Abstract

A double-periodic array of pairs of parallel gold nanorods is shown to have a negative refractive index in the optical range. Such behavior results from the plasmon resonance in the pairs of nanorods for both the electric and the magnetic components of light. The refractive index is retrieved from direct phase and amplitude measurements for transmission and reflection, which are all in excellent agreement with simulations. Both experiments and simulations demonstrate that a negative refractive index n0.3 is achieved at the optical communication wavelength of 1.5μm using the array of nanorods. The retrieved refractive index critically depends on the phase of the transmitted wave, which emphasizes the importance of phase measurements in finding n.

© 2005 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  6. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  8. S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R.J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. A. Taflove and S. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech, 2000).
  15. D. R. Smith, S. Schultz, P. Markôs, and C. M. Soukoulis, Phys. Rev. B 65, 195104 (2002).
    [CrossRef]

2005 (4)

N. Fang, H. Lee, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

D. O.S. Melville and R J. Blaikie, Opt. Express 13, 2127 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R.J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef]

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, IEEE Photon. Technol. Lett. 17, 1196 (2005).
[CrossRef]

2004 (3)

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

2003 (1)

2002 (2)

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, J. Nonlinear Opt. Phys. Mater. 11, 65 (2002).
[CrossRef]

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

2001 (2)

Y. Svirko, N. Zheludev, and M. Osipov, Appl. Phys. Lett. 78, 498 (2001).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

2000 (1)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

1968 (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968)V. G. Veselago, [Usp. Fiz. Nauk 92, 517 (1964)].
[CrossRef]

Anand, S.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Berrier, A.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Blaikie, R J.

Brueck, S. R.J.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R.J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef]

Enkrich, C.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Fan, W.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R.J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef]

Fang, N.

N. Fang, H. Lee, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Frauenglass, A.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R.J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef]

Hagness, S.

A. Taflove and S. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech, 2000).

Koschny, T.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Lee, H.

N. Fang, H. Lee, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

Lee, J.-B.

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, IEEE Photon. Technol. Lett. 17, 1196 (2005).
[CrossRef]

Linden, S.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Malloy, K. J.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R.J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef]

Markôs, P.

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

Melville, D. O.S.

Minhas, B. K.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R.J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef]

Mulot, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Osipov, M.

Y. Svirko, N. Zheludev, and M. Osipov, Appl. Phys. Lett. 78, 498 (2001).
[CrossRef]

Padilla, W. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Park, W.

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, IEEE Photon. Technol. Lett. 17, 1196 (2005).
[CrossRef]

Pendry, J. B.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

Podolskiy, V. A.

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, Opt. Express 11, 735 (2003).
[CrossRef] [PubMed]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, J. Nonlinear Opt. Phys. Mater. 11, 65 (2002).
[CrossRef]

Qiu, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Sarychev, A. K.

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, Opt. Express 11, 735 (2003).
[CrossRef] [PubMed]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, J. Nonlinear Opt. Phys. Mater. 11, 65 (2002).
[CrossRef]

Schonbrun, E.

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, IEEE Photon. Technol. Lett. 17, 1196 (2005).
[CrossRef]

Schultz, S.

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

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Shalaev, V. M.

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, Opt. Express 11, 735 (2003).
[CrossRef] [PubMed]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, J. Nonlinear Opt. Phys. Mater. 11, 65 (2002).
[CrossRef]

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Smith, D. R.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

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

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Soukoulis, C.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Soukoulis, C. M.

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

Svirko, Y.

Y. Svirko, N. Zheludev, and M. Osipov, Appl. Phys. Lett. 78, 498 (2001).
[CrossRef]

Swillo, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Taflove, A.

A. Taflove and S. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech, 2000).

Talneau, A.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Thylén, L.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Tinker, M.

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, IEEE Photon. Technol. Lett. 17, 1196 (2005).
[CrossRef]

Veselago, V. G.

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968)V. G. Veselago, [Usp. Fiz. Nauk 92, 517 (1964)].
[CrossRef]

Vier, D. C.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Wegener, M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Yen, T. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Zhang, S.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R.J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef]

Zhang, X.

N. Fang, H. Lee, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

Zheludev, N.

Y. Svirko, N. Zheludev, and M. Osipov, Appl. Phys. Lett. 78, 498 (2001).
[CrossRef]

Zhou, J.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

Appl. Phys. Lett. (1)

Y. Svirko, N. Zheludev, and M. Osipov, Appl. Phys. Lett. 78, 498 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, IEEE Photon. Technol. Lett. 17, 1196 (2005).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, J. Nonlinear Opt. Phys. Mater. 11, 65 (2002).
[CrossRef]

Opt. Express (2)

Phys. Rev. B (1)

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

Phys. Rev. Lett. (3)

J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[CrossRef] [PubMed]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R.J. Brueck, Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef]

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef]

Science (4)

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, Science 303, 1494 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, Science 306, 1351 (2004).
[CrossRef] [PubMed]

N. Fang, H. Lee, and X. Zhang, Science 308, 534 (2005).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, Science 292, 77 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

V. G. Veselago, Sov. Phys. Usp. 10, 509 (1968)V. G. Veselago, [Usp. Fiz. Nauk 92, 517 (1964)].
[CrossRef]

Other (1)

A. Taflove and S. Hagness, Computational Electrodynamics: the Finite-Difference Time-Domain Method (Artech, 2000).

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Figures (3)

Fig. 1
Fig. 1

(a) Schematic for the array of nanorod pairs. (b) Field-emission scanning electron microscope images. (c) Elementary cell.

Fig. 2
Fig. 2

(Color online) (a) Reflection and transmission spectra: experiments (solid curves) and simulations (squares and circles). (b) Phase anisotropy Δ φ for reflection (squares) and transmission (circles), from experiments and simulations. Inset, absolute phase shifts δ φ in transmission for the parallel (lower) and perpendicular (upper) polarizations of light.

Fig. 3
Fig. 3

(Color online) (a) Real and imaginary parts of the refractive index retrieved from simulations. (b) Real part of the refractive index retrieved from simulations (triangles) and experiments (circles). The inset in (b) is a magnified view of the region of negative refraction; the dashed curve shows the quadratic least-squares fit for the experimental data.

Equations (1)

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cos n k Δ = 1 r 2 + n s t 2 ( n s + 1 ) t + r t ( n s 1 ) ,

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