Abstract

Specially designed metal–dielectric composites can have a negative refractive index in the optical range. Specifically, it is shown that arrays of single and paired nanorods can provide such negative refraction. For pairs of metal rods, a negative refractive index has been observed at 1.5μm. The inverted structure of paired voids in metal films can also exhibit a negative refractive index. A similar effect can be accomplished with metal strips in which the refractive index can reach 2. The refractive index retrieval procedure and the critical role of light phases in determining the refractive index are discussed.

© 2006 Optical Society of America

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  1. L. I. Mandel'shtam, "Group velocity in crystal lattice," JETP 15, 475 (1945). See also Ref. .
  2. L. I. Mandel'shtam, "The 4th lecture of L. I. Mandel'shtam given at Moscow State University (05/05/1944)," in Collection of Scientific Works (Nauka, 1994), Vol. 5, pp. 461-467.
  3. V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsi and µ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  4. H. Lamb, "On group-velocity," Proc. London Math. Soc. , 1, 473-479 (1904).
    [CrossRef]
  5. A. Schuster, An Introduction to the Theory of Optics (Edward Arnold, 1904).
  6. J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
    [CrossRef] [PubMed]
  7. V. A. Podolskiy and E. E. Narimanov, "Near-sighted superlens," Opt. Lett. 30, 75-77 (2005).
    [CrossRef] [PubMed]
  8. K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, "Metrics for negative-refractive-index materials," Phys. Rev. E 70, 035602(R) (2004).
    [CrossRef]
  9. N. A. Khizhnyak, "Artificial anisotropic dielectrics formed from two-dimensional lattices of infinite bars and rods," Sov. Phys. Tech. Phys. 29, 604-614 (1959).
  10. A. N. Lagarkov and A. K. Sarychev, "Electromagnetic properties of composites containing elongated conducting inclusions," Phys. Rev. B 53, 06318 (1996).
    [CrossRef]
  11. T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
    [CrossRef] [PubMed]
  12. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
    [CrossRef] [PubMed]
  13. S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
    [CrossRef] [PubMed]
  14. A. K. Sarychev and V. M. Shalaev, "Magnetic resonance in metal nanoantennas," in Complex Mediums V: Light and Complexity, M.W.McCall and G.Dewar, eds., Proc. SPIE 5508, 128-137 (2004).
  15. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," arXiv:cond-mat/0504774v1, Apr. 29, 2005.
  16. A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, "Negative refraction at infrared wavelengths in a two-dimensional photonic crystal," Phys. Rev. Lett. 93, 073902 (2004).
    [CrossRef] [PubMed]
  17. E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
    [CrossRef]
  18. V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
    [CrossRef]
  19. V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735-745 (2003).
    [CrossRef] [PubMed]
  20. V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A Pure Appl. Opt. 7, S32-S37 (2005).
    [CrossRef]
  21. A. K. Sarychev, V. P. Drachev, H.-K. Yuan, V. A. Podolskiy, and V. M. Shalaev, "Optical properties of metal nanowires," in Nanotubes and Nanowires, A.Lakhtakia and S.Maksinenku, eds., Proc. SPIE 5219, 92-98 (2003).
  22. V. M. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
    [CrossRef]
  23. S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Demonstration of near-infrared negative-index materials," arXiv: physics/0504208.
  24. S. Zhang, W. Fan, K. J. MalloyS. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies," J. Opt. Soc. Am. B 23, 434-438 (2006).
    [CrossRef]
  25. J. D. Jackson, Classical Electrodynamics (Wiley, 1962), p. 291.
  26. Y. Svirko, N. Zheludev, and M. Osipov, "Layered chiral metallic microstructures with inductive coupling," Appl. Phys. Lett. 78, 498-500 (2001).
    [CrossRef]
  27. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
    [CrossRef]
  28. A. Taflove and S. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method (Artech House, 2000).
  29. A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice Hall, 1991).

2006

2005

V. A. Podolskiy and E. E. Narimanov, "Near-sighted superlens," Opt. Lett. 30, 75-77 (2005).
[CrossRef] [PubMed]

V. M. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A Pure Appl. Opt. 7, S32-S37 (2005).
[CrossRef]

2004

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, "Negative refraction at infrared wavelengths in a two-dimensional photonic crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, "Metrics for negative-refractive-index materials," Phys. Rev. E 70, 035602(R) (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, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

2003

2002

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

2001

Y. Svirko, N. Zheludev, and M. Osipov, "Layered chiral metallic microstructures with inductive coupling," Appl. Phys. Lett. 78, 498-500 (2001).
[CrossRef]

2000

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

1996

A. N. Lagarkov and A. K. Sarychev, "Electromagnetic properties of composites containing elongated conducting inclusions," Phys. Rev. B 53, 06318 (1996).
[CrossRef]

1968

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsi and µ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

1959

N. A. Khizhnyak, "Artificial anisotropic dielectrics formed from two-dimensional lattices of infinite bars and rods," Sov. Phys. Tech. Phys. 29, 604-614 (1959).

1945

L. I. Mandel'shtam, "Group velocity in crystal lattice," JETP 15, 475 (1945). See also Ref. .

1904

H. Lamb, "On group-velocity," Proc. London Math. Soc. , 1, 473-479 (1904).
[CrossRef]

Anand, S.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, "Negative refraction at infrared wavelengths in a two-dimensional photonic crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

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, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Berrier, A.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, "Negative refraction at infrared wavelengths in a two-dimensional photonic crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Brueck, S. R.

S. Zhang, W. Fan, K. J. MalloyS. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies," J. Opt. Soc. Am. B 23, 434-438 (2006).
[CrossRef]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Demonstration of near-infrared negative-index materials," arXiv: physics/0504208.

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," arXiv:cond-mat/0504774v1, Apr. 29, 2005.

Cai, W.

Chettiar, U.

Drachev, V. P.

V. M. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

A. K. Sarychev, V. P. Drachev, H.-K. Yuan, V. A. Podolskiy, and V. M. Shalaev, "Optical properties of metal nanowires," in Nanotubes and Nanowires, A.Lakhtakia and S.Maksinenku, eds., Proc. SPIE 5219, 92-98 (2003).

Enkrich, C.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," arXiv:cond-mat/0504774v1, Apr. 29, 2005.

Fan, W.

S. Zhang, W. Fan, K. J. MalloyS. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies," J. Opt. Soc. Am. B 23, 434-438 (2006).
[CrossRef]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Demonstration of near-infrared negative-index materials," arXiv: physics/0504208.

Fang, N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Frauenglass, A.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

Hagness, S.

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

Ishimaru, A.

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice Hall, 1991).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1962), p. 291.

Khizhnyak, N. A.

N. A. Khizhnyak, "Artificial anisotropic dielectrics formed from two-dimensional lattices of infinite bars and rods," Sov. Phys. Tech. Phys. 29, 604-614 (1959).

Kildishev, A. V.

Koschny, T.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Koschny, Th.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," arXiv:cond-mat/0504774v1, Apr. 29, 2005.

Lagarkov, A. N.

A. N. Lagarkov and A. K. Sarychev, "Electromagnetic properties of composites containing elongated conducting inclusions," Phys. Rev. B 53, 06318 (1996).
[CrossRef]

Lamb, H.

H. Lamb, "On group-velocity," Proc. London Math. Soc. , 1, 473-479 (1904).
[CrossRef]

Lee, J.-B.

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

Linden, S.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," arXiv:cond-mat/0504774v1, Apr. 29, 2005.

Malloy, K. J.

S. Zhang, W. Fan, K. J. MalloyS. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies," J. Opt. Soc. Am. B 23, 434-438 (2006).
[CrossRef]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Demonstration of near-infrared negative-index materials," arXiv: physics/0504208.

Mandel'shtam, L. I.

L. I. Mandel'shtam, "Group velocity in crystal lattice," JETP 15, 475 (1945). See also Ref. .

L. I. Mandel'shtam, "The 4th lecture of L. I. Mandel'shtam given at Moscow State University (05/05/1944)," in Collection of Scientific Works (Nauka, 1994), Vol. 5, pp. 461-467.

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Minhas, B. K.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

Mulot, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, "Negative refraction at infrared wavelengths in a two-dimensional photonic crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Narimanov, E. E.

V. A. Podolskiy and E. E. Narimanov, "Near-sighted superlens," Opt. Lett. 30, 75-77 (2005).
[CrossRef] [PubMed]

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A Pure Appl. Opt. 7, S32-S37 (2005).
[CrossRef]

Nelson, K. A.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, "Metrics for negative-refractive-index materials," Phys. Rev. E 70, 035602(R) (2004).
[CrossRef]

Osgood, R. M.

S. Zhang, W. Fan, K. J. MalloyS. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies," J. Opt. Soc. Am. B 23, 434-438 (2006).
[CrossRef]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Demonstration of near-infrared negative-index materials," arXiv: physics/0504208.

Osipov, M.

Y. Svirko, N. Zheludev, and M. Osipov, "Layered chiral metallic microstructures with inductive coupling," Appl. Phys. Lett. 78, 498-500 (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, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Panoiu, N. C.

S. Zhang, W. Fan, K. J. MalloyS. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies," J. Opt. Soc. Am. B 23, 434-438 (2006).
[CrossRef]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Demonstration of near-infrared negative-index materials," arXiv: physics/0504208.

Park, W.

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (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, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Podolskiy, V. A.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A Pure Appl. Opt. 7, S32-S37 (2005).
[CrossRef]

V. A. Podolskiy and E. E. Narimanov, "Near-sighted superlens," Opt. Lett. 30, 75-77 (2005).
[CrossRef] [PubMed]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735-745 (2003).
[CrossRef] [PubMed]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

A. K. Sarychev, V. P. Drachev, H.-K. Yuan, V. A. Podolskiy, and V. M. Shalaev, "Optical properties of metal nanowires," in Nanotubes and Nanowires, A.Lakhtakia and S.Maksinenku, eds., Proc. SPIE 5219, 92-98 (2003).

Qiu, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, "Negative refraction at infrared wavelengths in a two-dimensional photonic crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Sarychev, A. K.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A Pure Appl. Opt. 7, S32-S37 (2005).
[CrossRef]

V. M. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735-745 (2003).
[CrossRef] [PubMed]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

A. N. Lagarkov and A. K. Sarychev, "Electromagnetic properties of composites containing elongated conducting inclusions," Phys. Rev. B 53, 06318 (1996).
[CrossRef]

A. K. Sarychev and V. M. Shalaev, "Magnetic resonance in metal nanoantennas," in Complex Mediums V: Light and Complexity, M.W.McCall and G.Dewar, eds., Proc. SPIE 5508, 128-137 (2004).

A. K. Sarychev, V. P. Drachev, H.-K. Yuan, V. A. Podolskiy, and V. M. Shalaev, "Optical properties of metal nanowires," in Nanotubes and Nanowires, A.Lakhtakia and S.Maksinenku, eds., Proc. SPIE 5219, 92-98 (2003).

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," arXiv:cond-mat/0504774v1, Apr. 29, 2005.

Schonbrun, E.

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Schuster, A.

A. Schuster, An Introduction to the Theory of Optics (Edward Arnold, 1904).

Shalaev, V. M.

V. M. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A Pure Appl. Opt. 7, S32-S37 (2005).
[CrossRef]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes and negative refraction in metal nanowire composites," Opt. Express 11, 735-745 (2003).
[CrossRef] [PubMed]

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

A. K. Sarychev and V. M. Shalaev, "Magnetic resonance in metal nanoantennas," in Complex Mediums V: Light and Complexity, M.W.McCall and G.Dewar, eds., Proc. SPIE 5508, 128-137 (2004).

A. K. Sarychev, V. P. Drachev, H.-K. Yuan, V. A. Podolskiy, and V. M. Shalaev, "Optical properties of metal nanowires," in Nanotubes and Nanowires, A.Lakhtakia and S.Maksinenku, eds., Proc. SPIE 5219, 92-98 (2003).

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, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

Soukoulis, C.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Soukoulis, C. M.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," arXiv:cond-mat/0504774v1, Apr. 29, 2005.

Svirko, Y.

Y. Svirko, N. Zheludev, and M. Osipov, "Layered chiral metallic microstructures with inductive coupling," Appl. Phys. Lett. 78, 498-500 (2001).
[CrossRef]

Swillo, M.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, "Negative refraction at infrared wavelengths in a two-dimensional photonic crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Taflove, A.

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

Talneau, A.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, "Negative refraction at infrared wavelengths in a two-dimensional photonic crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Thylén, L.

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, "Negative refraction at infrared wavelengths in a two-dimensional photonic crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

Tinker, M.

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsi and µ," Sov. Phys. Usp. 10, 509-514 (1968).
[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, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Ward, D. W.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, "Metrics for negative-refractive-index materials," Phys. Rev. E 70, 035602(R) (2004).
[CrossRef]

Webb, K. J.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, "Metrics for negative-refractive-index materials," Phys. Rev. E 70, 035602(R) (2004).
[CrossRef]

Wegener, M.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," arXiv:cond-mat/0504774v1, Apr. 29, 2005.

Yang, M.

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, "Metrics for negative-refractive-index materials," Phys. Rev. E 70, 035602(R) (2004).
[CrossRef]

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, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Yuan, H.-K.

V. M. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

A. K. Sarychev, V. P. Drachev, H.-K. Yuan, V. A. Podolskiy, and V. M. Shalaev, "Optical properties of metal nanowires," in Nanotubes and Nanowires, A.Lakhtakia and S.Maksinenku, eds., Proc. SPIE 5219, 92-98 (2003).

Zhang, S.

S. Zhang, W. Fan, K. J. MalloyS. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, "Demonstration of metal-dielectric negative-index metamaterials with improved performance at optical frequencies," J. Opt. Soc. Am. B 23, 434-438 (2006).
[CrossRef]

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Demonstration of near-infrared negative-index materials," arXiv: physics/0504208.

Zhang, X.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

Zheludev, N.

Y. Svirko, N. Zheludev, and M. Osipov, "Layered chiral metallic microstructures with inductive coupling," Appl. Phys. Lett. 78, 498-500 (2001).
[CrossRef]

Zhou, J.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," arXiv:cond-mat/0504774v1, Apr. 29, 2005.

Zschiedrich, L.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," arXiv:cond-mat/0504774v1, Apr. 29, 2005.

Appl. Phys. Lett.

Y. Svirko, N. Zheludev, and M. Osipov, "Layered chiral metallic microstructures with inductive coupling," Appl. Phys. Lett. 78, 498-500 (2001).
[CrossRef]

IEEE Photon. Technol. Lett.

E. Schonbrun, M. Tinker, W. Park, and J.-B. Lee, "Negative refraction in a Si-polymer photonic crystal membrane," IEEE Photon. Technol. Lett. 17, 1196-1198 (2005).
[CrossRef]

J. Nonlinear Opt. Phys. Mater.

V. A. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

J. Opt. A Pure Appl. Opt.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A Pure Appl. Opt. 7, S32-S37 (2005).
[CrossRef]

J. Opt. Soc. Am. B

JETP

L. I. Mandel'shtam, "Group velocity in crystal lattice," JETP 15, 475 (1945). See also Ref. .

Opt. Express

Opt. Lett.

Phys. Rev. B

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, "Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients," Phys. Rev. B 65, 195104 (2002).
[CrossRef]

A. N. Lagarkov and A. K. Sarychev, "Electromagnetic properties of composites containing elongated conducting inclusions," Phys. Rev. B 53, 06318 (1996).
[CrossRef]

Phys. Rev. E

K. J. Webb, M. Yang, D. W. Ward, and K. A. Nelson, "Metrics for negative-refractive-index materials," Phys. Rev. E 70, 035602(R) (2004).
[CrossRef]

Phys. Rev. Lett.

S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 037402 (2005).
[CrossRef] [PubMed]

A. Berrier, M. Mulot, M. Swillo, M. Qiu, L. Thylén, A. Talneau, and S. Anand, "Negative refraction at infrared wavelengths in a two-dimensional photonic crystal," Phys. Rev. Lett. 93, 073902 (2004).
[CrossRef] [PubMed]

J. B. Pendry, "Negative refraction makes a perfect lens," Phys. Rev. Lett. 85, 3966-3969 (2000).
[CrossRef] [PubMed]

Proc. London Math. Soc.

H. Lamb, "On group-velocity," Proc. London Math. Soc. , 1, 473-479 (1904).
[CrossRef]

Science

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "Terahertz magnetic response from artificial materials," Science 303, 1494-1496 (2004).
[CrossRef] [PubMed]

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

Sov. Phys. Tech. Phys.

N. A. Khizhnyak, "Artificial anisotropic dielectrics formed from two-dimensional lattices of infinite bars and rods," Sov. Phys. Tech. Phys. 29, 604-614 (1959).

Sov. Phys. Usp.

V. G. Veselago, "The electrodynamics of substances with simultaneously negative values of epsi and µ," Sov. Phys. Usp. 10, 509-514 (1968).
[CrossRef]

Other

A. K. Sarychev and V. M. Shalaev, "Magnetic resonance in metal nanoantennas," in Complex Mediums V: Light and Complexity, M.W.McCall and G.Dewar, eds., Proc. SPIE 5508, 128-137 (2004).

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," arXiv:cond-mat/0504774v1, Apr. 29, 2005.

A. K. Sarychev, V. P. Drachev, H.-K. Yuan, V. A. Podolskiy, and V. M. Shalaev, "Optical properties of metal nanowires," in Nanotubes and Nanowires, A.Lakhtakia and S.Maksinenku, eds., Proc. SPIE 5219, 92-98 (2003).

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Demonstration of near-infrared negative-index materials," arXiv: physics/0504208.

J. D. Jackson, Classical Electrodynamics (Wiley, 1962), p. 291.

L. I. Mandel'shtam, "The 4th lecture of L. I. Mandel'shtam given at Moscow State University (05/05/1944)," in Collection of Scientific Works (Nauka, 1994), Vol. 5, pp. 461-467.

A. Schuster, An Introduction to the Theory of Optics (Edward Arnold, 1904).

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

A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering (Prentice Hall, 1991).

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Figures (17)

Fig. 1
Fig. 1

(a) Snell’s law at an interface between vacuum and a positive-refractive-index material, (b) reversed Snell’s law at the interface with NIM ( n = 1 ) , and (c) the superlens.

Fig. 2
Fig. 2

Multilayer structure illuminated from left to right by a monochromatic plane wave at normal incidence. Each layer is made of a homogeneous material and characterized by refractive index ( n ) , impedance ( Z ) , and thickness ( Δ ) .

Fig. 3
Fig. 3

(a) NIM layer in air ( n 0 = n 2 = 1 ) , (b) a single NIM layer on a bare glass substrate ( n 0 = 1 , n 2 = n s ), and (c) a NIM layer on an ITO–glass substrate ( n 0 = 1 , n 2 = n ITO , n 3 = n s ).

Fig. 4
Fig. 4

(a) Cross-section view of a NIM layer arranged from coupled gold strips separated by a layer of silica. The strips are infinite along the y axis (which is perpendicular to the cross-section plane). (b) Transverse magnetic field ( H y ) between the strips (for two different thicknesses of gold) for linear E x polarization of the incident field. (c) and (d) Reflectance (R), absorbance (A), and the refractive index ( n ) of the strips versus the wavelength of the incident light.

Fig. 5
Fig. 5

Refractive index of periodic paired strips obtained for six different geometries from FEM simulations and approximations at the same wavelength range. (a), (c), and (e) Strips are 440 nm wide; (b), (d), and (f), strips are 450 nm wide. Approximating function Ψ is given by expression (17).

Fig. 6
Fig. 6

Schematics of (a) polarization and (b) walk-off interferometers for measuring phase anisotropy and absolute phase induced by a NIM sample. LC is a liquid-crystal phase compensator, P is 45-deg linear polarizer, AC is an anisotropic calcite crystal with a walk-off effect, λ 2 is a half-wave plate, and PD is a photodetector.

Fig. 7
Fig. 7

Refractive index of a NIM layer restored from (a) FDTD simulations and (b) measurements. Approximations in both cases are obtained using expressions (16, 17).

Fig. 8
Fig. 8

(a) and (c), Single-periodic and (b) and (d) double-periodic models for numerical simulations of noncoupled rods deposited on an ITO–glass or bare glass substrate. Geometry in (b) and (d) represents sample A fabricated by electron-beam lithography.

Fig. 9
Fig. 9

Index of refraction for (a) parallel, and (b) perpendicular polarizations of incident light obtained from FDTD simulations with the geometry of Figs. 8a, 8c. (c) and (d) Transmittance (T), reflectance (R), and absorbance (A) calculated for the same polarizations.

Fig. 10
Fig. 10

(a) Index of refraction for parallel polarization and (b) the phase anisotropy in transmission obtained from FDTD simulations with the geometry of Figs. 8b, 8d. (c) Transmittance (T), reflectance (R), and absorbance (A) calculated for the same polarization. (d) Calculated values of the normalized transmission ( T T s ) are compared with the experimental data. (e) The refractive index for the identical composite structure but without any background. (f) T, R, and A for this case.

Fig. 11
Fig. 11

(a)–(d) Field maps for noncoupled rods on an ITO–glass substrate. (e)–(h) Similar maps for the sample without any background. In (a) and (e) electric field component E z is mapped at x y cross sections, through the middle of the rod; in (b) and (f), just 10 nm beyond the rod inside ITO. E z in (c) and (g) and H y in (d) and (h) are mapped at the x z cross section through the middle of the rod. All magnetic field values are normalized by the magnetic incident field taken at the geometrical center of the rod.

Fig. 12
Fig. 12

(c) Single-periodic and (d) skewed-periodic structures of coupled gold rods deposited on a bare glass substrate. Both models used the same rod pairs shown in (a). Geometry in (d) simulates a fabricated sample (sample B). (b) SEM image of sample B.

Fig. 13
Fig. 13

(a) Index of refraction for parallel polarization of incident light obtained from FDTD simulations with the geometry of Fig. 12a. (b) Simulated transmittance (T), reflectance (R), and absorbance (A) for parallel polarization.

Fig. 14
Fig. 14

Index of refraction for (a) parallel and (b) perpendicular polarizations of incident light obtained from FDTD simulations with the geometry of Figs. 8b, 8d. (c) and (d) Simulated and experimental transmittance ( T sim and T exp ) and reflectance ( R sim and R exp ) calculated for the same polarizations.

Fig. 15
Fig. 15

Simulated maps of E z obtained for two samples. (a) and (b) Field maps are calculated for the sample deposited on an ITO–glass substrate; (c) and (d) field maps are calculated for a similar sample deposited on bare glass (sample B). Electric field ( E z ) is mapped at two x y cross sections: through the middle of the rod, as in (a) and (c), or just 10 nm beyond the rod inside, ITO or glass, as in (b) and (d).

Fig. 16
Fig. 16

(a) Elementary cell of coupled elliptic voids as an inversion of coupled nanorods. (b) A cross-sectional view of the elementary cell shown in (a).

Fig. 17
Fig. 17

Index of refraction for (a) parallel polarization, and (b) perpendicular polarization of incident light is obtained from simulations for the inverted geometry of Figs. 16a, 16b. Approximations with expressions (16, 17) are also tested for the inverted geometry. Transmittance (T), reflectance (R), and absorbance (A) calculated for the same polarizations are shown in (c) and (d).

Equations (24)

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t = 2 z 11 + z 12 + z 21 + z 22 ,
r = ( z 11 + z 12 ) ( z 21 + z 22 ) z 11 + z 12 + z 21 + z 22 .
Z = ν = 1 max ( ν ) Z ν .
Z ν = [ cos ( n ν k Δ ν ) ι Z ν sin ( n ν k Δ ν ) ι Z ν 1 sin ( n ν k Δ ν ) cos ( n ν k Δ ν ) ] ,
cosh ζ = ( 1 t 2 + r 2 ) ( 2 r ) ,
cos N = ( 1 r 2 + t 2 ) ( 2 t ) ,
( t E , ν t H , ν ) = Z ν ( t E , ν + 1 t H , ν + 1 ) .
Z ν 2 = ( t E , ν 2 t E , ν + 1 2 ) ( t H , ν 2 t H , ν + 1 2 ) ,
n ν = N ν ( k Δ ν ) ,
N ν = cos 1 ( t E , ν t H , ν + t E , ν + 1 t H , ν + 1 t E , ν t H , ν + 1 + t E , ν + 1 t H , ν ) .
n ν = [ sign ( N ν ) N ν + 2 π l ] ( k Δ ν ) ,
n ν = sign ( N ν ) N ν ( k Δ ν ) ,
t E , 1 = 1 + r , t H , 1 = 1 r ,
N 1 = cos 1 [ 1 r 2 + n s t 2 ( n s + 1 ) t + r t ( n s 1 ) ] ,
( t E , 2 t H , 2 ) = Z 2 ( t n s t ) ,
Z 2 = [ cos ( n 2 k Δ 2 ) ι n 2 1 sin ( n 2 k Δ 2 ) ι n 2 sin ( n 2 k Δ 2 ) cos ( n 2 k Δ 2 ) ] ,
n arg t k Δ = τ k Δ ( r 1 ) ,
n ψ = ( arg t arg r π 2 ) k Δ ( r 1 ) ,
ε r ( ω ) = ε ω p 2 ω ( ω + i Γ ) ,
ε r ( ω ) = ε + χ 1 1 i ω t 0 σ i ω ε 0 ,
I 1 ( ω ) = χ 1 1 i ω t 0 E ( ω ) ,
I 2 ( ω ) = σ i ω ε 0 E ( ω ) .
I 1 ( t ) = ω p 2 t 0 0 t exp [ ( t τ ) t 0 ] E ( τ ) d τ ,
I 2 ( t ) = ω p 2 t 0 0 t E ( τ ) d τ .

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