Abstract

We measure, simulate, and analyze the optical transmission through arrays of Ag nanorod pairs and U-shaped nanostructures as a function of polarization and angle of incidence. The bianisotropic nature of the metamaterials is exhibited in data and in simulations, and we argue that the electric field rather than the magnetic field excites the low frequency “magnetic” mode. We also observe spatial dispersion in the form of frequency shifts as a function of incident angle which we attribute to coupling effects between neighboring structures. A simple model based upon coupled electromagnetic dipoles is found to provide a qualitative description for the main features observed in the spectra.

© 2010 OSA

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  1. J. B. Pendry, “Negative refraction makes a perfect lens,” Phys. Rev. Lett. 85(18), 3966–3969 (2000).
    [CrossRef] [PubMed]
  2. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science 292(5514), 77–79 (2001).
    [CrossRef] [PubMed]
  3. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
    [CrossRef] [PubMed]
  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(20), 203901 (2005).
    [CrossRef] [PubMed]
  5. 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(24), 3356–3358 (2005).
    [CrossRef]
  6. G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32(1), 53–55 (2007).
    [CrossRef]
  7. Y. A. Urzhumov and G. Shvets, “Optical magnetism and negative refraction in plasmonic metamaterials,” Solid State Commun. 146(5-6), 208–220 (2008).
    [CrossRef]
  8. R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A. 106(6), 1693–1698 (2009).
    [CrossRef] [PubMed]
  9. I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
    [CrossRef]
  10. J. J. Hopfield and D. G. Thomas, “Theoretical and Experimental Effects of Spatial Dispersion on the Optical Properties of Crystals,” Phys. Rev. 132(2), 563–572 (1963).
    [CrossRef]
  11. D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig, “Calculation and measurement of bianisotropy in a split ring resonator material,” J. Appl. Phys. 100(2), 024507 (2006).
    [CrossRef]
  12. J. A. Kong, Electromagnetic Wave Theory, 2nd ed. (Wiley, 1990).
  13. I. V. Lindell, A. H. Sihvola, S. A. Tretyakov, and A. J. Viitanen, Electromagnetic Waves in Chiral and Bi-Isotropic Media (Artech House, 1994).
  14. C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: The two dimensional equivalent of metamaterials,” Metamaterials (Amst.) 3(2), 100–112 (2009).
    [CrossRef]
  15. D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
    [CrossRef]
  16. C. Rockstuhl, T. Zentgraf, T. P. Meyrath, H. Giessen, and F. Lederer, “Resonances in complementary metamaterials and nanoapertures,” Opt. Express 16(3), 2080–2090 (2008).
    [CrossRef] [PubMed]
  17. M. W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express 15(8), 5238–5247 (2007).
    [CrossRef] [PubMed]
  18. T. D. Corrigan, P. W. Kolb, A. B. Sushkov, H. D. Drew, D. C. Schmadel, and R. J. Phaneuf, “Optical plasmonic resonances in split-ring resonator structures: an improved LC model,” Opt. Express 16(24), 19850–19864 (2008).
    [CrossRef] [PubMed]
  19. T. D. Corrigan, P. W. Kolb, A. B. Sushkov, H. D. Drew, R. J. Phaneuf, G. Shvets, “Wood’s anomaly in arrays of highly anisotropic plasmonic antennas,” to be published. Here conservation of crystal momentum is used to derive the equation for the onset of diffraction fmj=famsinθ+(msinθ)2+(n2−sin2θ)(m2+j2)(n2−sin2θ) where a is the period of the array, fa = c/a, the incident angle θ is taken to be within the plane defined by k and the substrate normal, n is the index of refraction of the medium (1.00 for air and 1.46 for glass), and m and j are integers specifying the component of momentum transfer along the reciprocal lattice unit vectors along k∥ and perpendicular to k∥, respectively.
  20. L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98(26), 266802 (2007).
    [CrossRef] [PubMed]
  21. The simulation current plots (Figs. 3 and 4) show the currents in response to an exciting wave of frequency ω. If ω is chosen at or near one of the resonances the corresponding resonance dominates the response. However, the other nearby resonances also contributes to the observed field patterns. In addition the response has in-phase and out-of-phase components that depend both on the dissipation and ω. These factors cause small distortions in the current distribution from the ideal patterns expected from symmetry. The significant deviation seen in Fig. 3 (e, f) can be understood as a mode of coupled oscillators where the individual oscillators are driven out of phase; at the resonant frequency their motion will in general not be in phase.
  22. D. J. Cho, F. Wang, X. Zhang, and Y. R. Shen, “Contribution of the electric quadropole resonance in optical metamaterials,” Phys. Rev. B 78, 12101 (2008).
    [CrossRef]
  23. M. G. Silveirinha, “Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters,” Phys. Rev. B 75(11), 115104 (2007).
    [CrossRef]
  24. W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70(12), 125429 (2004).
    [CrossRef]

2009 (3)

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A. 106(6), 1693–1698 (2009).
[CrossRef] [PubMed]

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
[CrossRef]

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: The two dimensional equivalent of metamaterials,” Metamaterials (Amst.) 3(2), 100–112 (2009).
[CrossRef]

2008 (4)

Y. A. Urzhumov and G. Shvets, “Optical magnetism and negative refraction in plasmonic metamaterials,” Solid State Commun. 146(5-6), 208–220 (2008).
[CrossRef]

C. Rockstuhl, T. Zentgraf, T. P. Meyrath, H. Giessen, and F. Lederer, “Resonances in complementary metamaterials and nanoapertures,” Opt. Express 16(3), 2080–2090 (2008).
[CrossRef] [PubMed]

T. D. Corrigan, P. W. Kolb, A. B. Sushkov, H. D. Drew, D. C. Schmadel, and R. J. Phaneuf, “Optical plasmonic resonances in split-ring resonator structures: an improved LC model,” Opt. Express 16(24), 19850–19864 (2008).
[CrossRef] [PubMed]

D. J. Cho, F. Wang, X. Zhang, and Y. R. Shen, “Contribution of the electric quadropole resonance in optical metamaterials,” Phys. Rev. B 78, 12101 (2008).
[CrossRef]

2007 (4)

M. G. Silveirinha, “Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters,” Phys. Rev. B 75(11), 115104 (2007).
[CrossRef]

L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98(26), 266802 (2007).
[CrossRef] [PubMed]

M. W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express 15(8), 5238–5247 (2007).
[CrossRef] [PubMed]

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32(1), 53–55 (2007).
[CrossRef]

2006 (1)

D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig, “Calculation and measurement of bianisotropy in a split ring resonator material,” J. Appl. Phys. 100(2), 024507 (2006).
[CrossRef]

2005 (2)

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

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(24), 3356–3358 (2005).
[CrossRef]

2004 (2)

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70(12), 125429 (2004).
[CrossRef]

2002 (1)

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

2001 (1)

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

2000 (1)

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

1963 (1)

J. J. Hopfield and D. G. Thomas, “Theoretical and Experimental Effects of Spatial Dispersion on the Optical Properties of Crystals,” Phys. Rev. 132(2), 563–572 (1963).
[CrossRef]

Azad, A. K.

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: The two dimensional equivalent of metamaterials,” Metamaterials (Amst.) 3(2), 100–112 (2009).
[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(20), 203901 (2005).
[CrossRef] [PubMed]

Cai, W.

Chettiar, U. K.

Cho, D. J.

D. J. Cho, F. Wang, X. Zhang, and Y. R. Shen, “Contribution of the electric quadropole resonance in optical metamaterials,” Phys. Rev. B 78, 12101 (2008).
[CrossRef]

Corrigan, T. D.

Dienstfrey, A.

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: The two dimensional equivalent of metamaterials,” Metamaterials (Amst.) 3(2), 100–112 (2009).
[CrossRef]

Dolling, G.

Drachev, V. P.

Drew, H. D.

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(20), 203901 (2005).
[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(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Feth, N.

Ford, G. W.

W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70(12), 125429 (2004).
[CrossRef]

Frimmer, M.

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
[CrossRef]

Giessen, H.

Gollub, J.

D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig, “Calculation and measurement of bianisotropy in a split ring resonator material,” J. Appl. Phys. 100(2), 024507 (2006).
[CrossRef]

Holloway, C. L.

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: The two dimensional equivalent of metamaterials,” Metamaterials (Amst.) 3(2), 100–112 (2009).
[CrossRef]

Hopfield, J. J.

J. J. Hopfield and D. G. Thomas, “Theoretical and Experimental Effects of Spatial Dispersion on the Optical Properties of Crystals,” Phys. Rev. 132(2), 563–572 (1963).
[CrossRef]

Kildishev, A. V.

Klein, M. W.

Koenderink, A. F.

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
[CrossRef]

Kolb, P. W.

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(5700), 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(20), 203901 (2005).
[CrossRef] [PubMed]

Kuester, E. F.

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: The two dimensional equivalent of metamaterials,” Metamaterials (Amst.) 3(2), 100–112 (2009).
[CrossRef]

Lederer, F.

Linden, S.

M. W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express 15(8), 5238–5247 (2007).
[CrossRef] [PubMed]

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32(1), 53–55 (2007).
[CrossRef]

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

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Markos, P.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Merlin, R.

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A. 106(6), 1693–1698 (2009).
[CrossRef] [PubMed]

Meyrath, T. P.

Mock, J. J.

D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig, “Calculation and measurement of bianisotropy in a split ring resonator material,” J. Appl. Phys. 100(2), 024507 (2006).
[CrossRef]

Novotny, L.

L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98(26), 266802 (2007).
[CrossRef] [PubMed]

O’Hara, J. F.

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: The two dimensional equivalent of metamaterials,” Metamaterials (Amst.) 3(2), 100–112 (2009).
[CrossRef]

Padilla, W. J.

D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig, “Calculation and measurement of bianisotropy in a split ring resonator material,” J. Appl. Phys. 100(2), 024507 (2006).
[CrossRef]

Pendry, J. B.

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

Phaneuf, R. J.

Rockstuhl, C.

Sarychev, A. K.

Schmadel, D. C.

Schmidt, F.

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

Schultz, S.

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

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

Schurig, D.

D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig, “Calculation and measurement of bianisotropy in a split ring resonator material,” J. Appl. Phys. 100(2), 024507 (2006).
[CrossRef]

Sersic, I.

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
[CrossRef]

Shalaev, V. M.

Shelby, R. A.

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

Shen, Y. R.

D. J. Cho, F. Wang, X. Zhang, and Y. R. Shen, “Contribution of the electric quadropole resonance in optical metamaterials,” Phys. Rev. B 78, 12101 (2008).
[CrossRef]

Shvets, G.

Y. A. Urzhumov and G. Shvets, “Optical magnetism and negative refraction in plasmonic metamaterials,” Solid State Commun. 146(5-6), 208–220 (2008).
[CrossRef]

Silveirinha, M. G.

M. G. Silveirinha, “Metamaterial homogenization approach with application to the characterization of microstructured composites with negative parameters,” Phys. Rev. B 75(11), 115104 (2007).
[CrossRef]

Smith, D. R.

D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig, “Calculation and measurement of bianisotropy in a split ring resonator material,” J. Appl. Phys. 100(2), 024507 (2006).
[CrossRef]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

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

Soukoulis, C. M.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32(1), 53–55 (2007).
[CrossRef]

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

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

D. R. Smith, S. Schultz, P. Markos, and C. M. Soukoulis, “Determination of effective permittivity and permeability of metamaterials from reflection and transmission coefficients,” Phys. Rev. B 65(19), 195104 (2002).
[CrossRef]

Sushkov, A. B.

Taylor, A. J.

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: The two dimensional equivalent of metamaterials,” Metamaterials (Amst.) 3(2), 100–112 (2009).
[CrossRef]

Thomas, D. G.

J. J. Hopfield and D. G. Thomas, “Theoretical and Experimental Effects of Spatial Dispersion on the Optical Properties of Crystals,” Phys. Rev. 132(2), 563–572 (1963).
[CrossRef]

Urzhumov, Y. A.

Y. A. Urzhumov and G. Shvets, “Optical magnetism and negative refraction in plasmonic metamaterials,” Solid State Commun. 146(5-6), 208–220 (2008).
[CrossRef]

Verhagen, E.

I. Sersic, M. Frimmer, E. Verhagen, and A. F. Koenderink, “Electric and magnetic dipole coupling in near-infrared split-ring metamaterial arrays,” Phys. Rev. Lett. 103(21), 213902 (2009).
[CrossRef]

Wang, F.

D. J. Cho, F. Wang, X. Zhang, and Y. R. Shen, “Contribution of the electric quadropole resonance in optical metamaterials,” Phys. Rev. B 78, 12101 (2008).
[CrossRef]

Weber, W. H.

W. H. Weber and G. W. Ford, “Propagation of optical excitations by dipolar interactions in metal nanoparticle chains,” Phys. Rev. B 70(12), 125429 (2004).
[CrossRef]

Wegener, M.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index metamaterial at 780 nm wavelength,” Opt. Lett. 32(1), 53–55 (2007).
[CrossRef]

M. W. Klein, M. Wegener, N. Feth, and S. Linden, “Experiments on second- and third-harmonic generation from magnetic metamaterials,” Opt. Express 15(8), 5238–5247 (2007).
[CrossRef] [PubMed]

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

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306(5700), 1351–1353 (2004).
[CrossRef] [PubMed]

Yuan, H.-K.

Zentgraf, T.

Zhang, X.

D. J. Cho, F. Wang, X. Zhang, and Y. R. Shen, “Contribution of the electric quadropole resonance in optical metamaterials,” Phys. Rev. B 78, 12101 (2008).
[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(5700), 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(20), 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(20), 203901 (2005).
[CrossRef] [PubMed]

J. Appl. Phys. (1)

D. R. Smith, J. Gollub, J. J. Mock, W. J. Padilla, and D. Schurig, “Calculation and measurement of bianisotropy in a split ring resonator material,” J. Appl. Phys. 100(2), 024507 (2006).
[CrossRef]

Metamaterials (Amst.) (1)

C. L. Holloway, A. Dienstfrey, E. F. Kuester, J. F. O’Hara, A. K. Azad, and A. J. Taylor, “A discussion on the interpretation and characterization of metafilms/metasurfaces: The two dimensional equivalent of metamaterials,” Metamaterials (Amst.) 3(2), 100–112 (2009).
[CrossRef]

Opt. Express (3)

Opt. Lett. (2)

Phys. Rev. (1)

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[CrossRef]

Phys. Rev. B (4)

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[CrossRef]

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[CrossRef]

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[CrossRef]

Phys. Rev. Lett. (4)

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Proc. Natl. Acad. Sci. U.S.A. (1)

R. Merlin, “Metamaterials and the Landau-Lifshitz permeability argument: large permittivity begets high-frequency magnetism,” Proc. Natl. Acad. Sci. U.S.A. 106(6), 1693–1698 (2009).
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Science (2)

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Solid State Commun. (1)

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[CrossRef]

Other (4)

T. D. Corrigan, P. W. Kolb, A. B. Sushkov, H. D. Drew, R. J. Phaneuf, G. Shvets, “Wood’s anomaly in arrays of highly anisotropic plasmonic antennas,” to be published. Here conservation of crystal momentum is used to derive the equation for the onset of diffraction fmj=famsinθ+(msinθ)2+(n2−sin2θ)(m2+j2)(n2−sin2θ) where a is the period of the array, fa = c/a, the incident angle θ is taken to be within the plane defined by k and the substrate normal, n is the index of refraction of the medium (1.00 for air and 1.46 for glass), and m and j are integers specifying the component of momentum transfer along the reciprocal lattice unit vectors along k∥ and perpendicular to k∥, respectively.

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The simulation current plots (Figs. 3 and 4) show the currents in response to an exciting wave of frequency ω. If ω is chosen at or near one of the resonances the corresponding resonance dominates the response. However, the other nearby resonances also contributes to the observed field patterns. In addition the response has in-phase and out-of-phase components that depend both on the dissipation and ω. These factors cause small distortions in the current distribution from the ideal patterns expected from symmetry. The significant deviation seen in Fig. 3 (e, f) can be understood as a mode of coupled oscillators where the individual oscillators are driven out of phase; at the resonant frequency their motion will in general not be in phase.

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Figures (5)

Fig. 1
Fig. 1

Transmission curves of rod pairs and U-shapes for different polarizations and orientations as shown in the inset of each figure. In (c) and (d), tall (short) color-coded ticks indicate the potential onset of the (−1,0) diffraction modes into the glass (air) for (a-f) according to ref [19].

Fig. 2
Fig. 2

HFSS simulations of total transmission as a function of incident angle for the experimental rod pairs in (a) and U-shapes in (b) for the polarization shown in the inset. The sample height, arm length, and lattice periodicity are 75 nm, 320 nm and 600 nm respectively for both rods and U-shapes. The plots are not normalized for ease in viewing. Dips associated with plasmonic resonances are labeled. In (a) the dashed curve shows the simulated intensity of the beam diffracted into the substrate for θ = 20°. In (b) the dashed line helps to mark the slight red shift of U1 with increasing angle. Tall (short) color-coded ticks indicate the potential onset of the (−1,0) diffraction modes into the glass (air) according to ref [19].

Fig. 3
Fig. 3

HFSS simulations of transmission as a function of incident angle for modified rod pairs (a) and U-shapes (b) for the polarization shown in the inset. The sample height, arm length, and lattice periodicity are 20 nm, 320 nm and 600 nm respectively for the rods and 30 nm, 200 nm, and 325 nm respectively for the U-shapes. The plots are not normalized for ease in viewing. In (a) the dashed curve shows the simulated intensity of the beam diffracted into the substrate for θ = 45°. In (b) the dashed line helps to mark the slight red shift of U1 with increasing angle. In (b) only the s-polarized transmission is calculated in contrast to Fig. 2(b) where the total transmission is calculated disregarding polarization rotation of the incident beam. Tall (short) color-coded ticks indicate the potential onset of the (−1,0) diffraction modes into the glass (air) according to ref [19].

Fig. 4
Fig. 4

Simulated current distributions for the anti-symmetric mode R1 (a) and the symmetric mode R2 (c) at normal incidence corresponding to Fig. 2(a), and the idealized currents for each in (b) and (d), respectively. (e) and (f) show the simulations for R2 at 80° incidence with a chosen phase to show maximum current in the left rod (e) and in the right rod (f).

Fig. 5
Fig. 5

Idealized current distributions along with simulated currents at 80° incidence for the modes U1 (a,b), U2 (c,d), and U3 (e,f) corresponding to Fig. 3(b). The phase is chosen in (e) so as to show maximum current in the left arm. Similar cartoons and plots have been reported elsewhere [4,16].

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