Abstract

We present the design for a hexagonal cell made of quasi-periodic dendritic arranged collections of plasmonic metallic wires that may exhibit a resonant magnetic collective response. When such quasi-periodic dendritic cells are etched on a host medium, they may provide metamaterials with negative effective permeability. We also show that a clear point image is observed, as expected, with our left-handed metamaterials (LHMs) lens composed of metallic dendritic cells and wire strips. These prominent characteristics of quasi-periodic dendritic cells potentially enable us to prepare infrared or visible domain LHMs by using a general chemical method.

©2006 Optical Society of America

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References

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  1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85, 3966–3969 (2000).
    [Crossref] [PubMed]
  2. J. B. Pendry, “Perfect cylindrical lenses,” Opt. Express 11, 755–760 (2003).
    [Crossref] [PubMed]
  3. V. G. Veselago, “Electrodynamics of substances with simultaneously negative values of ϵ and μ,” Sov.Phys. Usp. 10, 509-514 (1968).
    [Crossref]
  4. D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004.)
    [Crossref] [PubMed]
  5. M. T. Grzegorczyk and J. A. Kong, “Left-handed materials composed of only S-shaped resonators,” Phys.Rev. E 70, 057605 (2004).
    [Crossref]
  6. M. T. Grzegorczyk and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004).
    [Crossref]
  7. I. Bulu, H. Caglayan, and E. Ozbay, “Experimental demonstration of labyrinth-based left-handed metamaterials,” Opt. Express 13, 10238–10247 (2005).
    [Crossref] [PubMed]
  8. J. Rothman, M. Klaui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C. Bland, Z. Cui, and R. Speaks, “Observation of a bi-domain state and nucleation free switching in Mesoscopic Ring Magnets,” Phys. Rev. Lett. 86, 1098–1101 (2001).
    [Crossref] [PubMed]
  9. L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 264–270 (Oxford, Pergamon,1960).
  10. 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. 95,203901 (2005).
    [Crossref] [PubMed]
  11. A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
    [Crossref] [PubMed]
  12. Y. Sawada, A. Dougherty, and J. P. Gollub, “Dendritic and fractal patterns in electrolytic metal deposits,” Phys. Rev. Lett. 56, 1260–1263 (1986).
    [Crossref] [PubMed]
  13. Y. J. Song, Y. Yang, C. J. Medforll, E. Pereira, A. K. Singh, Y. B. Jiang, C. J. Brinker, F. V. Swol, and J. A. Shelnutt, “Controlled synthesis of 2-D and 3-D dendritic platinum nanostructures,” J. Am. Chem. Soc. 126, 635–645 (2004).
    [Crossref] [PubMed]
  14. X. Q. Wang, H. Itoh, K. Naka, and Y. Chujo, “Tetrathiafulvalene-assisted formation of silver dendritic nanostructures in acetonitrile,” Langmuir 19, 6242–6246 (2003).
    [Crossref]
  15. J. J. Flory, “Molecular size distribution in three-dimensional polymersVI. Branched polymers containing A -R-Bf-1-type units,” J. Am. Chem. Soc. 74, 2718–2718 (1952).
    [Crossref]
  16. J. S. Patko and D. H. Werner, “Miniature reconfigurable three-dimensional fractal tree antennas,” IEEETrans. Antennas Propag. 52, 1945–1956 (2004).
    [Crossref]
  17. D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
    [Crossref]
  18. F. L. Zhang, Q Zhao, Y. H. Liu, C. R. Luo, and X. P. Zhao, “Behaviour of hexagon split ring resonators andleft-handed metamaterials,” Chin. Phys. Lett. 21, 1330–1332 (2004).
    [Crossref]
  19. X. P. Zhao, Q. Zhao, L. Kang, J. Song, and Q. H. Fu, “Defect effect of split ring resonators in left-handed metamaterials,” Phys. Lett. A 346, 87–91 (2005).
    [Crossref]
  20. X. P. Zhao, Q. Zhao, F. L. Zhang, W. Zhao, and Y. H. Liu, “Stopband phenomena in the passband of left-handed metamaterials,” Chin. Phys. Lett. 23, 99–102 (2006).
    [Crossref]
  21. T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93, 107402 (2004).
    [Crossref] [PubMed]
  22. D. H. Werner and R. Mittra, Frontiers in Electromagnetics, 732–770 (IEEE Press, Piscataway, 2000).
  23. A. N. Lagarkov and V. N. Kissel, “Near-perfect imaging in a focusing system based on a left-handed material plate,” Phys. Rev. Lett. 92, 077401 (2004).
    [Crossref] [PubMed]

2006 (2)

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
[Crossref]

X. P. Zhao, Q. Zhao, F. L. Zhang, W. Zhao, and Y. H. Liu, “Stopband phenomena in the passband of left-handed metamaterials,” Chin. Phys. Lett. 23, 99–102 (2006).
[Crossref]

2005 (4)

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. 95,203901 (2005).
[Crossref] [PubMed]

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

X. P. Zhao, Q. Zhao, L. Kang, J. Song, and Q. H. Fu, “Defect effect of split ring resonators in left-handed metamaterials,” Phys. Lett. A 346, 87–91 (2005).
[Crossref]

I. Bulu, H. Caglayan, and E. Ozbay, “Experimental demonstration of labyrinth-based left-handed metamaterials,” Opt. Express 13, 10238–10247 (2005).
[Crossref] [PubMed]

2004 (8)

Y. J. Song, Y. Yang, C. J. Medforll, E. Pereira, A. K. Singh, Y. B. Jiang, C. J. Brinker, F. V. Swol, and J. A. Shelnutt, “Controlled synthesis of 2-D and 3-D dendritic platinum nanostructures,” J. Am. Chem. Soc. 126, 635–645 (2004).
[Crossref] [PubMed]

F. L. Zhang, Q Zhao, Y. H. Liu, C. R. Luo, and X. P. Zhao, “Behaviour of hexagon split ring resonators andleft-handed metamaterials,” Chin. Phys. Lett. 21, 1330–1332 (2004).
[Crossref]

J. S. Patko and D. H. Werner, “Miniature reconfigurable three-dimensional fractal tree antennas,” IEEETrans. Antennas Propag. 52, 1945–1956 (2004).
[Crossref]

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93, 107402 (2004).
[Crossref] [PubMed]

A. N. Lagarkov and V. N. Kissel, “Near-perfect imaging in a focusing system based on a left-handed material plate,” Phys. Rev. Lett. 92, 077401 (2004).
[Crossref] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004.)
[Crossref] [PubMed]

M. T. Grzegorczyk and J. A. Kong, “Left-handed materials composed of only S-shaped resonators,” Phys.Rev. E 70, 057605 (2004).
[Crossref]

M. T. Grzegorczyk and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004).
[Crossref]

2003 (2)

X. Q. Wang, H. Itoh, K. Naka, and Y. Chujo, “Tetrathiafulvalene-assisted formation of silver dendritic nanostructures in acetonitrile,” Langmuir 19, 6242–6246 (2003).
[Crossref]

J. B. Pendry, “Perfect cylindrical lenses,” Opt. Express 11, 755–760 (2003).
[Crossref] [PubMed]

2001 (1)

J. Rothman, M. Klaui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C. Bland, Z. Cui, and R. Speaks, “Observation of a bi-domain state and nucleation free switching in Mesoscopic Ring Magnets,” Phys. Rev. Lett. 86, 1098–1101 (2001).
[Crossref] [PubMed]

2000 (1)

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

1986 (1)

Y. Sawada, A. Dougherty, and J. P. Gollub, “Dendritic and fractal patterns in electrolytic metal deposits,” Phys. Rev. Lett. 56, 1260–1263 (1986).
[Crossref] [PubMed]

1968 (1)

V. G. Veselago, “Electrodynamics of substances with simultaneously negative values of ϵ and μ,” Sov.Phys. Usp. 10, 509-514 (1968).
[Crossref]

1952 (1)

J. J. Flory, “Molecular size distribution in three-dimensional polymersVI. Branched polymers containing A -R-Bf-1-type units,” J. Am. Chem. Soc. 74, 2718–2718 (1952).
[Crossref]

Bland, J. A. C.

J. Rothman, M. Klaui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C. Bland, Z. Cui, and R. Speaks, “Observation of a bi-domain state and nucleation free switching in Mesoscopic Ring Magnets,” Phys. Rev. Lett. 86, 1098–1101 (2001).
[Crossref] [PubMed]

Bleloch, A.

J. Rothman, M. Klaui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C. Bland, Z. Cui, and R. Speaks, “Observation of a bi-domain state and nucleation free switching in Mesoscopic Ring Magnets,” Phys. Rev. Lett. 86, 1098–1101 (2001).
[Crossref] [PubMed]

Brinker, C. J.

Y. J. Song, Y. Yang, C. J. Medforll, E. Pereira, A. K. Singh, Y. B. Jiang, C. J. Brinker, F. V. Swol, and J. A. Shelnutt, “Controlled synthesis of 2-D and 3-D dendritic platinum nanostructures,” J. Am. Chem. Soc. 126, 635–645 (2004).
[Crossref] [PubMed]

Bulu, I.

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. 95,203901 (2005).
[Crossref] [PubMed]

Caglayan, H.

Chujo, Y.

X. Q. Wang, H. Itoh, K. Naka, and Y. Chujo, “Tetrathiafulvalene-assisted formation of silver dendritic nanostructures in acetonitrile,” Langmuir 19, 6242–6246 (2003).
[Crossref]

Cui, Z.

J. Rothman, M. Klaui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C. Bland, Z. Cui, and R. Speaks, “Observation of a bi-domain state and nucleation free switching in Mesoscopic Ring Magnets,” Phys. Rev. Lett. 86, 1098–1101 (2001).
[Crossref] [PubMed]

Dougherty, A.

Y. Sawada, A. Dougherty, and J. P. Gollub, “Dendritic and fractal patterns in electrolytic metal deposits,” Phys. Rev. Lett. 56, 1260–1263 (1986).
[Crossref] [PubMed]

Economou, E. N.

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93, 107402 (2004).
[Crossref] [PubMed]

Enkrich, C.

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. 95,203901 (2005).
[Crossref] [PubMed]

Firsov, A. A.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

Flory, J. J.

J. J. Flory, “Molecular size distribution in three-dimensional polymersVI. Branched polymers containing A -R-Bf-1-type units,” J. Am. Chem. Soc. 74, 2718–2718 (1952).
[Crossref]

Fu, Q. H.

X. P. Zhao, Q. Zhao, L. Kang, J. Song, and Q. H. Fu, “Defect effect of split ring resonators in left-handed metamaterials,” Phys. Lett. A 346, 87–91 (2005).
[Crossref]

Geim, A. K.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

Gleeson, H. F.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

Gollub, J. P.

Y. Sawada, A. Dougherty, and J. P. Gollub, “Dendritic and fractal patterns in electrolytic metal deposits,” Phys. Rev. Lett. 56, 1260–1263 (1986).
[Crossref] [PubMed]

Grigorenko, A. N.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

Grzegorczyk, M. T.

M. T. Grzegorczyk and J. A. Kong, “Left-handed materials composed of only S-shaped resonators,” Phys.Rev. E 70, 057605 (2004).
[Crossref]

M. T. Grzegorczyk and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004).
[Crossref]

Itoh, H.

X. Q. Wang, H. Itoh, K. Naka, and Y. Chujo, “Tetrathiafulvalene-assisted formation of silver dendritic nanostructures in acetonitrile,” Langmuir 19, 6242–6246 (2003).
[Crossref]

Jiang, Y. B.

Y. J. Song, Y. Yang, C. J. Medforll, E. Pereira, A. K. Singh, Y. B. Jiang, C. J. Brinker, F. V. Swol, and J. A. Shelnutt, “Controlled synthesis of 2-D and 3-D dendritic platinum nanostructures,” J. Am. Chem. Soc. 126, 635–645 (2004).
[Crossref] [PubMed]

Kafesaki, M.

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93, 107402 (2004).
[Crossref] [PubMed]

Kang, L.

X. P. Zhao, Q. Zhao, L. Kang, J. Song, and Q. H. Fu, “Defect effect of split ring resonators in left-handed metamaterials,” Phys. Lett. A 346, 87–91 (2005).
[Crossref]

Khrushchev, I. Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

Kissel, V. N.

A. N. Lagarkov and V. N. Kissel, “Near-perfect imaging in a focusing system based on a left-handed material plate,” Phys. Rev. Lett. 92, 077401 (2004).
[Crossref] [PubMed]

Klaui, M.

J. Rothman, M. Klaui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C. Bland, Z. Cui, and R. Speaks, “Observation of a bi-domain state and nucleation free switching in Mesoscopic Ring Magnets,” Phys. Rev. Lett. 86, 1098–1101 (2001).
[Crossref] [PubMed]

Kong, J. A.

M. T. Grzegorczyk and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004).
[Crossref]

M. T. Grzegorczyk and J. A. Kong, “Left-handed materials composed of only S-shaped resonators,” Phys.Rev. E 70, 057605 (2004).
[Crossref]

Koschny, T.

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93, 107402 (2004).
[Crossref] [PubMed]

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. 95,203901 (2005).
[Crossref] [PubMed]

Lagarkov, A. N.

A. N. Lagarkov and V. N. Kissel, “Near-perfect imaging in a focusing system based on a left-handed material plate,” Phys. Rev. Lett. 92, 077401 (2004).
[Crossref] [PubMed]

Landau, L. D.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 264–270 (Oxford, Pergamon,1960).

Lifshitz, E. M.

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 264–270 (Oxford, Pergamon,1960).

Linden, 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. 95,203901 (2005).
[Crossref] [PubMed]

Liu, Y. H.

X. P. Zhao, Q. Zhao, F. L. Zhang, W. Zhao, and Y. H. Liu, “Stopband phenomena in the passband of left-handed metamaterials,” Chin. Phys. Lett. 23, 99–102 (2006).
[Crossref]

F. L. Zhang, Q Zhao, Y. H. Liu, C. R. Luo, and X. P. Zhao, “Behaviour of hexagon split ring resonators andleft-handed metamaterials,” Chin. Phys. Lett. 21, 1330–1332 (2004).
[Crossref]

Lopez-Diaz, L.

J. Rothman, M. Klaui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C. Bland, Z. Cui, and R. Speaks, “Observation of a bi-domain state and nucleation free switching in Mesoscopic Ring Magnets,” Phys. Rev. Lett. 86, 1098–1101 (2001).
[Crossref] [PubMed]

Luo, C. R.

F. L. Zhang, Q Zhao, Y. H. Liu, C. R. Luo, and X. P. Zhao, “Behaviour of hexagon split ring resonators andleft-handed metamaterials,” Chin. Phys. Lett. 21, 1330–1332 (2004).
[Crossref]

Medforll, C. J.

Y. J. Song, Y. Yang, C. J. Medforll, E. Pereira, A. K. Singh, Y. B. Jiang, C. J. Brinker, F. V. Swol, and J. A. Shelnutt, “Controlled synthesis of 2-D and 3-D dendritic platinum nanostructures,” J. Am. Chem. Soc. 126, 635–645 (2004).
[Crossref] [PubMed]

Mittra, R.

D. H. Werner and R. Mittra, Frontiers in Electromagnetics, 732–770 (IEEE Press, Piscataway, 2000).

Mock, J. J.

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
[Crossref]

Naka, K.

X. Q. Wang, H. Itoh, K. Naka, and Y. Chujo, “Tetrathiafulvalene-assisted formation of silver dendritic nanostructures in acetonitrile,” Langmuir 19, 6242–6246 (2003).
[Crossref]

Ozbay, E.

Patko, J. S.

J. S. Patko and D. H. Werner, “Miniature reconfigurable three-dimensional fractal tree antennas,” IEEETrans. Antennas Propag. 52, 1945–1956 (2004).
[Crossref]

Pendry, J. B.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004.)
[Crossref] [PubMed]

J. B. Pendry, “Perfect cylindrical lenses,” Opt. Express 11, 755–760 (2003).
[Crossref] [PubMed]

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

Pereira, E.

Y. J. Song, Y. Yang, C. J. Medforll, E. Pereira, A. K. Singh, Y. B. Jiang, C. J. Brinker, F. V. Swol, and J. A. Shelnutt, “Controlled synthesis of 2-D and 3-D dendritic platinum nanostructures,” J. Am. Chem. Soc. 126, 635–645 (2004).
[Crossref] [PubMed]

Petrovic, J.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

Rothman, J.

J. Rothman, M. Klaui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C. Bland, Z. Cui, and R. Speaks, “Observation of a bi-domain state and nucleation free switching in Mesoscopic Ring Magnets,” Phys. Rev. Lett. 86, 1098–1101 (2001).
[Crossref] [PubMed]

Sawada, Y.

Y. Sawada, A. Dougherty, and J. P. Gollub, “Dendritic and fractal patterns in electrolytic metal deposits,” Phys. Rev. Lett. 56, 1260–1263 (1986).
[Crossref] [PubMed]

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. 95,203901 (2005).
[Crossref] [PubMed]

Schurig, D.

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
[Crossref]

Shelnutt, J. A.

Y. J. Song, Y. Yang, C. J. Medforll, E. Pereira, A. K. Singh, Y. B. Jiang, C. J. Brinker, F. V. Swol, and J. A. Shelnutt, “Controlled synthesis of 2-D and 3-D dendritic platinum nanostructures,” J. Am. Chem. Soc. 126, 635–645 (2004).
[Crossref] [PubMed]

Singh, A. K.

Y. J. Song, Y. Yang, C. J. Medforll, E. Pereira, A. K. Singh, Y. B. Jiang, C. J. Brinker, F. V. Swol, and J. A. Shelnutt, “Controlled synthesis of 2-D and 3-D dendritic platinum nanostructures,” J. Am. Chem. Soc. 126, 635–645 (2004).
[Crossref] [PubMed]

Smith, D. R.

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
[Crossref]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004.)
[Crossref] [PubMed]

Song, J.

X. P. Zhao, Q. Zhao, L. Kang, J. Song, and Q. H. Fu, “Defect effect of split ring resonators in left-handed metamaterials,” Phys. Lett. A 346, 87–91 (2005).
[Crossref]

Song, Y. J.

Y. J. Song, Y. Yang, C. J. Medforll, E. Pereira, A. K. Singh, Y. B. Jiang, C. J. Brinker, F. V. Swol, and J. A. Shelnutt, “Controlled synthesis of 2-D and 3-D dendritic platinum nanostructures,” J. Am. Chem. Soc. 126, 635–645 (2004).
[Crossref] [PubMed]

Soukoulis, C. M.

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93, 107402 (2004).
[Crossref] [PubMed]

Soukoulis, C.M.

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. 95,203901 (2005).
[Crossref] [PubMed]

Speaks, R.

J. Rothman, M. Klaui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C. Bland, Z. Cui, and R. Speaks, “Observation of a bi-domain state and nucleation free switching in Mesoscopic Ring Magnets,” Phys. Rev. Lett. 86, 1098–1101 (2001).
[Crossref] [PubMed]

Swol, F. V.

Y. J. Song, Y. Yang, C. J. Medforll, E. Pereira, A. K. Singh, Y. B. Jiang, C. J. Brinker, F. V. Swol, and J. A. Shelnutt, “Controlled synthesis of 2-D and 3-D dendritic platinum nanostructures,” J. Am. Chem. Soc. 126, 635–645 (2004).
[Crossref] [PubMed]

Vaz, C. A. F.

J. Rothman, M. Klaui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C. Bland, Z. Cui, and R. Speaks, “Observation of a bi-domain state and nucleation free switching in Mesoscopic Ring Magnets,” Phys. Rev. Lett. 86, 1098–1101 (2001).
[Crossref] [PubMed]

Veselago, V. G.

V. G. Veselago, “Electrodynamics of substances with simultaneously negative values of ϵ and μ,” Sov.Phys. Usp. 10, 509-514 (1968).
[Crossref]

Wang, X. Q.

X. Q. Wang, H. Itoh, K. Naka, and Y. Chujo, “Tetrathiafulvalene-assisted formation of silver dendritic nanostructures in acetonitrile,” Langmuir 19, 6242–6246 (2003).
[Crossref]

Wegener, M.

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. 95,203901 (2005).
[Crossref] [PubMed]

Werner, D. H.

J. S. Patko and D. H. Werner, “Miniature reconfigurable three-dimensional fractal tree antennas,” IEEETrans. Antennas Propag. 52, 1945–1956 (2004).
[Crossref]

D. H. Werner and R. Mittra, Frontiers in Electromagnetics, 732–770 (IEEE Press, Piscataway, 2000).

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004.)
[Crossref] [PubMed]

Yang, Y.

Y. J. Song, Y. Yang, C. J. Medforll, E. Pereira, A. K. Singh, Y. B. Jiang, C. J. Brinker, F. V. Swol, and J. A. Shelnutt, “Controlled synthesis of 2-D and 3-D dendritic platinum nanostructures,” J. Am. Chem. Soc. 126, 635–645 (2004).
[Crossref] [PubMed]

Zhang, F. L.

X. P. Zhao, Q. Zhao, F. L. Zhang, W. Zhao, and Y. H. Liu, “Stopband phenomena in the passband of left-handed metamaterials,” Chin. Phys. Lett. 23, 99–102 (2006).
[Crossref]

F. L. Zhang, Q Zhao, Y. H. Liu, C. R. Luo, and X. P. Zhao, “Behaviour of hexagon split ring resonators andleft-handed metamaterials,” Chin. Phys. Lett. 21, 1330–1332 (2004).
[Crossref]

Zhang, Y.

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

Zhao, Q

F. L. Zhang, Q Zhao, Y. H. Liu, C. R. Luo, and X. P. Zhao, “Behaviour of hexagon split ring resonators andleft-handed metamaterials,” Chin. Phys. Lett. 21, 1330–1332 (2004).
[Crossref]

Zhao, Q.

X. P. Zhao, Q. Zhao, F. L. Zhang, W. Zhao, and Y. H. Liu, “Stopband phenomena in the passband of left-handed metamaterials,” Chin. Phys. Lett. 23, 99–102 (2006).
[Crossref]

X. P. Zhao, Q. Zhao, L. Kang, J. Song, and Q. H. Fu, “Defect effect of split ring resonators in left-handed metamaterials,” Phys. Lett. A 346, 87–91 (2005).
[Crossref]

Zhao, W.

X. P. Zhao, Q. Zhao, F. L. Zhang, W. Zhao, and Y. H. Liu, “Stopband phenomena in the passband of left-handed metamaterials,” Chin. Phys. Lett. 23, 99–102 (2006).
[Crossref]

Zhao, X. P.

X. P. Zhao, Q. Zhao, F. L. Zhang, W. Zhao, and Y. H. Liu, “Stopband phenomena in the passband of left-handed metamaterials,” Chin. Phys. Lett. 23, 99–102 (2006).
[Crossref]

X. P. Zhao, Q. Zhao, L. Kang, J. Song, and Q. H. Fu, “Defect effect of split ring resonators in left-handed metamaterials,” Phys. Lett. A 346, 87–91 (2005).
[Crossref]

F. L. Zhang, Q Zhao, Y. H. Liu, C. R. Luo, and X. P. Zhao, “Behaviour of hexagon split ring resonators andleft-handed metamaterials,” Chin. Phys. Lett. 21, 1330–1332 (2004).
[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. 95,203901 (2005).
[Crossref] [PubMed]

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. 95,203901 (2005).
[Crossref] [PubMed]

Appl. Phys. Lett. (2)

D. Schurig, J. J. Mock, and D. R. Smith, “Electric-field-coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett. 88, 041109 (2006).
[Crossref]

M. T. Grzegorczyk and J. A. Kong, “Experimental confirmation of negative refractive index of a metamaterial composed of Ω-like metallic patterns,” Appl. Phys. Lett. 84, 1537–1539 (2004).
[Crossref]

Chin. Phys. Lett. (2)

F. L. Zhang, Q Zhao, Y. H. Liu, C. R. Luo, and X. P. Zhao, “Behaviour of hexagon split ring resonators andleft-handed metamaterials,” Chin. Phys. Lett. 21, 1330–1332 (2004).
[Crossref]

X. P. Zhao, Q. Zhao, F. L. Zhang, W. Zhao, and Y. H. Liu, “Stopband phenomena in the passband of left-handed metamaterials,” Chin. Phys. Lett. 23, 99–102 (2006).
[Crossref]

IEEETrans. Antennas Propag. (1)

J. S. Patko and D. H. Werner, “Miniature reconfigurable three-dimensional fractal tree antennas,” IEEETrans. Antennas Propag. 52, 1945–1956 (2004).
[Crossref]

J. Am. Chem. Soc. (2)

Y. J. Song, Y. Yang, C. J. Medforll, E. Pereira, A. K. Singh, Y. B. Jiang, C. J. Brinker, F. V. Swol, and J. A. Shelnutt, “Controlled synthesis of 2-D and 3-D dendritic platinum nanostructures,” J. Am. Chem. Soc. 126, 635–645 (2004).
[Crossref] [PubMed]

J. J. Flory, “Molecular size distribution in three-dimensional polymersVI. Branched polymers containing A -R-Bf-1-type units,” J. Am. Chem. Soc. 74, 2718–2718 (1952).
[Crossref]

Langmuir (1)

X. Q. Wang, H. Itoh, K. Naka, and Y. Chujo, “Tetrathiafulvalene-assisted formation of silver dendritic nanostructures in acetonitrile,” Langmuir 19, 6242–6246 (2003).
[Crossref]

Nature (1)

A. N. Grigorenko, A. K. Geim, H. F. Gleeson, Y. Zhang, A. A. Firsov, I. Y. Khrushchev, and J. Petrovic, “Nanofabricated media with negative permeability at visible frequencies,” Nature 438, 335–338 (2005).
[Crossref] [PubMed]

Opt. Express (2)

Phys. Lett. A (1)

X. P. Zhao, Q. Zhao, L. Kang, J. Song, and Q. H. Fu, “Defect effect of split ring resonators in left-handed metamaterials,” Phys. Lett. A 346, 87–91 (2005).
[Crossref]

Phys. Rev. Lett. (6)

T. Koschny, M. Kafesaki, E. N. Economou, and C. M. Soukoulis, “Effective medium theory of left-handed materials,” Phys. Rev. Lett. 93, 107402 (2004).
[Crossref] [PubMed]

A. N. Lagarkov and V. N. Kissel, “Near-perfect imaging in a focusing system based on a left-handed material plate,” Phys. Rev. Lett. 92, 077401 (2004).
[Crossref] [PubMed]

Y. Sawada, A. Dougherty, and J. P. Gollub, “Dendritic and fractal patterns in electrolytic metal deposits,” Phys. Rev. Lett. 56, 1260–1263 (1986).
[Crossref] [PubMed]

J. Rothman, M. Klaui, L. Lopez-Diaz, C. A. F. Vaz, A. Bleloch, J. A. C. Bland, Z. Cui, and R. Speaks, “Observation of a bi-domain state and nucleation free switching in Mesoscopic Ring Magnets,” Phys. Rev. Lett. 86, 1098–1101 (2001).
[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. 95,203901 (2005).
[Crossref] [PubMed]

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

Phys.Rev. E (1)

M. T. Grzegorczyk and J. A. Kong, “Left-handed materials composed of only S-shaped resonators,” Phys.Rev. E 70, 057605 (2004).
[Crossref]

Science (1)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, “Metamaterials and negative refractive index,” Science 305, 788–792 (2004.)
[Crossref] [PubMed]

Sov.Phys. Usp. (1)

V. G. Veselago, “Electrodynamics of substances with simultaneously negative values of ϵ and μ,” Sov.Phys. Usp. 10, 509-514 (1968).
[Crossref]

Other (2)

D. H. Werner and R. Mittra, Frontiers in Electromagnetics, 732–770 (IEEE Press, Piscataway, 2000).

L. D. Landau and E. M. Lifshitz, Electrodynamics of Continuous Media, 264–270 (Oxford, Pergamon,1960).

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Figures (7)

Fig. 1.
Fig. 1. Morphology of the dendritic geometry, defining the dimension of a dendritic geometry with parameter a, b, c, and θ. Some split irregular polygon rings (SIPRs) are shown in the dendritic geometry.

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Fig. 2.
Fig. 2. (a) Simulated and experimental transmission spectrums of the two branches, 3rd-order dendritic cell (black curves), Simulated transmission spectrum of SIPRs (red curve); (b) Simulated and experimental transmission spectrum of the circular dendritic cell (black curve), experimental transmission spectrum of the “closed” circular dendritic cell (blue).

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Fig. 3.
Fig. 3. (a) [left panel] Induced magnetic field at a plane perpendicular to the dendritic structure plane, [right panel] Induced surface current at the dendritic structure plane. (b) [left panel] Induced magnetic field at a plane perpendicular to the SIRP plane, [right panel] Induced surface current at the SIRP plane. (c) Induced surface current at the circular dendritic structure plane.

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Fig. 4.
Fig. 4. Calculated effective permeability for sample 2.

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Fig. 5.
Fig. 5. Measured transmission spectrum of circular dendritic structures combined with wires. Inset: Measured phase spectrum of circular dendritic structures combined with wires and Teflon slab.

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Fig. 6.
Fig. 6. Top view of the experimental setup for flat lens focusing. The left side of the LHMs monopole antenna used as the point source, and the right one used as the receiver.

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Fig. 7.
Fig. 7. (a) Measured result of field amplitude at 9.4 GHz with the receiving antenna moving parallel to the plate, (b) 3D view of Schematic (a), (c) measured intensity distribution along the transverse (Y) direction at the image plane (x = 0 mm) with and without LHMs lens.

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Equations (8)

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{ D = ε r ̿ ε 0 E + j ε 0 μ 0 χ ̿ T H B = μ r ̿ μ 0 H − j ε 0 μ 0 χ ̿ E ,
{ D = ε 0 E + P = ε 0 E + N p B = μ 0 ( H + M ) = μ 0 ( H + N m ) ,
{ p = ε 0 ( a e e ̿ E l o c + a e m ̿ η H l o c ) m = a m m ̿ H l o c + a m e ̿ E l o c η ,
{ E l o c = E + P ( 3 ε 0 ) H l o c = H + M 3 .
{ ε r ̿ = I ̿ + K ̿ 1 − 1 [ N a e e ̿ + N 2 3 a e m ̿ ( I ̿ − N a m m ̿ 3 ) − 1 a m e ̿ ] μ r ̿ = I ̿ + K ̿ 2 − 1 [ N a m m ̿ + N 2 3 a m e ̿ ( I ̿ − N a e e ̿ 3 ) − 1 a e m ̿ ] χ ̿ = j K ̿ 2 − 1 N a m e ̿ ̿ [ I ̿ + ( I ̿ − N a e e ̿ 3 ) − 1 N a e e ̿ 3 ]
{ K 1 ̿ = I ̿ − N a e e ̿ 3 − N 2 9 a e m ̿ ( I ̿ − N a m m ̿ 3 ) − 1 a m e ̿ K 2 ̿ = I ̿ − N a m m ̿ 3 − N 2 9 a m e ̿ ( I ̿ − N a e e ̿ 3 ) − 1 a e m ̿ .
μ r ̿ = ( 1 0 0 0 1 + N a m m y y ( 1 − N a m m y y 3 ) 0 0 0 1 ) .
μ r y y = 1 + N a m m y y ( 1 − N a m m y y 3 )

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