Realization of an all-dielectric zero-index optical metamaterial

Journal name:
Nature Photonics
Volume:
7,
Pages:
791–795
Year published:
DOI:
doi:10.1038/nphoton.2013.214
Received
Accepted
Published online

Abstract

Metamaterials offer unprecedented flexibility for manipulating the optical properties of matter, including the ability to access negative index1, 2, 3, 4, ultrahigh index5 and chiral optical properties6, 7, 8. Recently, metamaterials with near-zero refractive index have attracted much attention9, 10, 11, 12, 13. Light inside such materials experiences no spatial phase change and extremely large phase velocity, properties that can be applied for realizing directional emission14, 15, 16, tunnelling waveguides17, large-area single-mode devices18 and electromagnetic cloaks19. However, at optical frequencies, the previously demonstrated zero- or 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 transverse-magnetic polarized light, leading to angular selectivity of transmission and directive emission from quantum dots placed within the material.

At a glance

Figures

  1. Diagram and images of fabricated ZIM structure.
    Figure 1: Diagram and images of fabricated ZIM structure.

    a, Diagram of the ZIM structure with a unit-cell period of a = 600 nm and w = t = 260 nm. b, False-colour focused ion beam image of the ZIM before spin-coating PMMA. Inset: cross-section of the structure after PMMA filling. The fabricated sample has 11 alternating Si/SiO2 layers with silicon rod widths of 270 nm, 280 nm, 310 nm, 320 nm and 380 nm, from top to bottom.

  2. Optical properties of bulk ZIM.
    Figure 2: Optical properties of bulk ZIM.

    a, Band diagram of uniform bulk ZIM (infinitely thick) for TM polarization. Dirac cone dispersion is observed at the point with triple degeneracy at 211 THz. The shaded area denotes regions outside the free-space light line. b, Retrieved effective permittivity and permeability of the bulk ZIM acquired using field-averaging. Inset: electric and magnetic fields within a single unit cell at zero-index frequency, indicating a strong electric monopole and magnetic dipole response. c, IFC of the TM4 band. The contours are nearly circular (that is, isotropic) for a broad frequency range and increase in size away from the zero-index frequency, indicating a progressively larger refractive index.

  3. Optical properties and transmittance of fabricated ZIM.
    Figure 3: Optical properties and transmittance of fabricated ZIM.

    a, Effective permittivity and permeability of the fabricated ZIM obtained using S-parameter retrieval. Regions corresponding to positive index, metallic properties and negative index are denoted by blue, grey and yellow shading, respectively. b, Effective refractive index of the fabricated structured obtained using S-parameter retrieval. c, Experimental (red) and theoretical (dotted blue) transmittance curves of the ZIM (total pattern area, 200 × 200 µm2).

  4. Angular selectivity of transmission.
    Figure 4: Angular selectivity of transmission.

    a, IFCs of air and a low-index metamaterial, illustrating angularly selective transmission due to conservation of the wave vector parallel to the surface. b, Simulated angle- and wavelength-dependent transmittance of the fabricated structure. cf, Fourier-plane images of a beam passing through the fabricated ZIM structure within the low-index band. Angularly selective transmission can be observed in the y-direction due to the low effective index. Along the x-direction, angular selectivity is not preserved due to the one-dimensional nature of silicon rods. g, Fourier-plane image of the illumination beam demonstrating uniform intensity over the measured angular range.

  5. Directional quantum dot emission from within the ZIM.
    Figure 5: Directional quantum dot emission from within the ZIM.

    a, Schematic of laser-pumped quantum dot emission from within the ZIM structure. b, Calculated emission profile for a line source placed in the centre of the material (centred) and the average profile from line sources placed throughout the material (averaged). c, Two-dimensional Fourier-plane image of quantum dot emission on the substrate. Intensity is scaled by a factor of two. d, Cross-section of the emission taken at kx = 0. e, Two-dimensional Fourier-plane image of quantum dot emission within the ZIM, showing enhanced rate and directivity of spontaneous emission. f, Cross-section of the emission taken at kx = 0. CCD, charge-coupled device.

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Author information

  1. These authors contributed equally to this work

    • Parikshit Moitra &
    • Yuanmu Yang

Affiliations

  1. Interdisciplinary Materials Science Program, Vanderbilt University, Nashville, Tennessee 37212, USA

    • Parikshit Moitra &
    • Yuanmu Yang
  2. School for Science and Math at Vanderbilt, Nashville, Tennessee 37232, USA

    • Zachary Anderson
  3. Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA

    • Ivan I. Kravchenko &
    • Dayrl P. Briggs
  4. Department of Mechanical Engineering, Vanderbilt University, Nashville, Tennessee 37212, USA

    • Jason Valentine

Contributions

P.M. fabricated the metamaterials and both P.M. and Y.Y. conducted the numerical simulations and experimental characterization. Z.A. assisted in measuring transmission as a function of incident angle. I.I.K. assisted in developing the electron-beam lithography and RIE processes and D.P.B. performed the low-pressure chemical vapour deposition. The idea was developed by J.V., who assisted in all aspects of the work and supervised the project. All authors discussed the results and contributed to writing the manuscript.

Competing financial interests

The authors declare no competing financial interests.

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