Abstract

As a consequent work of the two-dimensional (2D) dendritic metamaterial which has been systematically studied in our previous work, a model of three-dimensional (3D) sphere-rod shaped structure is presented. Based on Drude model of the dielectric function of silver in the visible region, the parametric curves of electromagnetic response to the incident fields have been retrieved from detailed simulations. It is shown that the simultaneously negative values of permittivity and permeability in the optical range lead to a negative refractive index (NIM) through adjusting structural parameters, only the dimensions of the unit cells satisfy the effective medium theory. We therefore conclude that the proposed model offers a feasible route to fabricating 3D optical NIMs by ‘bottom-up’ approach.

© 2010 OSA

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  3. R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78(4), 489–491 (2001).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  7. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006).
    [CrossRef] [PubMed]
  8. G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
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    [CrossRef] [PubMed]
  11. S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
    [CrossRef] [PubMed]
  12. C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
    [CrossRef] [PubMed]
  13. C. Enkrich, F. Perez-Williard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17(21), 2547 (2005).
    [CrossRef]
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    [CrossRef]
  17. X. Zhou and X. P. Zhao, “Resonant condition of unitary dendritic structure with overlapping negative permittivity and permeability,” Appl. Phys. Lett. 91(18), 181908 (2007).
    [CrossRef]
  18. H. Liu, X. P. Zhao, Y. Yang, Q. W. Li, and J. Lv, “Fabrication of infrared left-handed metamaterials via double template-assisted electrochemical deposition,” Adv. Mater. 20(11), 2050–2054 (2008).
    [CrossRef]
  19. B. Q. Liu, X. P. Zhao, W. R. Zhu, W. Luo, and X. C. Cheng, “Multiple Pass-Band Optical Left-Handed Metamaterials Based on Random Dendritic Cells,” Adv. Funct. Mater. 18(21), 3523–3528 (2008).
    [CrossRef]
  20. X. P. Zhao, W. Luo, J. X. Huang, Q. H. Fu, K. Song, X. C. Cheng, and C. R. Luo, “Trapped rainbow effect in visible light left-handed heterostructures,” Appl. Phys. Lett. 95(7), 071111 (2009).
    [CrossRef]
  21. J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
    [CrossRef] [PubMed]
  22. P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
    [CrossRef]
  23. X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
    [CrossRef] [PubMed]
  24. V. D. Lam, J. B. Kim, S. J. Lee, and Y. P. Lee, “Left-handed behavior of combined and fishnet structures,” J. Appl. Phys. 103(3), 033107 (2008).
    [CrossRef]
  25. R. A. Depine and A. A. Lakhtakia, “New condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity,” Microw. Opt. Technol. Lett. 41(4), 315–316 (2004).
    [CrossRef]

2009 (2)

Y. Yao, Q. H. Fu, and X. P. Zhao, “Three-level dendritic structure with simultaneously negative permeability and permittivity under normal incidence of electromagnetic wave,” J. Appl. Phys. 105(2), 024911 (2009).
[CrossRef]

X. P. Zhao, W. Luo, J. X. Huang, Q. H. Fu, K. Song, X. C. Cheng, and C. R. Luo, “Trapped rainbow effect in visible light left-handed heterostructures,” Appl. Phys. Lett. 95(7), 071111 (2009).
[CrossRef]

2008 (4)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

H. Liu, X. P. Zhao, Y. Yang, Q. W. Li, and J. Lv, “Fabrication of infrared left-handed metamaterials via double template-assisted electrochemical deposition,” Adv. Mater. 20(11), 2050–2054 (2008).
[CrossRef]

B. Q. Liu, X. P. Zhao, W. R. Zhu, W. Luo, and X. C. Cheng, “Multiple Pass-Band Optical Left-Handed Metamaterials Based on Random Dendritic Cells,” Adv. Funct. Mater. 18(21), 3523–3528 (2008).
[CrossRef]

V. D. Lam, J. B. Kim, S. J. Lee, and Y. P. Lee, “Left-handed behavior of combined and fishnet structures,” J. Appl. Phys. 103(3), 033107 (2008).
[CrossRef]

2007 (4)

Y. Yao and X. P. Zhao, “Multilevel dendritic structure with simultaneously negative permeability and permittivity,” J. Appl. Phys. 101(12), 124904 (2007).
[CrossRef]

X. Zhou and X. P. Zhao, “Resonant condition of unitary dendritic structure with overlapping negative permittivity and permeability,” Appl. Phys. Lett. 91(18), 181908 (2007).
[CrossRef]

G. Dolling, M. Wegener, and S. Linden, “Realization of a three-founctional-layer negative-index photonic metamaterial,” Opt. Lett. 32(5), 551–553 (2007).
[CrossRef] [PubMed]

U. K. Chettiar, A. V. Kildishev, H. K. Yuan, W. Cai, S. Xiao, V. P. Drachev, and V. M. Shalaev, “Dual-band negative index metamaterial: double negative at 813 nm and single negative at 772 nm,” Opt. Lett. 32(12), 1671–1673 (2007).
[CrossRef] [PubMed]

2006 (3)

2005 (4)

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005).
[CrossRef] [PubMed]

S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[CrossRef] [PubMed]

C. Enkrich, F. Perez-Williard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17(21), 2547 (2005).
[CrossRef]

2004 (2)

X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

R. A. Depine and A. A. Lakhtakia, “New condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity,” Microw. Opt. Technol. Lett. 41(4), 315–316 (2004).
[CrossRef]

2003 (2)

2001 (2)

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78(4), 489–491 (2001).
[CrossRef]

2000 (1)

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

1972 (1)

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Alù, A.

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005).
[CrossRef] [PubMed]

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Bearpark, T.

N. Seddon and T. Bearpark, “Observation of the inverse Doppler effect,” Science 302(5650), 1537–1540 (2003).
[CrossRef] [PubMed]

Brueck, S. R. J.

S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[CrossRef] [PubMed]

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[CrossRef] [PubMed]

Cai, W.

Chen, M.

Chen, X. D.

X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

Cheng, X. C.

X. P. Zhao, W. Luo, J. X. Huang, Q. H. Fu, K. Song, X. C. Cheng, and C. R. Luo, “Trapped rainbow effect in visible light left-handed heterostructures,” Appl. Phys. Lett. 95(7), 071111 (2009).
[CrossRef]

B. Q. Liu, X. P. Zhao, W. R. Zhu, W. Luo, and X. C. Cheng, “Multiple Pass-Band Optical Left-Handed Metamaterials Based on Random Dendritic Cells,” Adv. Funct. Mater. 18(21), 3523–3528 (2008).
[CrossRef]

Chettiar, U. K.

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Depine, R. A.

R. A. Depine and A. A. Lakhtakia, “New condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity,” Microw. Opt. Technol. Lett. 41(4), 315–316 (2004).
[CrossRef]

Dolling, G.

Drachev, V. P.

Engheta, N.

A. Alù and N. Engheta, “Achieving transparency with plasmonic and metamaterial coatings,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 72(1), 016623 (2005).
[CrossRef] [PubMed]

Enkrich, C.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006).
[CrossRef] [PubMed]

C. Enkrich, F. Perez-Williard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17(21), 2547 (2005).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[CrossRef] [PubMed]

Fan, W. J.

S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[CrossRef] [PubMed]

Fu, Q. H.

X. P. Zhao, W. Luo, J. X. Huang, Q. H. Fu, K. Song, X. C. Cheng, and C. R. Luo, “Trapped rainbow effect in visible light left-handed heterostructures,” Appl. Phys. Lett. 95(7), 071111 (2009).
[CrossRef]

Y. Yao, Q. H. Fu, and X. P. Zhao, “Three-level dendritic structure with simultaneously negative permeability and permittivity under normal incidence of electromagnetic wave,” J. Appl. Phys. 105(2), 024911 (2009).
[CrossRef]

X. Zhou, Q. H. Fu, J. Zhao, Y. Yang, and X. P. Zhao, “Negative permeability and subwavelength focusing of quasi-periodic dendritic cell metamaterials,” Opt. Express 14(16), 7188–7197 (2006).
[CrossRef] [PubMed]

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Gerthsen, D.

C. Enkrich, F. Perez-Williard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17(21), 2547 (2005).
[CrossRef]

Grzegorczyk, T. M.

X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

J. Lu, T. M. Grzegorczyk, Y. Zhang, J. Pacheco, B. I. Wu, J. A. Kong, and M. Chen, “Cerenkov radiation in materials with negative permittivity and permeability,” Opt. Express 11(7), 723–734 (2003).
[CrossRef] [PubMed]

Huang, J. X.

X. P. Zhao, W. Luo, J. X. Huang, Q. H. Fu, K. Song, X. C. Cheng, and C. R. Luo, “Trapped rainbow effect in visible light left-handed heterostructures,” Appl. Phys. Lett. 95(7), 071111 (2009).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical Constants of the Noble Metals,” Phys. Rev. B 6(12), 4370–4379 (1972).
[CrossRef]

Kildishev, A. V.

Kim, J. B.

V. D. Lam, J. B. Kim, S. J. Lee, and Y. P. Lee, “Left-handed behavior of combined and fishnet structures,” J. Appl. Phys. 103(3), 033107 (2008).
[CrossRef]

Kong, J. A.

X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

J. Lu, T. M. Grzegorczyk, Y. Zhang, J. Pacheco, B. I. Wu, J. A. Kong, and M. Chen, “Cerenkov radiation in materials with negative permittivity and permeability,” Opt. Express 11(7), 723–734 (2003).
[CrossRef] [PubMed]

Koschny, T.

C. Enkrich, F. Perez-Williard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17(21), 2547 (2005).
[CrossRef]

Koschny, Th.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[CrossRef] [PubMed]

Lakhtakia, A. A.

R. A. Depine and A. A. Lakhtakia, “New condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity,” Microw. Opt. Technol. Lett. 41(4), 315–316 (2004).
[CrossRef]

Lam, V. D.

V. D. Lam, J. B. Kim, S. J. Lee, and Y. P. Lee, “Left-handed behavior of combined and fishnet structures,” J. Appl. Phys. 103(3), 033107 (2008).
[CrossRef]

Lee, S. J.

V. D. Lam, J. B. Kim, S. J. Lee, and Y. P. Lee, “Left-handed behavior of combined and fishnet structures,” J. Appl. Phys. 103(3), 033107 (2008).
[CrossRef]

Lee, Y. P.

V. D. Lam, J. B. Kim, S. J. Lee, and Y. P. Lee, “Left-handed behavior of combined and fishnet structures,” J. Appl. Phys. 103(3), 033107 (2008).
[CrossRef]

Li, Q. W.

H. Liu, X. P. Zhao, Y. Yang, Q. W. Li, and J. Lv, “Fabrication of infrared left-handed metamaterials via double template-assisted electrochemical deposition,” Adv. Mater. 20(11), 2050–2054 (2008).
[CrossRef]

Linden, S.

G. Dolling, M. Wegener, and S. Linden, “Realization of a three-founctional-layer negative-index photonic metamaterial,” Opt. Lett. 32(5), 551–553 (2007).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[CrossRef] [PubMed]

C. Enkrich, F. Perez-Williard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17(21), 2547 (2005).
[CrossRef]

Liu, B. Q.

B. Q. Liu, X. P. Zhao, W. R. Zhu, W. Luo, and X. C. Cheng, “Multiple Pass-Band Optical Left-Handed Metamaterials Based on Random Dendritic Cells,” Adv. Funct. Mater. 18(21), 3523–3528 (2008).
[CrossRef]

Liu, H.

H. Liu, X. P. Zhao, Y. Yang, Q. W. Li, and J. Lv, “Fabrication of infrared left-handed metamaterials via double template-assisted electrochemical deposition,” Adv. Mater. 20(11), 2050–2054 (2008).
[CrossRef]

Lu, J.

Luo, C. R.

X. P. Zhao, W. Luo, J. X. Huang, Q. H. Fu, K. Song, X. C. Cheng, and C. R. Luo, “Trapped rainbow effect in visible light left-handed heterostructures,” Appl. Phys. Lett. 95(7), 071111 (2009).
[CrossRef]

Luo, W.

X. P. Zhao, W. Luo, J. X. Huang, Q. H. Fu, K. Song, X. C. Cheng, and C. R. Luo, “Trapped rainbow effect in visible light left-handed heterostructures,” Appl. Phys. Lett. 95(7), 071111 (2009).
[CrossRef]

B. Q. Liu, X. P. Zhao, W. R. Zhu, W. Luo, and X. C. Cheng, “Multiple Pass-Band Optical Left-Handed Metamaterials Based on Random Dendritic Cells,” Adv. Funct. Mater. 18(21), 3523–3528 (2008).
[CrossRef]

Lv, J.

H. Liu, X. P. Zhao, Y. Yang, Q. W. Li, and J. Lv, “Fabrication of infrared left-handed metamaterials via double template-assisted electrochemical deposition,” Adv. Mater. 20(11), 2050–2054 (2008).
[CrossRef]

Malloy, K. J.

S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[CrossRef] [PubMed]

Nemat-Nasser, S. C.

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78(4), 489–491 (2001).
[CrossRef]

Osgood, R. M.

S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[CrossRef] [PubMed]

Pacheco, J.

X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
[CrossRef] [PubMed]

J. Lu, T. M. Grzegorczyk, Y. Zhang, J. Pacheco, B. I. Wu, J. A. Kong, and M. Chen, “Cerenkov radiation in materials with negative permittivity and permeability,” Opt. Express 11(7), 723–734 (2003).
[CrossRef] [PubMed]

Panoiu, N. C.

S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

Perez-Williard, F.

C. Enkrich, F. Perez-Williard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17(21), 2547 (2005).
[CrossRef]

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[CrossRef] [PubMed]

Schultz, S.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78(4), 489–491 (2001).
[CrossRef]

Seddon, N.

N. Seddon and T. Bearpark, “Observation of the inverse Doppler effect,” Science 302(5650), 1537–1540 (2003).
[CrossRef] [PubMed]

Shalaev, V. M.

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78(4), 489–491 (2001).
[CrossRef]

Smith, D. R.

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78(4), 489–491 (2001).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

Song, K.

X. P. Zhao, W. Luo, J. X. Huang, Q. H. Fu, K. Song, X. C. Cheng, and C. R. Luo, “Trapped rainbow effect in visible light left-handed heterostructures,” Appl. Phys. Lett. 95(7), 071111 (2009).
[CrossRef]

Soukoulis, C. M.

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
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C. Enkrich, F. Perez-Williard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17(21), 2547 (2005).
[CrossRef]

Ulin-Avila, E.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

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J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

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G. Dolling, M. Wegener, and S. Linden, “Realization of a three-founctional-layer negative-index photonic metamaterial,” Opt. Lett. 32(5), 551–553 (2007).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Low-loss negative-index metamaterial at telecommunication wavelengths,” Opt. Lett. 31(12), 1800–1802 (2006).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[CrossRef] [PubMed]

C. Enkrich, F. Perez-Williard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17(21), 2547 (2005).
[CrossRef]

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Wu, B.-I.

X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
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Yang, Y.

H. Liu, X. P. Zhao, Y. Yang, Q. W. Li, and J. Lv, “Fabrication of infrared left-handed metamaterials via double template-assisted electrochemical deposition,” Adv. Mater. 20(11), 2050–2054 (2008).
[CrossRef]

X. Zhou, Q. H. Fu, J. Zhao, Y. Yang, and X. P. Zhao, “Negative permeability and subwavelength focusing of quasi-periodic dendritic cell metamaterials,” Opt. Express 14(16), 7188–7197 (2006).
[CrossRef] [PubMed]

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Y. Yao, Q. H. Fu, and X. P. Zhao, “Three-level dendritic structure with simultaneously negative permeability and permittivity under normal incidence of electromagnetic wave,” J. Appl. Phys. 105(2), 024911 (2009).
[CrossRef]

Y. Yao and X. P. Zhao, “Multilevel dendritic structure with simultaneously negative permeability and permittivity,” J. Appl. Phys. 101(12), 124904 (2007).
[CrossRef]

Yuan, H. K.

Zentgraf, T.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

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J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[CrossRef] [PubMed]

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J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Zhang, Y.

Zhao, J.

Zhao, X. P.

Y. Yao, Q. H. Fu, and X. P. Zhao, “Three-level dendritic structure with simultaneously negative permeability and permittivity under normal incidence of electromagnetic wave,” J. Appl. Phys. 105(2), 024911 (2009).
[CrossRef]

X. P. Zhao, W. Luo, J. X. Huang, Q. H. Fu, K. Song, X. C. Cheng, and C. R. Luo, “Trapped rainbow effect in visible light left-handed heterostructures,” Appl. Phys. Lett. 95(7), 071111 (2009).
[CrossRef]

B. Q. Liu, X. P. Zhao, W. R. Zhu, W. Luo, and X. C. Cheng, “Multiple Pass-Band Optical Left-Handed Metamaterials Based on Random Dendritic Cells,” Adv. Funct. Mater. 18(21), 3523–3528 (2008).
[CrossRef]

H. Liu, X. P. Zhao, Y. Yang, Q. W. Li, and J. Lv, “Fabrication of infrared left-handed metamaterials via double template-assisted electrochemical deposition,” Adv. Mater. 20(11), 2050–2054 (2008).
[CrossRef]

X. Zhou and X. P. Zhao, “Resonant condition of unitary dendritic structure with overlapping negative permittivity and permeability,” Appl. Phys. Lett. 91(18), 181908 (2007).
[CrossRef]

Y. Yao and X. P. Zhao, “Multilevel dendritic structure with simultaneously negative permeability and permittivity,” J. Appl. Phys. 101(12), 124904 (2007).
[CrossRef]

X. Zhou, Q. H. Fu, J. Zhao, Y. Yang, and X. P. Zhao, “Negative permeability and subwavelength focusing of quasi-periodic dendritic cell metamaterials,” Opt. Express 14(16), 7188–7197 (2006).
[CrossRef] [PubMed]

Zhou, J.

C. Enkrich, F. Perez-Williard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17(21), 2547 (2005).
[CrossRef]

Zhou, J. F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[CrossRef] [PubMed]

Zhou, X.

X. Zhou and X. P. Zhao, “Resonant condition of unitary dendritic structure with overlapping negative permittivity and permeability,” Appl. Phys. Lett. 91(18), 181908 (2007).
[CrossRef]

X. Zhou, Q. H. Fu, J. Zhao, Y. Yang, and X. P. Zhao, “Negative permeability and subwavelength focusing of quasi-periodic dendritic cell metamaterials,” Opt. Express 14(16), 7188–7197 (2006).
[CrossRef] [PubMed]

Zhu, W. R.

B. Q. Liu, X. P. Zhao, W. R. Zhu, W. Luo, and X. C. Cheng, “Multiple Pass-Band Optical Left-Handed Metamaterials Based on Random Dendritic Cells,” Adv. Funct. Mater. 18(21), 3523–3528 (2008).
[CrossRef]

Zschiedrich, L.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[CrossRef] [PubMed]

Adv. Funct. Mater. (1)

B. Q. Liu, X. P. Zhao, W. R. Zhu, W. Luo, and X. C. Cheng, “Multiple Pass-Band Optical Left-Handed Metamaterials Based on Random Dendritic Cells,” Adv. Funct. Mater. 18(21), 3523–3528 (2008).
[CrossRef]

Adv. Mater. (2)

H. Liu, X. P. Zhao, Y. Yang, Q. W. Li, and J. Lv, “Fabrication of infrared left-handed metamaterials via double template-assisted electrochemical deposition,” Adv. Mater. 20(11), 2050–2054 (2008).
[CrossRef]

C. Enkrich, F. Perez-Williard, D. Gerthsen, J. Zhou, T. Koschny, C. M. Soukoulis, M. Wegener, and S. Linden, “Focused-ion-beam nanofabrication of near-infrared magnetic metamaterials,” Adv. Mater. 17(21), 2547 (2005).
[CrossRef]

Appl. Phys. Lett. (3)

X. Zhou and X. P. Zhao, “Resonant condition of unitary dendritic structure with overlapping negative permittivity and permeability,” Appl. Phys. Lett. 91(18), 181908 (2007).
[CrossRef]

X. P. Zhao, W. Luo, J. X. Huang, Q. H. Fu, K. Song, X. C. Cheng, and C. R. Luo, “Trapped rainbow effect in visible light left-handed heterostructures,” Appl. Phys. Lett. 95(7), 071111 (2009).
[CrossRef]

R. A. Shelby, D. R. Smith, S. C. Nemat-Nasser, and S. Schultz, “Microwave transmission through a two-dimensional, isotropic, left-handed metamaterial,” Appl. Phys. Lett. 78(4), 489–491 (2001).
[CrossRef]

J. Appl. Phys. (3)

Y. Yao and X. P. Zhao, “Multilevel dendritic structure with simultaneously negative permeability and permittivity,” J. Appl. Phys. 101(12), 124904 (2007).
[CrossRef]

Y. Yao, Q. H. Fu, and X. P. Zhao, “Three-level dendritic structure with simultaneously negative permeability and permittivity under normal incidence of electromagnetic wave,” J. Appl. Phys. 105(2), 024911 (2009).
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V. D. Lam, J. B. Kim, S. J. Lee, and Y. P. Lee, “Left-handed behavior of combined and fishnet structures,” J. Appl. Phys. 103(3), 033107 (2008).
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R. A. Depine and A. A. Lakhtakia, “New condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity,” Microw. Opt. Technol. Lett. 41(4), 315–316 (2004).
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Nature (1)

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature 455(7211), 376–379 (2008).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. B (1)

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[CrossRef]

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

X. D. Chen, T. M. Grzegorczyk, B.-I. Wu, J. Pacheco, and J. A. Kong, “Robust method to retrieve the constitutive effective parameters of metamaterials,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70(1), 016608 (2004).
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J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
[CrossRef] [PubMed]

S. Zhang, W. J. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, “Experimental demonstration of near-infrared negative-index metamaterials,” Phys. Rev. Lett. 95(13), 137404 (2005).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, Th. Koschny, and C. M. Soukoulis, “Magnetic metamaterials at telecommunication and visible frequencies,” Phys. Rev. Lett. 95(20), 203901 (2005).
[CrossRef] [PubMed]

Science (3)

N. Seddon and T. Bearpark, “Observation of the inverse Doppler effect,” Science 302(5650), 1537–1540 (2003).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
[CrossRef] [PubMed]

G. Dolling, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, “Simultaneous negative phase and group velocity of light in a metamaterial,” Science 312(5775), 892–894 (2006).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

The structural unit and its all dimensions. The electromagnetic radiation is set as the transverse electric and magnetic (TEM) mode.

Fig. 2
Fig. 2

The real and imaginary parts of the permeability of the unit structure composed of (a) only the rods (L = 60 nm, r = 15 nm, t = 15 nm, a = 130 nm) and (b) only the nucleus (L = 60 nm, r = 62 nm, t = 15 nm, a = 132 nm).

Fig. 3
Fig. 3

The spectra of transmission, reflection, permeability, permittivity and refractive index from simulations for specific dimensions: L = 65 nm, r = 39 nm, t = 19 nm, a = 140 nm. (a) Transmission and reflection coefficients. (b) The effective permeability. (c) The effective permittivity. (d) The effective refractive index.

Fig. 4
Fig. 4

The spectra of the retrieved parameters from simulations for L = 50 nm, r = 39 nm, t = 18 nm, a = 110 nm. (a) Transmission and reflection coefficients. (b) The effective permeability. (c) The effective permittivity. (d) The effective refractive index.

Fig. 5
Fig. 5

The distribution of induced currents in the cross section and the configuration of the incident fields. (a) The resonance occurs at red-light frequencies. (b) The resonance occurs at blue-light frequencies.

Fig. 6
Fig. 6

The calculated value of P (a) for the structure with L = 65nm, r = 39nm, a = 140nm, t = 19nm and (c) for the structure with L = 50nm, r = 39nm, a = 110nm, t = 18nm.

Fig. 7
Fig. 7

The retrieved impedance for the up two cases. (a) Response to red-light. (b) Response to blue-light.

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