Abstract

We review both the theoretical electromagnetic response and the spectroscopic measurements of metamaterials. To critically examine published results for metamaterial structures operating in the range from terahertz to optical frequencies, we focus on protocols allowing one to extract the optical constants from experimental observables. We discuss the complexity of this task when applied to metamaterials exhibiting electric, magnetic, and magneto-optical response. The general theory of the electromagnetic response of such systems is presented and methods are described. Finally, we briefly overview possible solutions for implementing metamaterials with tunable resonant behavior.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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  6. 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).
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  7. This is a valid requirement for isotropic materials; however, the situation is more complicated for anisotropic and bianisotropic materials, and perhaps the requirement V¯g∙V¯p<0 should be conisdered.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  12. 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).
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  13. S. Zhang, W. Fan, B. K. Minhas, A. Frauenglass, K. J. Malloy, and S. R. J. Brueck, "Midinfrared resonant magnetic nanostructures exhibiting a negative permeability," Phys. Rev. Lett. 94, 37402 (2005).
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  20. C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401 (2003).
    [CrossRef] [PubMed]
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  27. If the self-inductance of the wires is sufficiently large, by design, then the effective mass of the electrons may be renormalized, and a factor in addition to the number density must be taken into account. See Ref. .
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    [CrossRef]
  29. R. Marques, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B 65, 144440 (2002).
    [CrossRef]
  30. J. A. Kong, Electromagnetic Wave Theory (Wiley, 1990).
  31. Media are reciprocal if epsilon=epsilon^T and µ=µ^T and xi=−zeta^T, where T denotes the transpose. For example, see Ref. .
  32. A.-C. Hsu, Y.-K. Cheng, K.-H. Chen, J.-L. Chern, S.-C. Wu, C.-F. Chen, H. Chang, Y.-H. Lien, and J.-T. Shy, "Far-infrared resonance in split ring resonators," Jpn. J. Appl. Phys., Part 1 43, L176-L179 (2004).
    [CrossRef]
  33. H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 63901 (2005).
    [CrossRef]
  34. W. J. Padilla, "Group theoretical description of artificial magnetic metamaterials utilized for negative index of refraction," http://xxx.lanl.gov/abs/cond-mat/0508307.
  35. 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]
  36. 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 (2005).
    [CrossRef] [PubMed]
  37. T. Weiland, R. Schuhmann, A. M. Vetter, D. R. Smith, D. C. Vier, and S. Schultz, "Ab initio numerical simulation of left-handed metamaterials: comparison of calculations and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
    [CrossRef]
  38. Z. Q. Li, G. M. Wang, K. J. Mikolaitis, D. Moses, A. J. Heeger, and D. N. Basov, "An infrared probe of tunable dielectrics in metal-oxide-semiconductor structures," Appl. Phys. Lett. 86, 223506 (2005).
    [CrossRef]
  39. J. Shan, F. Wang, E. Knoesel, M. Bonn, and T. F. Heinz, "Measurement of the frequency-dependent conductivity in sapphire," Phys. Rev. Lett. 90, 247401 (2003).
    [CrossRef] [PubMed]

2005 (5)

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, 37402 (2005).
[CrossRef]

K. Aydina, K. Guven, C. M. Soukoulis, and E. Ozbay, "Observation of negative refraction and negative phase velocity in left-handed metamaterials," Appl. Phys. Lett. 86, 124102 (2005).
[CrossRef]

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 63901 (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 (2005).
[CrossRef] [PubMed]

Z. Q. Li, G. M. Wang, K. J. Mikolaitis, D. Moses, A. J. Heeger, and D. N. Basov, "An infrared probe of tunable dielectrics in metal-oxide-semiconductor structures," Appl. Phys. Lett. 86, 223506 (2005).
[CrossRef]

2004 (5)

A.-C. Hsu, Y.-K. Cheng, K.-H. Chen, J.-L. Chern, S.-C. Wu, C.-F. Chen, H. Chang, Y.-H. Lien, and J.-T. Shy, "Far-infrared resonance in split ring resonators," Jpn. J. Appl. Phys., Part 1 43, L176-L179 (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]

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]

J. B. Pendry and D. R. Smith, "Reversing light with negative refraction," Phys. Today 57, 37-45 (2004).
[CrossRef]

2003 (3)

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef] [PubMed]

D. Wu, N. Fang, C. Sun, X. Zhang, W. J. Padilla, D. N. Basov, D. R. Smith, and S. Schultz, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[CrossRef]

J. Shan, F. Wang, E. Knoesel, M. Bonn, and T. F. Heinz, "Measurement of the frequency-dependent conductivity in sapphire," Phys. Rev. Lett. 90, 247401 (2003).
[CrossRef] [PubMed]

2002 (2)

R. Marques, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B 65, 144440 (2002).
[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]

2001 (3)

T. Weiland, R. Schuhmann, A. M. Vetter, D. R. Smith, D. C. Vier, and S. Schultz, "Ab initio numerical simulation of left-handed metamaterials: comparison of calculations and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[CrossRef]

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

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured magnetic materials for RF flux guides in magnetic resonance imaging," Science 291, 849-851 (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]

1998 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

1996 (1)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

1990 (1)

1981 (1)

1968 (1)

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

1966 (1)

R. Ulrich, "Far-infrared properties of metallic mesh and its complementary structure," Infrared Phys. 7, 37-55 (1966).
[CrossRef]

1963 (1)

A. J. Sievers III and M. Tinkham, "Far-infrared exchange resonance in ytterbium iron garnet," Phys. Rev. 124, 321-325 (1963).
[CrossRef]

1962 (1)

W. Rotman, "Plasma simulation by artificial dielectrics and parallel-plate media," IRE Trans. Antennas Propag. AP10, 82-95 (1962).
[CrossRef]

Aydina, K.

K. Aydina, K. Guven, C. M. Soukoulis, and E. Ozbay, "Observation of negative refraction and negative phase velocity in left-handed metamaterials," Appl. Phys. Lett. 86, 124102 (2005).
[CrossRef]

Basov, D. N.

Z. Q. Li, G. M. Wang, K. J. Mikolaitis, D. Moses, A. J. Heeger, and D. N. Basov, "An infrared probe of tunable dielectrics in metal-oxide-semiconductor structures," Appl. Phys. Lett. 86, 223506 (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]

D. Wu, N. Fang, C. Sun, X. Zhang, W. J. Padilla, D. N. Basov, D. R. Smith, and S. Schultz, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[CrossRef]

Bonn, M.

J. Shan, F. Wang, E. Knoesel, M. Bonn, and T. F. Heinz, "Measurement of the frequency-dependent conductivity in sapphire," Phys. Rev. Lett. 90, 247401 (2003).
[CrossRef] [PubMed]

Born, M.

For example, see M. Born and E. Wolf, Principles of Optics6th ed. (Cambridge U. Press, 1997), p. 312.

Bracewell, R. N.

R. N. Bracewell, "Analogues of an ionized medium," Wireless Eng. 31, 320-326 (1954).

Brueck, S. R.

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 (2005).
[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, 37402 (2005).
[CrossRef]

Cai, W.

V. M. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," http://xxx.lanl.gov/abs/physics/0504091.

Casse, B. D.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 63901 (2005).
[CrossRef]

Chang, H.

A.-C. Hsu, Y.-K. Cheng, K.-H. Chen, J.-L. Chern, S.-C. Wu, C.-F. Chen, H. Chang, Y.-H. Lien, and J.-T. Shy, "Far-infrared resonance in split ring resonators," Jpn. J. Appl. Phys., Part 1 43, L176-L179 (2004).
[CrossRef]

Chen, C.-F.

A.-C. Hsu, Y.-K. Cheng, K.-H. Chen, J.-L. Chern, S.-C. Wu, C.-F. Chen, H. Chang, Y.-H. Lien, and J.-T. Shy, "Far-infrared resonance in split ring resonators," Jpn. J. Appl. Phys., Part 1 43, L176-L179 (2004).
[CrossRef]

Chen, K.-H.

A.-C. Hsu, Y.-K. Cheng, K.-H. Chen, J.-L. Chern, S.-C. Wu, C.-F. Chen, H. Chang, Y.-H. Lien, and J.-T. Shy, "Far-infrared resonance in split ring resonators," Jpn. J. Appl. Phys., Part 1 43, L176-L179 (2004).
[CrossRef]

Cheng, Y.-K.

A.-C. Hsu, Y.-K. Cheng, K.-H. Chen, J.-L. Chern, S.-C. Wu, C.-F. Chen, H. Chang, Y.-H. Lien, and J.-T. Shy, "Far-infrared resonance in split ring resonators," Jpn. J. Appl. Phys., Part 1 43, L176-L179 (2004).
[CrossRef]

Chern, J.-L.

A.-C. Hsu, Y.-K. Cheng, K.-H. Chen, J.-L. Chern, S.-C. Wu, C.-F. Chen, H. Chang, Y.-H. Lien, and J.-T. Shy, "Far-infrared resonance in split ring resonators," Jpn. J. Appl. Phys., Part 1 43, L176-L179 (2004).
[CrossRef]

Chettiar, U.

V. M. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," http://xxx.lanl.gov/abs/physics/0504091.

Drachev, V. P.

V. M. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," http://xxx.lanl.gov/abs/physics/0504091.

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.

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, 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, 37402 (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 (2005).
[CrossRef] [PubMed]

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]

D. Wu, N. Fang, C. Sun, X. Zhang, W. J. Padilla, D. N. Basov, D. R. Smith, and S. Schultz, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[CrossRef]

Fattinger, Ch.

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, 37402 (2005).
[CrossRef]

Gilderdale, D. J.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured magnetic materials for RF flux guides in magnetic resonance imaging," Science 291, 849-851 (2001).
[CrossRef] [PubMed]

Greegor, R. B.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef] [PubMed]

Grischkowsky, D.

Guven, K.

K. Aydina, K. Guven, C. M. Soukoulis, and E. Ozbay, "Observation of negative refraction and negative phase velocity in left-handed metamaterials," Appl. Phys. Lett. 86, 124102 (2005).
[CrossRef]

Hajnal, J. V.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured magnetic materials for RF flux guides in magnetic resonance imaging," Science 291, 849-851 (2001).
[CrossRef] [PubMed]

Heeger, A. J.

Z. Q. Li, G. M. Wang, K. J. Mikolaitis, D. Moses, A. J. Heeger, and D. N. Basov, "An infrared probe of tunable dielectrics in metal-oxide-semiconductor structures," Appl. Phys. Lett. 86, 223506 (2005).
[CrossRef]

Heinz, T. F.

J. Shan, F. Wang, E. Knoesel, M. Bonn, and T. F. Heinz, "Measurement of the frequency-dependent conductivity in sapphire," Phys. Rev. Lett. 90, 247401 (2003).
[CrossRef] [PubMed]

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]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Hsu, A.-C.

A.-C. Hsu, Y.-K. Cheng, K.-H. Chen, J.-L. Chern, S.-C. Wu, C.-F. Chen, H. Chang, Y.-H. Lien, and J.-T. Shy, "Far-infrared resonance in split ring resonators," Jpn. J. Appl. Phys., Part 1 43, L176-L179 (2004).
[CrossRef]

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]

Keiding, S.

Kildishev, A. V.

V. M. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," http://xxx.lanl.gov/abs/physics/0504091.

Knoesel, E.

J. Shan, F. Wang, E. Knoesel, M. Bonn, and T. F. Heinz, "Measurement of the frequency-dependent conductivity in sapphire," Phys. Rev. Lett. 90, 247401 (2003).
[CrossRef] [PubMed]

Koltenbah, B. E.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef] [PubMed]

Kong, J. A.

J. A. Kong, Electromagnetic Wave Theory (Wiley, 1990).

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]

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]

Larkman, D. J.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured magnetic materials for RF flux guides in magnetic resonance imaging," Science 291, 849-851 (2001).
[CrossRef] [PubMed]

Li, K.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef] [PubMed]

Li, Z. Q.

Z. Q. Li, G. M. Wang, K. J. Mikolaitis, D. Moses, A. J. Heeger, and D. N. Basov, "An infrared probe of tunable dielectrics in metal-oxide-semiconductor structures," Appl. Phys. Lett. 86, 223506 (2005).
[CrossRef]

Lien, Y.-H.

A.-C. Hsu, Y.-K. Cheng, K.-H. Chen, J.-L. Chern, S.-C. Wu, C.-F. Chen, H. Chang, Y.-H. Lien, and J.-T. Shy, "Far-infrared resonance in split ring resonators," Jpn. J. Appl. Phys., Part 1 43, L176-L179 (2004).
[CrossRef]

Linden, S.

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, 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, 37402 (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 (2005).
[CrossRef] [PubMed]

Mandelshtam, L. I.

L. I. Mandelshtam, "Lectures on some problems of the theory of oscillations (1944)," in Complete Collection of Works (Academy of Sciences, 1950), Vol. 5, pp. 428-467 (in Russian).

Marques, R.

R. Marques, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Medina, F.

R. Marques, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Mikolaitis, K. J.

Z. Q. Li, G. M. Wang, K. J. Mikolaitis, D. Moses, A. J. Heeger, and D. N. Basov, "An infrared probe of tunable dielectrics in metal-oxide-semiconductor structures," Appl. Phys. Lett. 86, 223506 (2005).
[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, 37402 (2005).
[CrossRef]

Moser, H. O.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 63901 (2005).
[CrossRef]

Moses, D.

Z. Q. Li, G. M. Wang, K. J. Mikolaitis, D. Moses, A. J. Heeger, and D. N. Basov, "An infrared probe of tunable dielectrics in metal-oxide-semiconductor structures," Appl. Phys. Lett. 86, 223506 (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 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 (2005).
[CrossRef] [PubMed]

Ozbay, E.

K. Aydina, K. Guven, C. M. Soukoulis, and E. Ozbay, "Observation of negative refraction and negative phase velocity in left-handed metamaterials," Appl. Phys. Lett. 86, 124102 (2005).
[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. Wu, N. Fang, C. Sun, X. Zhang, W. J. Padilla, D. N. Basov, D. R. Smith, and S. Schultz, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[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]

W. J. Padilla, "Group theoretical description of artificial magnetic metamaterials utilized for negative index of refraction," http://xxx.lanl.gov/abs/cond-mat/0508307.

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 (2005).
[CrossRef] [PubMed]

Parazzoli, C. G.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef] [PubMed]

Pendry, J. B.

J. B. Pendry and D. R. Smith, "Reversing light with negative refraction," Phys. Today 57, 37-45 (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 and J. B. Pendry, "Magnetic activity at infrared frequencies in structured metallic photonic crystals," J. Phys.: Condens. Matter 14, 6383-6394 (2002).
[CrossRef]

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured magnetic materials for RF flux guides in magnetic resonance imaging," Science 291, 849-851 (2001).
[CrossRef] [PubMed]

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. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Rafii-El-Idrissi, R.

R. Marques, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Richards, P. L.

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]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

Rotman, W.

W. Rotman, "Plasma simulation by artificial dielectrics and parallel-plate media," IRE Trans. Antennas Propag. AP10, 82-95 (1962).
[CrossRef]

Sarychev, A. K.

V. M. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," http://xxx.lanl.gov/abs/physics/0504091.

Saw, B. T.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 63901 (2005).
[CrossRef]

Schuhmann, R.

T. Weiland, R. Schuhmann, A. M. Vetter, D. R. Smith, D. C. Vier, and S. Schultz, "Ab initio numerical simulation of left-handed metamaterials: comparison of calculations and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[CrossRef]

Schultz, S.

D. Wu, N. Fang, C. Sun, X. Zhang, W. J. Padilla, D. N. Basov, D. R. Smith, and S. Schultz, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[CrossRef]

T. Weiland, R. Schuhmann, A. M. Vetter, D. R. Smith, D. C. Vier, and S. Schultz, "Ab initio numerical simulation of left-handed metamaterials: comparison of calculations and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "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]

Shalaev, V. M.

V. M. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," http://xxx.lanl.gov/abs/physics/0504091.

Shan, J.

J. Shan, F. Wang, E. Knoesel, M. Bonn, and T. F. Heinz, "Measurement of the frequency-dependent conductivity in sapphire," Phys. Rev. Lett. 90, 247401 (2003).
[CrossRef] [PubMed]

Shelby, R. A.

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

Shy, J.-T.

A.-C. Hsu, Y.-K. Cheng, K.-H. Chen, J.-L. Chern, S.-C. Wu, C.-F. Chen, H. Chang, Y.-H. Lien, and J.-T. Shy, "Far-infrared resonance in split ring resonators," Jpn. J. Appl. Phys., Part 1 43, L176-L179 (2004).
[CrossRef]

Sievers, A. J.

A. J. Sievers III and M. Tinkham, "Far-infrared exchange resonance in ytterbium iron garnet," Phys. Rev. 124, 321-325 (1963).
[CrossRef]

Smith, D. R.

J. B. Pendry and D. R. Smith, "Reversing light with negative refraction," Phys. Today 57, 37-45 (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]

D. Wu, N. Fang, C. Sun, X. Zhang, W. J. Padilla, D. N. Basov, D. R. Smith, and S. Schultz, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[CrossRef]

T. Weiland, R. Schuhmann, A. M. Vetter, D. R. Smith, D. C. Vier, and S. Schultz, "Ab initio numerical simulation of left-handed metamaterials: comparison of calculations and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[CrossRef]

R. A. Shelby, D. R. Smith, and S. Schultz, "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]

D. R. Smith, Department of Electrical and Computer Engineering, Duke University, Durham, N.C. 27708 (personal communication, 2005).

Soukoulis, C. M.

K. Aydina, K. Guven, C. M. Soukoulis, and E. Ozbay, "Observation of negative refraction and negative phase velocity in left-handed metamaterials," Appl. Phys. Lett. 86, 124102 (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]

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]

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]

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, "Low frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Sun, C.

D. Wu, N. Fang, C. Sun, X. Zhang, W. J. Padilla, D. N. Basov, D. R. Smith, and S. Schultz, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[CrossRef]

Tanielian, M.

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef] [PubMed]

Timusk, T.

Tinkham, M.

A. J. Sievers III and M. Tinkham, "Far-infrared exchange resonance in ytterbium iron garnet," Phys. Rev. 124, 321-325 (1963).
[CrossRef]

Ulrich, R.

R. Ulrich, "Far-infrared properties of metallic mesh and its complementary structure," Infrared Phys. 7, 37-55 (1966).
[CrossRef]

van Exter, M.

Veselago, V. G.

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

Vetter, A. M.

T. Weiland, R. Schuhmann, A. M. Vetter, D. R. Smith, D. C. Vier, and S. Schultz, "Ab initio numerical simulation of left-handed metamaterials: comparison of calculations and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[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]

T. Weiland, R. Schuhmann, A. M. Vetter, D. R. Smith, D. C. Vier, and S. Schultz, "Ab initio numerical simulation of left-handed metamaterials: comparison of calculations and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[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]

Wang, F.

J. Shan, F. Wang, E. Knoesel, M. Bonn, and T. F. Heinz, "Measurement of the frequency-dependent conductivity in sapphire," Phys. Rev. Lett. 90, 247401 (2003).
[CrossRef] [PubMed]

Wang, G. M.

Z. Q. Li, G. M. Wang, K. J. Mikolaitis, D. Moses, A. J. Heeger, and D. N. Basov, "An infrared probe of tunable dielectrics in metal-oxide-semiconductor structures," Appl. Phys. Lett. 86, 223506 (2005).
[CrossRef]

Wegener, M.

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]

Weiland, T.

T. Weiland, R. Schuhmann, A. M. Vetter, D. R. Smith, D. C. Vier, and S. Schultz, "Ab initio numerical simulation of left-handed metamaterials: comparison of calculations and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[CrossRef]

Wilhelmi, O.

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 63901 (2005).
[CrossRef]

Wiltshire, M. C.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured magnetic materials for RF flux guides in magnetic resonance imaging," Science 291, 849-851 (2001).
[CrossRef] [PubMed]

Wolf, E.

For example, see M. Born and E. Wolf, Principles of Optics6th ed. (Cambridge U. Press, 1997), p. 312.

Wooten, F.

F. Wooten, Optical Properties of Solids (Academic, 1972).

Wu, D.

D. Wu, N. Fang, C. Sun, X. Zhang, W. J. Padilla, D. N. Basov, D. R. Smith, and S. Schultz, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[CrossRef]

Wu, S.-C.

A.-C. Hsu, Y.-K. Cheng, K.-H. Chen, J.-L. Chern, S.-C. Wu, C.-F. Chen, H. Chang, Y.-H. Lien, and J.-T. Shy, "Far-infrared resonance in split ring resonators," Jpn. J. Appl. Phys., Part 1 43, L176-L179 (2004).
[CrossRef]

Yen, T. J.

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

Young, I. R.

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured magnetic materials for RF flux guides in magnetic resonance imaging," Science 291, 849-851 (2001).
[CrossRef] [PubMed]

Youngs, I.

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

Yuan, H.-K.

V. M. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," http://xxx.lanl.gov/abs/physics/0504091.

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, 37402 (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 (2005).
[CrossRef] [PubMed]

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]

D. Wu, N. Fang, C. Sun, X. Zhang, W. J. Padilla, D. N. Basov, D. R. Smith, and S. Schultz, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[CrossRef]

Zhou, J.

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]

Appl. Opt. (1)

Appl. Phys. Lett. (3)

D. Wu, N. Fang, C. Sun, X. Zhang, W. J. Padilla, D. N. Basov, D. R. Smith, and S. Schultz, "Terahertz plasmonic high pass filter," Appl. Phys. Lett. 83, 201-203 (2003).
[CrossRef]

K. Aydina, K. Guven, C. M. Soukoulis, and E. Ozbay, "Observation of negative refraction and negative phase velocity in left-handed metamaterials," Appl. Phys. Lett. 86, 124102 (2005).
[CrossRef]

Z. Q. Li, G. M. Wang, K. J. Mikolaitis, D. Moses, A. J. Heeger, and D. N. Basov, "An infrared probe of tunable dielectrics in metal-oxide-semiconductor structures," Appl. Phys. Lett. 86, 223506 (2005).
[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]

Infrared Phys. (1)

R. Ulrich, "Far-infrared properties of metallic mesh and its complementary structure," Infrared Phys. 7, 37-55 (1966).
[CrossRef]

IRE Trans. Antennas Propag. (1)

W. Rotman, "Plasma simulation by artificial dielectrics and parallel-plate media," IRE Trans. Antennas Propag. AP10, 82-95 (1962).
[CrossRef]

J. Appl. Phys. (1)

T. Weiland, R. Schuhmann, A. M. Vetter, D. R. Smith, D. C. Vier, and S. Schultz, "Ab initio numerical simulation of left-handed metamaterials: comparison of calculations and experiments," J. Appl. Phys. 90, 5419-5424 (2001).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys.: Condens. Matter (2)

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, "Low frequency plasmons in thin-wire structures," J. Phys.: Condens. Matter 10, 4785-4809 (1998).
[CrossRef]

Jpn. J. Appl. Phys., Part 1 (1)

A.-C. Hsu, Y.-K. Cheng, K.-H. Chen, J.-L. Chern, S.-C. Wu, C.-F. Chen, H. Chang, Y.-H. Lien, and J.-T. Shy, "Far-infrared resonance in split ring resonators," Jpn. J. Appl. Phys., Part 1 43, L176-L179 (2004).
[CrossRef]

Phys. Rev. (1)

A. J. Sievers III and M. Tinkham, "Far-infrared exchange resonance in ytterbium iron garnet," Phys. Rev. 124, 321-325 (1963).
[CrossRef]

Phys. Rev. B (1)

R. Marques, F. Medina, and R. Rafii-El-Idrissi, "Role of bianisotropy in negative permeability and left-handed metamaterials," Phys. Rev. B 65, 144440 (2002).
[CrossRef]

Phys. Rev. Lett. (8)

J. B. Pendry, A. J. Holden, W. J. Stewart, and I. Youngs, "Extremely low frequency plasmons in metallic mesostructures," Phys. Rev. Lett. 76, 4773-4776 (1996).
[CrossRef] [PubMed]

C. G. Parazzoli, R. B. Greegor, K. Li, B. E. C. Koltenbah, and M. Tanielian, "Experimental verification and simulation of negative index of refraction using Snell's law," Phys. Rev. Lett. 90, 107401 (2003).
[CrossRef] [PubMed]

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]

H. O. Moser, B. D. F. Casse, O. Wilhelmi, and B. T. Saw, "Terahertz response of a microfabricated rod-split-ring-resonator electromagnetic metamaterial," Phys. Rev. Lett. 94, 63901 (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 (2005).
[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]

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, 37402 (2005).
[CrossRef]

J. Shan, F. Wang, E. Knoesel, M. Bonn, and T. F. Heinz, "Measurement of the frequency-dependent conductivity in sapphire," Phys. Rev. Lett. 90, 247401 (2003).
[CrossRef] [PubMed]

Phys. Today (1)

J. B. Pendry and D. R. Smith, "Reversing light with negative refraction," Phys. Today 57, 37-45 (2004).
[CrossRef]

Science (4)

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

M. C. K. Wiltshire, J. B. Pendry, I. R. Young, D. J. Larkman, D. J. Gilderdale, and J. V. Hajnal, "Microstructured magnetic materials for RF flux guides in magnetic resonance imaging," Science 291, 849-851 (2001).
[CrossRef] [PubMed]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, "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]

Sov. Phys. Usp. (1)

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

Other (11)

L. I. Mandelshtam, "Lectures on some problems of the theory of oscillations (1944)," in Complete Collection of Works (Academy of Sciences, 1950), Vol. 5, pp. 428-467 (in Russian).

F. Wooten, Optical Properties of Solids (Academic, 1972).

For example, see M. Born and E. Wolf, Principles of Optics6th ed. (Cambridge U. Press, 1997), p. 312.

This is a valid requirement for isotropic materials; however, the situation is more complicated for anisotropic and bianisotropic materials, and perhaps the requirement V¯g∙V¯p<0 should be conisdered.

D. R. Smith, Department of Electrical and Computer Engineering, Duke University, Durham, N.C. 27708 (personal communication, 2005).

V. M. Shalaev, W. Cai, U. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," http://xxx.lanl.gov/abs/physics/0504091.

W. J. Padilla, "Group theoretical description of artificial magnetic metamaterials utilized for negative index of refraction," http://xxx.lanl.gov/abs/cond-mat/0508307.

If the self-inductance of the wires is sufficiently large, by design, then the effective mass of the electrons may be renormalized, and a factor in addition to the number density must be taken into account. See Ref. .

R. N. Bracewell, "Analogues of an ionized medium," Wireless Eng. 31, 320-326 (1954).

J. A. Kong, Electromagnetic Wave Theory (Wiley, 1990).

Media are reciprocal if epsilon=epsilon^T and µ=µ^T and xi=−zeta^T, where T denotes the transpose. For example, see Ref. .

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Figures (10)

Fig. 1
Fig. 1

Some optical constants for a Lorentz oscillator. The oscillator is modeled using Eq. (2) with the parameters given as S = 50 , 000 cm 1 , ϵ = 1.5 , γ = 10 cm 1 , ω 0 = 300 cm 1 .

Fig. 2
Fig. 2

Oblique angle reflectance plotted for θ = 30 ° as determined by Eqs. (1) for both TE and TM polarizations. In the left panel the reflectance is a result of a magnetic contribution with ϵ = 1 in this case. The right panel displays R ( ω ) for an electric oscillator ϵ ( ω ) and μ = 1 .

Fig. 3
Fig. 3

Schematics of two artificial structures commonly used as EM metamaterials. Left panel shows a wire medium supporting ϵ < 0 for the polarization of the incident EM wave as shown and for frequencies ω < ω p . Right panel shows the unit cell for an artificial magnetic metamaterial. The E field lies along x ̂ , B along z ̂ , and k along y ̂ . By formation of a bipartite lattice utilizing both the electric and the magnetic metamaterial, a NI material may be constructed.

Fig. 4
Fig. 4

Transmission spectra for an electric metamaterial. The blue curves are for polarization perpendicular to the wires, and the red is for polarization along the wires. The transmission spectra near the predicted plasma frequency approach zero, indicating screening of the artificial medium. Inset shows a picture of the artificial wire medium.

Fig. 5
Fig. 5

Drude–Lorentz model for an oscillator model using Eq. (2). In (a) and (b) the real part (solid curve) and the imaginary portion (dashed curve) are given. (a) A Drude oscillator ( ω 0 = 0 ) ; (b) the same oscillator but now centered at ω 0 = 50 cm 1 . (c) and (d) A comparison between two magnetic oscillators given from Ref. [6] (grey curves) and a Lorentz oscillator (black curves) is shown. The real portions are plotted in (c) and the imaginary parts in (d).

Fig. 6
Fig. 6

Measurements of micrometer-sized SRRs designed for magnetic response at THz frequencies after Ref. [11]. Inset to bottom panel shows a picture of one SRR, and the corresponding dimensions: gap between the inner and outer ring ( G ) , the width of the metal lines ( W ) , the length of the outer ring ( L ) , and the lattice parameters were 2, 4, 26, and 36 μ m for the sample exhibiting the highest frequency resonance (red curve); 3, 4, 32, and 44 μ m (black curve), and 3, 6, 36, and 50 μ m for the sample with the lowest resonant frequency (blue curve). Top panel displays the ellipsometric parameter described in the text for the three SRR samples (red, black, and blue curves). The dashed black curve and the solid gray curve are for the same measured parameter for copper and quartz, respectively. Middle and bottom panels display the real and imaginary portions of μ ( ω ) , respectively, as simulated for the three different SRRs.

Fig. 7
Fig. 7

SRR arrays designed to operate in MIR and near-IR frequencies (after Ref. [12]). (a) A photograph of a typical SRR cell and (b) of an array used for spectroscopic studies in MIR near-IR frequencies. (c) The transmission (red) and reflectance (blue) spectra. The two polarization configurations are shown on top of the two columns. Lattice constant a = 450 nm corresponds to nominally identical SRRs.

Fig. 8
Fig. 8

Magnetic metamaterial constructed from Au designed for resonance at MIR frequencies.[13] (a) Depicts how charges will flow in the device upon the application of a time-varying magnetic field directed along the z ̂ axis. (b) Shows the currents from (a) as well as the resulting image charges. The charges and image charges thus form a net circulating current resulting in a magnetic response. Upon excitation by an external electric field E directed along the y ̂ axis, charges will flow as shown (c), as well as image charges shown in (d), and thus a net circulation and magnetic field B will be created.

Fig. 9
Fig. 9

Magnetic metamaterial designed for response at MIR frequencies. Two different structures are shown in (a) and (b), all constructed from Au. In (c) reflection measurements are shown for sample c, not shown. In (d) the calculated real and imaginary parts of μ ( ω ) are shown.

Fig. 10
Fig. 10

Metamaterials used for response at near-IR and optical frequencies. (a) A schematic of the mulitlayer structure used in Ref. [36] consisting of an Al 2 O 3 dielectric layer between two Au films with a square array of holes (pitch of 838 nm, diameter of 360 nm). (b) Shows the pairs of Au nanorods used in Ref. [19] separated by a SiO 2 layer on top of a glass substrate separated by a 180 nm layer of indium tin oxide (ITO).

Tables (1)

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Table 1 Material Definitions with Respect to the Symmetries of the Constitutive Relations a

Equations (13)

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R ( ω ) TE = cos θ μ 1 ϵ μ sin 2 θ cos θ + μ 1 ϵ μ sin 2 θ 2 ,
R ( ω ) TM = ϵ cos θ ϵ μ sin 2 θ ϵ cos θ + ϵ μ sin 2 θ 2 .
ϵ ̃ ( ω ) = ϵ + ω p 2 ω 0 2 ω 2 i γ ω ,
μ ̃ ( ω ) = 1 + F ω 2 ω 0 2 ω 2 i γ ω ,
μ ̃ ( ω ) = 1 + ω mp 2 ω 0 2 ω 2 i γ ω ,
[ D ¯ B ¯ ] = [ ϵ ¯ ¯ ξ ¯ ¯ ζ ¯ ¯ μ ¯ ¯ ] [ E ¯ H ¯ ] .
ϵ = [ ϵ x x 0 0 0 ϵ y y 0 0 0 1 ] ; μ = [ 1 0 0 0 1 0 0 0 μ z z ] ,
ξ = [ 0 0 0 0 0 ξ y z 0 0 0 ] ; ζ = [ 0 0 0 0 0 0 0 ζ z y 0 ] .
ϵ x x = a ,
ϵ y y ( ω ) = a + b ω 2 ω 0 2 ω 2 ,
μ z z ( ω ) = 1 + c ω 2 ω 0 2 ω 2 ,
ξ y z ( ω ) = ω 0 d ω ω 0 2 ω 2 ,
ω 0 = 3 π 2 μ 0 C r 3 ,

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