterial is based on a recent proposal reported in ref. 10 in which it was shown that a metamaterial made of purely dielectric high-index rods can exhibit a Dirac cone at the G point in the band structure, a feature that is similar to the electronic band structure in graphene31. At the Dirac point, the metamaterial exhibits zero effective permittivity and permeability, resulting in an impedance-matched ZIM. Experiments at microwave frequencies have demonstrated some of the unique properties arising from an effective index of zero10, such as cloaking and lensing. However, a demonstration at optical frequencies has yet to be provided. Here, we implement a ZIM at optical frequencies using vertically stacked silicon rods, allowing access from free space. We demonstrate that the optical ZIM serves as an angular optical filter while also enhancing the directivity of spontaneous emission from quantum dot light sources embedded inside the structure. The experimental results, together with numerical calculations, serve as direct evidence of impedance-matched near-zero index within the metamaterial. The fabricated ZIM consists of 200-mm-long silicon rods that support electric and magnetic resonances, and are separated by a low-index material—silicon dioxide (SiO2) (Fig. 1a). One of the consequences of low or zero index is that light will not be guided using a conventional slab waveguide, so the material must be fabricated for free-space access when metal or other reflective cladding layers cannot be utilized. To realize a free-space-accessible material, fabrication began with a multilayer stack of 11 alternating layers of a-Si (11⁄4 13.7, thickness1⁄4 260 nm) and SiO2 (11⁄4 2.25, thickness1⁄4 340 nm) followed by patterning and reactive ion etching (RIE) (see Supplementary Section S2 for details). In the final step, poly(methyl methacrylate) (PMMA) (11⁄4 2.23) was spin-coated onto the sample to fill the air gaps. Figure 1b presents a cross-section of the fabricated structure before final PMMA spin-coating, and the inset depicts a sample after spin-coating. A total of five functional layers (Si/SiO2 pairs) results in a metamaterial with a thickness of 3 mm, about twice the free-space wavelength at the zero-index point. The band structure corresponding to the bulk ZIM (infinitely thick), consisting of a stack of square-cross-section silicon rods