Abstract

We present the blueprint for a novel negative-index metamaterial. This structure is fabricated via three-dimensional two-photon direct laser writing and silver shadow evaporation. The comparison of measured linear optical spectra with theory shows good agreement and reveals a negative real part of the refractive index at around 3.85μm wavelength—despite the fact that the metamaterial structure is bianisotropic owing to the lack of inversion symmetry along its surface normal.

© 2008 Optical Society of America

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  1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
    [CrossRef]
  2. V. M. Shalaev, Nat. Photonics 1, 41 (2007).
    [CrossRef]
  3. C. M. Soukoulis, S. Linden, and M. Wegener, Science 315, 47 (2007).
    [CrossRef] [PubMed]
  4. G. Dolling, M. Wegener, and S. Linden, Opt. Lett. 32, 551 (2007).
    [CrossRef] [PubMed]
  5. N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nat. Mater. 7, 31 (2008).
    [CrossRef]
  6. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
    [CrossRef] [PubMed]
  7. M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, Nat. Mater. 7, 543 (2008).
    [CrossRef] [PubMed]
  8. H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, Phys. Status Solidi A 204, 3886 (2008).
    [CrossRef]
  9. R. Marqués, F. Medina, and R. Rafii-El-Idrissi, Phys. Rev. B 65, 144440 (2002).
    [CrossRef]
  10. D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
    [CrossRef]
  11. X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, Phys. Rev. E 71, 046610 (2005).
    [CrossRef]

2008 (4)

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nat. Mater. 7, 31 (2008).
[CrossRef]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, Nat. Mater. 7, 543 (2008).
[CrossRef] [PubMed]

H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, Phys. Status Solidi A 204, 3886 (2008).
[CrossRef]

2007 (3)

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

C. M. Soukoulis, S. Linden, and M. Wegener, Science 315, 47 (2007).
[CrossRef] [PubMed]

G. Dolling, M. Wegener, and S. Linden, Opt. Lett. 32, 551 (2007).
[CrossRef] [PubMed]

2005 (1)

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, Phys. Rev. E 71, 046610 (2005).
[CrossRef]

2002 (2)

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, Phys. Rev. B 65, 144440 (2002).
[CrossRef]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

Chen, X.

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, Phys. Rev. E 71, 046610 (2005).
[CrossRef]

Dolling, G.

Fu, L.

H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, Phys. Status Solidi A 204, 3886 (2008).
[CrossRef]

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nat. Mater. 7, 31 (2008).
[CrossRef]

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

Giessen, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nat. Mater. 7, 31 (2008).
[CrossRef]

H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, Phys. Status Solidi A 204, 3886 (2008).
[CrossRef]

Gräbeldinger, H.

H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, Phys. Status Solidi A 204, 3886 (2008).
[CrossRef]

Grzegorczyk, T. M.

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, Phys. Rev. E 71, 046610 (2005).
[CrossRef]

Guo, H.

H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, Phys. Status Solidi A 204, 3886 (2008).
[CrossRef]

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nat. Mater. 7, 31 (2008).
[CrossRef]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Kaiser, S.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nat. Mater. 7, 31 (2008).
[CrossRef]

H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, Phys. Status Solidi A 204, 3886 (2008).
[CrossRef]

Kong, J. A.

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, Phys. Rev. E 71, 046610 (2005).
[CrossRef]

Linden, S.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, Nat. Mater. 7, 543 (2008).
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, Science 315, 47 (2007).
[CrossRef] [PubMed]

G. Dolling, M. Wegener, and S. Linden, Opt. Lett. 32, 551 (2007).
[CrossRef] [PubMed]

Liu, N.

H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, Phys. Status Solidi A 204, 3886 (2008).
[CrossRef]

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nat. Mater. 7, 31 (2008).
[CrossRef]

Markoš, P.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Marqués, R.

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Medina, F.

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Pendry, J. B.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Plet, C.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, Nat. Mater. 7, 543 (2008).
[CrossRef] [PubMed]

Rafii-El-Idrissi, R.

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Rill, M. S.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, Nat. Mater. 7, 543 (2008).
[CrossRef] [PubMed]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Schultz, S.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Schweizer, H.

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nat. Mater. 7, 31 (2008).
[CrossRef]

H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, Phys. Status Solidi A 204, 3886 (2008).
[CrossRef]

Shalaev, V. M.

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

Smith, D. R.

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Soukoulis, C. M.

C. M. Soukoulis, S. Linden, and M. Wegener, Science 315, 47 (2007).
[CrossRef] [PubMed]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Staude, I.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, Nat. Mater. 7, 543 (2008).
[CrossRef] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Thiel, M.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, Nat. Mater. 7, 543 (2008).
[CrossRef] [PubMed]

Ulin-Avila, E.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

Valentine, J.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

von Freymann, G.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, Nat. Mater. 7, 543 (2008).
[CrossRef] [PubMed]

Wegener, M.

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, Nat. Mater. 7, 543 (2008).
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, Science 315, 47 (2007).
[CrossRef] [PubMed]

G. Dolling, M. Wegener, and S. Linden, Opt. Lett. 32, 551 (2007).
[CrossRef] [PubMed]

Wu, B.-I.

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, Phys. Rev. E 71, 046610 (2005).
[CrossRef]

Zentgraf, T.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

Zhang, S.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

Zhang, X.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
[CrossRef]

Nat. Mater. (2)

N. Liu, H. Guo, L. Fu, S. Kaiser, H. Schweizer, and H. Giessen, Nat. Mater. 7, 31 (2008).
[CrossRef]

M. S. Rill, C. Plet, M. Thiel, I. Staude, G. von Freymann, S. Linden, and M. Wegener, Nat. Mater. 7, 543 (2008).
[CrossRef] [PubMed]

Nat. Photonics (1)

V. M. Shalaev, Nat. Photonics 1, 41 (2007).
[CrossRef]

Nature (1)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, Nature 455, 376 (2008).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. B (2)

R. Marqués, F. Medina, and R. Rafii-El-Idrissi, Phys. Rev. B 65, 144440 (2002).
[CrossRef]

D. R. Smith, S. Schultz, P. Markoš, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Phys. Rev. E (1)

X. Chen, B.-I. Wu, J. A. Kong, and T. M. Grzegorczyk, Phys. Rev. E 71, 046610 (2005).
[CrossRef]

Phys. Status Solidi A (1)

H. Schweizer, L. Fu, H. Gräbeldinger, H. Guo, N. Liu, S. Kaiser, and H. Giessen, Phys. Status Solidi A 204, 3886 (2008).
[CrossRef]

Science (1)

C. M. Soukoulis, S. Linden, and M. Wegener, Science 315, 47 (2007).
[CrossRef] [PubMed]

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Figures (3)

Fig. 1
Fig. 1

(a) Metamaterial design. The white regions are the polymer (SU-8) located on a glass substrate. The sidewalls of the polymer (encapsulated by Si O 2 via ALD) are coated with silver. The polarization of the incident electromagnetic field is illustrated on the lower left-hand-side corner. (b) Oblique-view electron micrograph of a structure fabricated by direct laser writing and silver shadow evaporation that has been cut by a focused-ion beam (FIB) to reveal its interior. The complicated features visible underneath the glass-substrate surface are due to the FIB cutting and, hence, not relevant.

Fig. 2
Fig. 2

Measured linear-optical normal-incidence transmittance (red curve) and reflectance spectra of a structure similar to the one shown in Fig. 1b. Note that the reflectance taken from the air side R air (blue curve) and that taken from the glass-substrate side R glass (green curve) are distinctly different.  

Fig. 3
Fig. 3

Calculated optical response of the structure shown in Fig. 1a for normal incidence of light. (a) Transmittance and reflectance spectra that can be compared directly with experiment (Fig. 2). (b) Retrieved electric permittivity ϵ, (c) magnetic permeability μ, (d) bianisotropy parameter ξ, and (e) refractive index n. The corresponding real parts are shown as solid curves, the imaginary parts as dashed curves. The gray backgrounds aim at clarifying the origin of the negative real part of n.

Equations (2)

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( D B ) = ( ϵ 0 ϵ i c 0 1 ξ + i c 0 1 ξ μ 0 μ ) ( E H ) ,
n 2 = ϵ μ ξ 2 .

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