Abstract

The design principle of split-ring resonators (SRRs) for realizing negative magnetic metamaterial is proposed through theoretical investigation of magnetic properties of SRRs from terahertz (THz) to the visible light region. To describe the frequency dispersion of metal throughout the frequency range, we consider the exact expression of the internal impedance formula. Our results indicate that the design principle should be changed completely at the transition frequency of 100THz. Below 100THz, since the resistance of the SRRs determines the magnetic responses, low-resistance structures are essential. On the other hand, we should design the SRRs’ structures maintaining large geometrical inductance above the 100THz region, because the decrease of the geometrical inductance dominantly reduces the magnetic responses.

© 2007 Optical Society of America

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  1. J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
    [CrossRef]
  2. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
    [CrossRef] [PubMed]
  3. R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
    [CrossRef] [PubMed]
  4. V. G. Veselago, "The electrodynamics of substance with simultaneously negative value of epsilon and μ," Sov. Phys. Usp. 10, 509-514 (1968).
    [CrossRef]
  5. 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]
  6. 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, 037402-1-037402-4 (2005).
    [CrossRef]
  7. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
    [CrossRef] [PubMed]
  8. 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, 203901-1-203901-4 (2005).
    [CrossRef]
  9. N.-C. Panoiu and R. M. Osgood, Jr., "Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials," Phys. Rev. E 68, 016611-1-016611-12 (2003).
    [CrossRef]
  10. S. O'Brien and J. B. Pendry, "Magnetic activity at infrared frequencies in structured metallic photonic crystals," J. Phys. Condens. Matter 14, 6383-6394 (2002).
    [CrossRef]
  11. S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101-1-241101-4 (2004).
    [CrossRef]
  12. J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-1-223902-4 (2005).
    [CrossRef]
  13. A. Ishikawa, T. Tanaka, and S. Kawata, "Negative magnetic permeability in the visible light region," Phys. Rev. Lett. 95, 237401-1-237401-4 (2005).
    [CrossRef]
  14. M. Born and E. Wolf, Principle of Optics, 6th ed. (Pergamon Press, 1980), pp. 624-627.
  15. S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics, 3rd ed. (Wiley, 1993), pp. 149-155.
  16. P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
    [CrossRef]
  17. K. C. Gupta, R. Garg, I. Bahl, and P. Bhartia, Microstrip Lines and Slotlines, 2nd ed. (Artech House, 1996), pp. 375-456.
  18. R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design-theory and experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
    [CrossRef]
  19. I. A. Larkin, M. I. Stockman, M. Achermann, and V. I. Klimov, "Dipolar emitters at nanoscale proximity of metal surfaces: giant enhancement of relaxation in microscopic theory," Phys. Rev. B 69, 121403-1-121403-4 (2004).
    [CrossRef]
  20. V. M. Shalaev, W. Cai, U. K. 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]
  21. S. Zhang, W. 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, 137404-1-137404-4 (2005).
    [CrossRef]

2005 (6)

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, 037402-1-037402-4 (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, 203901-1-203901-4 (2005).
[CrossRef]

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-1-223902-4 (2005).
[CrossRef]

A. Ishikawa, T. Tanaka, and S. Kawata, "Negative magnetic permeability in the visible light region," Phys. Rev. Lett. 95, 237401-1-237401-4 (2005).
[CrossRef]

S. Zhang, W. 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, 137404-1-137404-4 (2005).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. 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]

2004 (4)

I. A. Larkin, M. I. Stockman, M. Achermann, and V. I. Klimov, "Dipolar emitters at nanoscale proximity of metal surfaces: giant enhancement of relaxation in microscopic theory," Phys. Rev. B 69, 121403-1-121403-4 (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. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101-1-241101-4 (2004).
[CrossRef]

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

2003 (2)

N.-C. Panoiu and R. M. Osgood, Jr., "Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials," Phys. Rev. E 68, 016611-1-016611-12 (2003).
[CrossRef]

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design-theory and experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

2002 (1)

S. O'Brien and J. B. Pendry, "Magnetic activity at infrared frequencies in structured metallic photonic crystals," J. Phys. Condens. Matter 14, 6383-6394 (2002).
[CrossRef]

2001 (1)

R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

2000 (1)

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

1968 (1)

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

Achermann, M.

I. A. Larkin, M. I. Stockman, M. Achermann, and V. I. Klimov, "Dipolar emitters at nanoscale proximity of metal surfaces: giant enhancement of relaxation in microscopic theory," Phys. Rev. B 69, 121403-1-121403-4 (2004).
[CrossRef]

Bahl, I.

K. C. Gupta, R. Garg, I. Bahl, and P. Bhartia, Microstrip Lines and Slotlines, 2nd ed. (Artech House, 1996), pp. 375-456.

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]

Bhartia, P.

K. C. Gupta, R. Garg, I. Bahl, and P. Bhartia, Microstrip Lines and Slotlines, 2nd ed. (Artech House, 1996), pp. 375-456.

Born, M.

M. Born and E. Wolf, Principle of Optics, 6th ed. (Pergamon Press, 1980), pp. 624-627.

Brueck, S. R. J.

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, 037402-1-037402-4 (2005).
[CrossRef]

S. Zhang, W. 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, 137404-1-137404-4 (2005).
[CrossRef]

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, 203901-1-203901-4 (2005).
[CrossRef]

Cai, W.

Chettiar, U. K.

Christy, R. W.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Drachev, V. P.

Duzer, T. V.

S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics, 3rd ed. (Wiley, 1993), pp. 149-155.

Economou, E. N.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-1-223902-4 (2005).
[CrossRef]

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, 203901-1-203901-4 (2005).
[CrossRef]

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

Fan, W.

S. Zhang, W. 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, 137404-1-137404-4 (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, 037402-1-037402-4 (2005).
[CrossRef]

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, 037402-1-037402-4 (2005).
[CrossRef]

Garg, R.

K. C. Gupta, R. Garg, I. Bahl, and P. Bhartia, Microstrip Lines and Slotlines, 2nd ed. (Artech House, 1996), pp. 375-456.

Gupta, K. C.

K. C. Gupta, R. Garg, I. Bahl, and P. Bhartia, Microstrip Lines and Slotlines, 2nd ed. (Artech House, 1996), pp. 375-456.

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Ishikawa, A.

A. Ishikawa, T. Tanaka, and S. Kawata, "Negative magnetic permeability in the visible light region," Phys. Rev. Lett. 95, 237401-1-237401-4 (2005).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Kafesaki, M.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-1-223902-4 (2005).
[CrossRef]

Kawata, S.

A. Ishikawa, T. Tanaka, and S. Kawata, "Negative magnetic permeability in the visible light region," Phys. Rev. Lett. 95, 237401-1-237401-4 (2005).
[CrossRef]

Kildishev, A. V.

Klimov, V. I.

I. A. Larkin, M. I. Stockman, M. Achermann, and V. I. Klimov, "Dipolar emitters at nanoscale proximity of metal surfaces: giant enhancement of relaxation in microscopic theory," Phys. Rev. B 69, 121403-1-121403-4 (2004).
[CrossRef]

Koschny, T.

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. 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. F. Zhou, Th. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95, 203901-1-203901-4 (2005).
[CrossRef]

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-1-223902-4 (2005).
[CrossRef]

Larkin, I. A.

I. A. Larkin, M. I. Stockman, M. Achermann, and V. I. Klimov, "Dipolar emitters at nanoscale proximity of metal surfaces: giant enhancement of relaxation in microscopic theory," Phys. Rev. B 69, 121403-1-121403-4 (2004).
[CrossRef]

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, 203901-1-203901-4 (2005).
[CrossRef]

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

Malloy, K. J.

S. Zhang, W. 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, 137404-1-137404-4 (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, 037402-1-037402-4 (2005).
[CrossRef]

Marques, R.

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design-theory and experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

Martel, J.

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design-theory and experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

McPeake, D.

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101-1-241101-4 (2004).
[CrossRef]

Medina, F.

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design-theory and experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

Mesa, F.

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design-theory and experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[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, 037402-1-037402-4 (2005).
[CrossRef]

Nemat-Nasser, S. C.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

O'Brien, S.

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101-1-241101-4 (2004).
[CrossRef]

S. O'Brien and J. B. Pendry, "Magnetic activity at infrared frequencies in structured metallic photonic crystals," J. Phys. Condens. Matter 14, 6383-6394 (2002).
[CrossRef]

Osgood, R. M.

S. Zhang, W. 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, 137404-1-137404-4 (2005).
[CrossRef]

N.-C. Panoiu and R. M. Osgood, Jr., "Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials," Phys. Rev. E 68, 016611-1-016611-12 (2003).
[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]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Panoiu, N. C.

S. Zhang, W. 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, 137404-1-137404-4 (2005).
[CrossRef]

Panoiu, N.-C.

N.-C. Panoiu and R. M. Osgood, Jr., "Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials," Phys. Rev. E 68, 016611-1-016611-12 (2003).
[CrossRef]

Pendry, J. B.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-1-223902-4 (2005).
[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. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101-1-241101-4 (2004).
[CrossRef]

S. O'Brien and J. B. Pendry, "Magnetic activity at infrared frequencies in structured metallic photonic crystals," J. Phys. Condens. Matter 14, 6383-6394 (2002).
[CrossRef]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Ramakrishna, S. A.

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101-1-241101-4 (2004).
[CrossRef]

Ramo, S.

S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics, 3rd ed. (Wiley, 1993), pp. 149-155.

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Sarychev, A. K.

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, 203901-1-203901-4 (2005).
[CrossRef]

Schultz, S.

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Shalaev, V. M.

Shelby, R. A.

R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Shultz, S.

R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Smith, D. R.

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

R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

Soukoulis, C. M.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-1-223902-4 (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, 203901-1-203901-4 (2005).
[CrossRef]

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

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

Stockman, M. I.

I. A. Larkin, M. I. Stockman, M. Achermann, and V. I. Klimov, "Dipolar emitters at nanoscale proximity of metal surfaces: giant enhancement of relaxation in microscopic theory," Phys. Rev. B 69, 121403-1-121403-4 (2004).
[CrossRef]

Tanaka, T.

A. Ishikawa, T. Tanaka, and S. Kawata, "Negative magnetic permeability in the visible light region," Phys. Rev. Lett. 95, 237401-1-237401-4 (2005).
[CrossRef]

Veselago, V. G.

V. G. Veselago, "The electrodynamics of substance with simultaneously negative value of epsilon 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]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

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, 203901-1-203901-4 (2005).
[CrossRef]

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

Whinnery, J. R.

S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics, 3rd ed. (Wiley, 1993), pp. 149-155.

Wolf, E.

M. Born and E. Wolf, Principle of Optics, 6th ed. (Pergamon Press, 1980), pp. 624-627.

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.

Zhang, S.

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, 037402-1-037402-4 (2005).
[CrossRef]

S. Zhang, W. 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, 137404-1-137404-4 (2005).
[CrossRef]

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]

Zhou, J.

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-1-223902-4 (2005).
[CrossRef]

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

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, 203901-1-203901-4 (2005).
[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, 203901-1-203901-4 (2005).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

R. Marques, F. Mesa, J. Martel, and F. Medina, "Comparative analysis of edge- and broadside-coupled split ring resonators for metamaterial design-theory and experiments," IEEE Trans. Antennas Propag. 51, 2572-2581 (2003).
[CrossRef]

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Magnetism from conductors and enhanced nonlinear phenomena," IEEE Trans. Microwave Theory Tech. 47, 2075-2084 (1999).
[CrossRef]

J. Phys. Condens. Matter (1)

S. O'Brien and J. B. Pendry, "Magnetic activity at infrared frequencies in structured metallic photonic crystals," J. Phys. Condens. Matter 14, 6383-6394 (2002).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (3)

S. O'Brien, D. McPeake, S. A. Ramakrishna, and J. B. Pendry, "Near-infrared photonic band gaps and nonlinear effects in negative magnetic metamaterials," Phys. Rev. B 69, 241101-1-241101-4 (2004).
[CrossRef]

I. A. Larkin, M. I. Stockman, M. Achermann, and V. I. Klimov, "Dipolar emitters at nanoscale proximity of metal surfaces: giant enhancement of relaxation in microscopic theory," Phys. Rev. B 69, 121403-1-121403-4 (2004).
[CrossRef]

P. B. Johnson and R. W. Christy, "Optical constants of the noble metals," Phys. Rev. B 6, 4370-4379 (1972).
[CrossRef]

Phys. Rev. E (1)

N.-C. Panoiu and R. M. Osgood, Jr., "Influence of the dispersive properties of metals on the transmission characteristics of left-handed materials," Phys. Rev. E 68, 016611-1-016611-12 (2003).
[CrossRef]

Phys. Rev. Lett. (6)

S. Zhang, W. 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, 137404-1-137404-4 (2005).
[CrossRef]

J. Zhou, Th. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-1-223902-4 (2005).
[CrossRef]

A. Ishikawa, T. Tanaka, and S. Kawata, "Negative magnetic permeability in the visible light region," Phys. Rev. Lett. 95, 237401-1-237401-4 (2005).
[CrossRef]

D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, "Composite medium with simultaneously negative permeability and permittivity," Phys. Rev. Lett. 84, 4184-4187 (2000).
[CrossRef] [PubMed]

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, 037402-1-037402-4 (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, 203901-1-203901-4 (2005).
[CrossRef]

Science (3)

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. M. Soukoulis, "Magnetic response of metamaterials at 100 terahertz," Science 306, 1351-1353 (2004).
[CrossRef] [PubMed]

R. A. Shelby, D. R. Smith, and S. Shultz, "Experimental verification of a negative index of refraction," Science 292, 77-79 (2001).
[CrossRef] [PubMed]

Sov. Phys. Usp. (1)

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

Other (3)

M. Born and E. Wolf, Principle of Optics, 6th ed. (Pergamon Press, 1980), pp. 624-627.

S. Ramo, J. R. Whinnery, and T. V. Duzer, Fields and Waves in Communication Electronics, 3rd ed. (Wiley, 1993), pp. 149-155.

K. C. Gupta, R. Garg, I. Bahl, and P. Bhartia, Microstrip Lines and Slotlines, 2nd ed. (Artech House, 1996), pp. 375-456.

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Figures (8)

Fig. 1
Fig. 1

Dispersion curves of the internal impedance of silver, gold, and copper; R s : surface resistivity; X s : internal reactance.

Fig. 2
Fig. 2

Models of SRRs used in calculations below 100 THz . (a) Element of the SRR and (b) array of the SRRs placed in the host material with relative permittivity of ϵ r .

Fig. 3
Fig. 3

Real and imaginary parts of the effective permeability of silver SRRs in the host material ( ϵ r = 2.25 ) as a function of the SRRs’ dimensions. The labeling in each case indicates the unit-cell dimension a. The corresponding other dimensions of each SRR are given in Table 1.

Fig. 4
Fig. 4

Frequency dependencies of the minimum μ R e of the SRRs made of silver, gold, and copper. The μ R e minimum frequency dependence of the unit-cell dimension a of the silver SRRs is also shown.

Fig. 5
Fig. 5

Models of single s-SRR used in calculations above 100 THz . (a) Element of the s-SRR and (b) array of the s-SRRs placed in the host material with relative permittivity of ϵ r .

Fig. 6
Fig. 6

Real and imaginary parts of the effective permeability of silver s-SRRs in the host material ( ϵ r = 2.25 ) as a function of the s-SRRs’ dimensions. The labeling in each case indicates the unit-cell dimension a. The corresponding other dimensions of each s-SRR are given in Table 2.

Fig. 7
Fig. 7

Frequency dependencies of the minimum μ R e of the s-SRRs made of silver, gold, and copper. The μ R e minimum frequency dependence of the unit-cell dimension a of the silver s-SRRs is also shown.

Fig. 8
Fig. 8

Frequency dependencies of the minimum μ R e of the silver s-SRRs according to the distance between adjacent planes of the s-SRRs along the z axis: l = 150 , 200, 250, 300, and 350 nm . The black circle, triangle, square, and cross symbols indicate that the unit-cell dimension a are 350, 525, 700, and 1050 nm , respectively.

Tables (2)

Tables Icon

Table 1 Dimensions of the SRRs Shown in Fig. 2 a

Tables Icon

Table 2 Dimensions of the s-SRRs Shown in Fig. 5 a

Equations (13)

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σ ( ω ) = ω p 2 ϵ 0 γ i ω ,
J ( ω , z ) = J 0 exp [ i k ( ω ) z ] , k ( ω ) = ω ϵ 0 μ 0 [ 1 + i σ ( ω ) ω ϵ 0 ] ,
Z s ( ω ) = E s I s = 1 σ ( ω ) 0 T exp [ i k ( ω ) z ] + exp [ i k ( ω ) ( T z ) ] 1 + exp [ i k ( ω ) T ] d z = R s ( ω ) + i X s ( ω ) ,
τ ( ω ) = 1 Im [ k ( ω ) ] ,
μ eff = μ Re + i μ Im = 1 F ω 2 ω 2 1 C L + i Z ( ω ) ω L ,
F = π r 2 a 2 ,
C = 2 π r 3 ϵ 0 ϵ r K [ ( 1 t 2 ) 1 2 ] K ( t ) ,
t = g 2 w + g ,
L = μ 0 π r 2 l ,
Z ( ω ) = 2 π r Z s ( ω ) w ,
f 0 = 1 2 π ( C L ) 1 2 .
C = 1 N ϵ 0 ϵ r w T g ,
Q = 1 R [ L C ] 1 2 ,

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