Abstract

We show that a resonant response with very high quality factors can be achieved in periodic metamaterials by radiatively coupling their structural elements. The coupling is mediated by lattice modes and can be efficiently controlled by tuning the lattice periodicity. Using a recently developed terahertz (THz) near-field imaging technique and conventional far-field spectroscopy together with numerical simulations we pinpoint the underlying mechanisms. In the strong coupling regimes we identify avoided crossings between the plasmonic eigenmodes and the diffractive lattice modes.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
  6. H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
    [CrossRef] [PubMed]
  7. H. T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, "Experimental demonstration of frequency-agile terahertz metamaterials," Nat. Photonics 2, 295-298 (2008).
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    [CrossRef]
  10. P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Low-Loss Metamaterials Based on Classical Electromagnetically Induced Transparency," Phys. Rev. Lett. 102, 053901 (2009).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  13. N. Liu, L. Langguth, T. Weiss, J. K¨astel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
    [CrossRef] [PubMed]
  14. F. Hao, P. Nordlander,M. T. Burnett, and S. A. Maier, "Enhanced tunability and linewidth sharpening of plasmon resonances in hybridized metallic ring/disk nanocavities," Phys. Rev. B 76, 245417 (2007).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

2009 (5)

R. Singh, C. Rockstuhl, F. Lederer, and W. L. Zhang, "Coupling between a dark and a bright eigenmode in a terahertz metamaterial," Phys. Rev. B 79, 085111 (2009).
[CrossRef]

N. Liu, L. Langguth, T. Weiss, J. K¨astel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
[CrossRef] [PubMed]

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Low-Loss Metamaterials Based on Classical Electromagnetically Induced Transparency," Phys. Rev. Lett. 102, 053901 (2009).
[CrossRef] [PubMed]

A. Bitzer, H. Merbold, A. Thoman, T. Feurer, H. Helm, and M. Walther, "Terahertz near-field imaging of electric and magnetic resonances of a planar metamaterial," Opt. Express 17, 3826-3834 (2009).
[CrossRef] [PubMed]

J. R. Knab, A. J. L. Adam, M. Nagel, E. Shaner, M. A. Seo, D. S. Kim, and P. C. M. Planken, "Terahertz Near-Field Vectorial Imaging of Subwavelength Apertures and Aperture Arrays," Opt. Express 17, 15072-15086 (2009).
[CrossRef] [PubMed]

2008 (8)

A. J. L. Adam, J. M. Brok, M. A. Seo, K. J. Ahn, D. S. Kim, J. H. Kang, Q. H. Park, M. Nagel, and P. C. M. Planken, "Advanced terahertz electric near-field measurements at sub-wavelength diameter metallic apertures," Opt. Express 16, 7407-7417 (2008).
[CrossRef] [PubMed]

G. Acuna, S. F. Heucke, F. Kuchler, H. T. Chen, A. J. Taylor, and R. Kersting, "Surface plasmons in terahertz metamaterials," Opt. Express 16, 18745-18751 (2008).
[CrossRef]

N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater. 7, 31-37 (2008).
[CrossRef]

B. Auguie and W. L. Barnes, "Collective resonances in gold nanoparticle arrays," Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef] [PubMed]

V. G. Kravets, F. Schedin, and A. N. Grigorenko, "Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles," Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef] [PubMed]

A. Bitzer and M. Walther, "Terahertz near-field imaging of metallic subwavelength holes and hole arrays," Appl. Phys. Lett. 92, 231101 (2008).
[CrossRef]

N. Liu, S. Kaiser, and H. Giessen, "Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules," Adv. Mater. 20, 4521-4525 (2008).
[CrossRef]

H. T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, "Experimental demonstration of frequency-agile terahertz metamaterials," Nat. Photonics 2, 295-298 (2008).
[CrossRef]

2007 (5)

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refractive index at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007).
[CrossRef]

F. Hao, P. Nordlander,M. T. Burnett, and S. A. Maier, "Enhanced tunability and linewidth sharpening of plasmon resonances in hybridized metallic ring/disk nanocavities," Phys. Rev. B 76, 245417 (2007).
[CrossRef]

N. Liu, H. C. Guo, L.W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmon hybridization in stacked cut-wire metamaterials," Adv. Mater. 19, 3628-3632 (2007).
[CrossRef]

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, "Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry," Phys. Rev. Lett. 99, 147401 (2007).
[CrossRef] [PubMed]

2006 (2)

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

2004 (1)

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

2003 (1)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, "A hybridization model for the plasmon response of complex nanostructures," Science 302, 419-422 (2003).
[CrossRef] [PubMed]

2001 (1)

S. Linden, J. Kuhl, and H. Giessen, "Controlling the interaction between light and gold nanoparticles: Selective suppression of extinction," Phys. Rev. Lett. 86, 4688-4691 (2001).
[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]

1935 (1)

R. W. Wood, "Anomalous Diffraction Gratings," Phys. Rev. 48, 928-936 (1935).
[CrossRef]

Acuna, G.

Adam, A. J. L.

Ahn, K. J.

Auguie, B.

B. Auguie and W. L. Barnes, "Collective resonances in gold nanoparticle arrays," Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef] [PubMed]

Averitt, R. D.

H. T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, "Experimental demonstration of frequency-agile terahertz metamaterials," Nat. Photonics 2, 295-298 (2008).
[CrossRef]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

Azad, A. K.

H. T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, "Experimental demonstration of frequency-agile terahertz metamaterials," Nat. Photonics 2, 295-298 (2008).
[CrossRef]

Barnes, W. L.

B. Auguie and W. L. Barnes, "Collective resonances in gold nanoparticle arrays," Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef] [PubMed]

Bitzer, A.

Brok, J. M.

Burnett, M. T.

F. Hao, P. Nordlander,M. T. Burnett, and S. A. Maier, "Enhanced tunability and linewidth sharpening of plasmon resonances in hybridized metallic ring/disk nanocavities," Phys. Rev. B 76, 245417 (2007).
[CrossRef]

Chen, H. T.

H. T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, "Experimental demonstration of frequency-agile terahertz metamaterials," Nat. Photonics 2, 295-298 (2008).
[CrossRef]

G. Acuna, S. F. Heucke, F. Kuchler, H. T. Chen, A. J. Taylor, and R. Kersting, "Surface plasmons in terahertz metamaterials," Opt. Express 16, 18745-18751 (2008).
[CrossRef]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

Economou, E. N.

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Low-Loss Metamaterials Based on Classical Electromagnetically Induced Transparency," Phys. Rev. Lett. 102, 053901 (2009).
[CrossRef] [PubMed]

Fedotov, V. A.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, "Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry," Phys. Rev. Lett. 99, 147401 (2007).
[CrossRef] [PubMed]

Feurer, T.

Fleischhauer, M.

N. Liu, L. Langguth, T. Weiss, J. K¨astel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
[CrossRef] [PubMed]

Fu, L. W.

N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater. 7, 31-37 (2008).
[CrossRef]

Fu, L.W.

N. Liu, H. C. Guo, L.W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmon hybridization in stacked cut-wire metamaterials," Adv. Mater. 19, 3628-3632 (2007).
[CrossRef]

Giessen, H.

N. Liu, L. Langguth, T. Weiss, J. K¨astel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
[CrossRef] [PubMed]

N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater. 7, 31-37 (2008).
[CrossRef]

N. Liu, S. Kaiser, and H. Giessen, "Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules," Adv. Mater. 20, 4521-4525 (2008).
[CrossRef]

N. Liu, H. C. Guo, L.W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmon hybridization in stacked cut-wire metamaterials," Adv. Mater. 19, 3628-3632 (2007).
[CrossRef]

S. Linden, J. Kuhl, and H. Giessen, "Controlling the interaction between light and gold nanoparticles: Selective suppression of extinction," Phys. Rev. Lett. 86, 4688-4691 (2001).
[CrossRef] [PubMed]

Gossard, A. C.

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

Grigorenko, A. N.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, "Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles," Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef] [PubMed]

Guo, H. C.

N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater. 7, 31-37 (2008).
[CrossRef]

N. Liu, H. C. Guo, L.W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmon hybridization in stacked cut-wire metamaterials," Adv. Mater. 19, 3628-3632 (2007).
[CrossRef]

Halas, N. J.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, "A hybridization model for the plasmon response of complex nanostructures," Science 302, 419-422 (2003).
[CrossRef] [PubMed]

Hao, F.

F. Hao, P. Nordlander,M. T. Burnett, and S. A. Maier, "Enhanced tunability and linewidth sharpening of plasmon resonances in hybridized metallic ring/disk nanocavities," Phys. Rev. B 76, 245417 (2007).
[CrossRef]

Helm, H.

Heucke, S. F.

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]

K¨astel, J.

N. Liu, L. Langguth, T. Weiss, J. K¨astel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
[CrossRef] [PubMed]

Kaiser, S.

N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater. 7, 31-37 (2008).
[CrossRef]

N. Liu, S. Kaiser, and H. Giessen, "Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules," Adv. Mater. 20, 4521-4525 (2008).
[CrossRef]

N. Liu, H. C. Guo, L.W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmon hybridization in stacked cut-wire metamaterials," Adv. Mater. 19, 3628-3632 (2007).
[CrossRef]

Kang, J. H.

Kersting, R.

Kim, D. S.

Knab, J. R.

Koschny, T.

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Low-Loss Metamaterials Based on Classical Electromagnetically Induced Transparency," Phys. Rev. Lett. 102, 053901 (2009).
[CrossRef] [PubMed]

Kravets, V. G.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, "Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles," Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef] [PubMed]

Kuchler, F.

Kuhl, J.

S. Linden, J. Kuhl, and H. Giessen, "Controlling the interaction between light and gold nanoparticles: Selective suppression of extinction," Phys. Rev. Lett. 86, 4688-4691 (2001).
[CrossRef] [PubMed]

Langguth, L.

N. Liu, L. Langguth, T. Weiss, J. K¨astel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
[CrossRef] [PubMed]

Lederer, F.

R. Singh, C. Rockstuhl, F. Lederer, and W. L. Zhang, "Coupling between a dark and a bright eigenmode in a terahertz metamaterial," Phys. Rev. B 79, 085111 (2009).
[CrossRef]

Linden, S.

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refractive index at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

S. Linden, J. Kuhl, and H. Giessen, "Controlling the interaction between light and gold nanoparticles: Selective suppression of extinction," Phys. Rev. Lett. 86, 4688-4691 (2001).
[CrossRef] [PubMed]

Liu, N.

N. Liu, L. Langguth, T. Weiss, J. K¨astel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
[CrossRef] [PubMed]

N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater. 7, 31-37 (2008).
[CrossRef]

N. Liu, S. Kaiser, and H. Giessen, "Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules," Adv. Mater. 20, 4521-4525 (2008).
[CrossRef]

N. Liu, H. C. Guo, L.W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmon hybridization in stacked cut-wire metamaterials," Adv. Mater. 19, 3628-3632 (2007).
[CrossRef]

Maier, S. A.

F. Hao, P. Nordlander,M. T. Burnett, and S. A. Maier, "Enhanced tunability and linewidth sharpening of plasmon resonances in hybridized metallic ring/disk nanocavities," Phys. Rev. B 76, 245417 (2007).
[CrossRef]

Merbold, H.

Nagel, M.

Nordlander, P.

F. Hao, P. Nordlander,M. T. Burnett, and S. A. Maier, "Enhanced tunability and linewidth sharpening of plasmon resonances in hybridized metallic ring/disk nanocavities," Phys. Rev. B 76, 245417 (2007).
[CrossRef]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, "A hybridization model for the plasmon response of complex nanostructures," Science 302, 419-422 (2003).
[CrossRef] [PubMed]

O’Hara, J. F.

H. T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, "Experimental demonstration of frequency-agile terahertz metamaterials," Nat. Photonics 2, 295-298 (2008).
[CrossRef]

Padilla, W. J.

H. T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, "Experimental demonstration of frequency-agile terahertz metamaterials," Nat. Photonics 2, 295-298 (2008).
[CrossRef]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

Papasimakis, N.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, "Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry," Phys. Rev. Lett. 99, 147401 (2007).
[CrossRef] [PubMed]

Park, Q. H.

Pendry, J. B.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

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]

Pfau, T.

N. Liu, L. Langguth, T. Weiss, J. K¨astel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
[CrossRef] [PubMed]

Planken, P. C. M.

Prodan, E.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, "A hybridization model for the plasmon response of complex nanostructures," Science 302, 419-422 (2003).
[CrossRef] [PubMed]

Prosvirnin, S. L.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, "Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry," Phys. Rev. Lett. 99, 147401 (2007).
[CrossRef] [PubMed]

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, "A hybridization model for the plasmon response of complex nanostructures," Science 302, 419-422 (2003).
[CrossRef] [PubMed]

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]

Rockstuhl, C.

R. Singh, C. Rockstuhl, F. Lederer, and W. L. Zhang, "Coupling between a dark and a bright eigenmode in a terahertz metamaterial," Phys. Rev. B 79, 085111 (2009).
[CrossRef]

Rose, M.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, "Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry," Phys. Rev. Lett. 99, 147401 (2007).
[CrossRef] [PubMed]

Schedin, F.

V. G. Kravets, F. Schedin, and A. N. Grigorenko, "Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles," Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef] [PubMed]

Schurig, D.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

Schweizer, H.

N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater. 7, 31-37 (2008).
[CrossRef]

N. Liu, H. C. Guo, L.W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmon hybridization in stacked cut-wire metamaterials," Adv. Mater. 19, 3628-3632 (2007).
[CrossRef]

Seo, M. A.

Shalaev, V. M.

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007).
[CrossRef]

Shaner, E.

Shrekenhamer, D. B.

H. T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, "Experimental demonstration of frequency-agile terahertz metamaterials," Nat. Photonics 2, 295-298 (2008).
[CrossRef]

Singh, R.

R. Singh, C. Rockstuhl, F. Lederer, and W. L. Zhang, "Coupling between a dark and a bright eigenmode in a terahertz metamaterial," Phys. Rev. B 79, 085111 (2009).
[CrossRef]

Smith, D. R.

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

Soukoulis, C. M.

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Low-Loss Metamaterials Based on Classical Electromagnetically Induced Transparency," Phys. Rev. Lett. 102, 053901 (2009).
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refractive index at optical wavelengths," Science 315, 47-49 (2007).
[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]

Tassin, P.

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Low-Loss Metamaterials Based on Classical Electromagnetically Induced Transparency," Phys. Rev. Lett. 102, 053901 (2009).
[CrossRef] [PubMed]

Taylor, A. J.

H. T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, "Experimental demonstration of frequency-agile terahertz metamaterials," Nat. Photonics 2, 295-298 (2008).
[CrossRef]

G. Acuna, S. F. Heucke, F. Kuchler, H. T. Chen, A. J. Taylor, and R. Kersting, "Surface plasmons in terahertz metamaterials," Opt. Express 16, 18745-18751 (2008).
[CrossRef]

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

Thoman, A.

Walther, M.

Wegener, M.

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refractive index at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

Weiss, T.

N. Liu, L. Langguth, T. Weiss, J. K¨astel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
[CrossRef] [PubMed]

Wiltshire, M. C. K.

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

Wood, R. W.

R. W. Wood, "Anomalous Diffraction Gratings," Phys. Rev. 48, 928-936 (1935).
[CrossRef]

Zhang, L.

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Low-Loss Metamaterials Based on Classical Electromagnetically Induced Transparency," Phys. Rev. Lett. 102, 053901 (2009).
[CrossRef] [PubMed]

Zhang, W. L.

R. Singh, C. Rockstuhl, F. Lederer, and W. L. Zhang, "Coupling between a dark and a bright eigenmode in a terahertz metamaterial," Phys. Rev. B 79, 085111 (2009).
[CrossRef]

Zheludev, N. I.

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, "Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry," Phys. Rev. Lett. 99, 147401 (2007).
[CrossRef] [PubMed]

Zide, J. M. O.

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

Adv. Mater. (2)

N. Liu, S. Kaiser, and H. Giessen, "Magnetoinductive and Electroinductive Coupling in Plasmonic Metamaterial Molecules," Adv. Mater. 20, 4521-4525 (2008).
[CrossRef]

N. Liu, H. C. Guo, L.W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Plasmon hybridization in stacked cut-wire metamaterials," Adv. Mater. 19, 3628-3632 (2007).
[CrossRef]

Appl. Phys. Lett. (1)

A. Bitzer and M. Walther, "Terahertz near-field imaging of metallic subwavelength holes and hole arrays," Appl. Phys. Lett. 92, 231101 (2008).
[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]

Nat. Mater. (2)

N. Liu, H. C. Guo, L. W. Fu, S. Kaiser, H. Schweizer, and H. Giessen, "Three-dimensional photonic metamaterials at optical frequencies," Nat. Mater. 7, 31-37 (2008).
[CrossRef]

N. Liu, L. Langguth, T. Weiss, J. K¨astel, M. Fleischhauer, T. Pfau, and H. Giessen, "Plasmonic analogue of electromagnetically induced transparency at the Drude damping limit," Nat. Mater. 8, 758-762 (2009).
[CrossRef] [PubMed]

Nat. Photonics (2)

V. M. Shalaev, "Optical negative-index metamaterials," Nat. Photonics 1, 41-48 (2007).
[CrossRef]

H. T. Chen, J. F. O’Hara, A. K. Azad, A. J. Taylor, R. D. Averitt, D. B. Shrekenhamer, and W. J. Padilla, "Experimental demonstration of frequency-agile terahertz metamaterials," Nat. Photonics 2, 295-298 (2008).
[CrossRef]

Nature (1)

H. T. Chen, W. J. Padilla, J. M. O. Zide, A. C. Gossard, A. J. Taylor, and R. D. Averitt, "Active terahertz metamaterial devices," Nature 444, 597-600 (2006).
[CrossRef] [PubMed]

Opt. Express (4)

Phys. Rev. (1)

R. W. Wood, "Anomalous Diffraction Gratings," Phys. Rev. 48, 928-936 (1935).
[CrossRef]

Phys. Rev. B (2)

R. Singh, C. Rockstuhl, F. Lederer, and W. L. Zhang, "Coupling between a dark and a bright eigenmode in a terahertz metamaterial," Phys. Rev. B 79, 085111 (2009).
[CrossRef]

F. Hao, P. Nordlander,M. T. Burnett, and S. A. Maier, "Enhanced tunability and linewidth sharpening of plasmon resonances in hybridized metallic ring/disk nanocavities," Phys. Rev. B 76, 245417 (2007).
[CrossRef]

Phys. Rev. Lett. (5)

P. Tassin, L. Zhang, T. Koschny, E. N. Economou, and C. M. Soukoulis, "Low-Loss Metamaterials Based on Classical Electromagnetically Induced Transparency," Phys. Rev. Lett. 102, 053901 (2009).
[CrossRef] [PubMed]

V. A. Fedotov, M. Rose, S. L. Prosvirnin, N. Papasimakis, and N. I. Zheludev, "Sharp trapped-mode resonances in planar metamaterials with a broken structural symmetry," Phys. Rev. Lett. 99, 147401 (2007).
[CrossRef] [PubMed]

S. Linden, J. Kuhl, and H. Giessen, "Controlling the interaction between light and gold nanoparticles: Selective suppression of extinction," Phys. Rev. Lett. 86, 4688-4691 (2001).
[CrossRef] [PubMed]

B. Auguie and W. L. Barnes, "Collective resonances in gold nanoparticle arrays," Phys. Rev. Lett. 101, 143902 (2008).
[CrossRef] [PubMed]

V. G. Kravets, F. Schedin, and A. N. Grigorenko, "Extremely narrow plasmon resonances based on diffraction coupling of localized plasmons in arrays of metallic nanoparticles," Phys. Rev. Lett. 101, 087403 (2008).
[CrossRef] [PubMed]

Science (4)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, "A hybridization model for the plasmon response of complex nanostructures," Science 302, 419-422 (2003).
[CrossRef] [PubMed]

D. R. Smith, J. B. Pendry, and M. C. K. Wiltshire, "Metamaterials and negative refractive index," Science 305, 788-792 (2004).
[CrossRef] [PubMed]

J. B. Pendry, D. Schurig, and D. R. Smith, "Controlling electromagnetic fields," Science 312, 1780-1782 (2006).
[CrossRef] [PubMed]

C. M. Soukoulis, S. Linden, and M. Wegener, "Negative refractive index at optical wavelengths," Science 315, 47-49 (2007).
[CrossRef] [PubMed]

Other (1)

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (John Wiley & Sons, Inc., New York, 1991).
[CrossRef]

Supplementary Material (3)

» Media 1: MOV (2586 KB)     
» Media 2: MOV (318 KB)     
» Media 3: MOV (321 KB)     

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Figures (4)

Fig. 1.
Fig. 1.

THz near-field scan (a) of a single SRR at its plasmonic resonances (n=1, n=3) showing the in-plane electric (arrows) and out-of-plane magnetic (color code) near-fields (Media 1). (b) Transmission through rectangular arrays of SRRs with gx =380µm and gy =380–653µm (bottom to top) (Media 2) showing their fundamental resonances and transmission minima that originate from the excitation of lattice modes (*). The spectra are vertically offset for clarity.

Fig. 2.
Fig. 2.

(a) Far-field intensity distributions of the scattered light calculated for a 1-D array consisting of five isotropic scatterers at different periodicities gy . The array is oriented along the y-axis and the incident beam propagates in z-direction. (b) Scattering distribution for gy =λ. Intensities are integrated over the angular intervals indicated by solid and dashed lines to determine the fractions of light scattered in and out of the sample plane. (c) Integrated intensities as a function of the lattice constant in units of the wavelength.

Fig. 3.
Fig. 3.

(a) Dispersion diagram obtained from the measured transmission spectra. In the measurement the lattice constant gy is changed in steps from 380 to 1200 µm while gx =380µm is constant. Plasmonic structure resonances are indicated by dotted lines (gray), and lattice modes by solid lines (green, blue). (b) Dispersion diagram of the simulated spectra. A and B mark weak and strong radiative coupling regimes for the n=3 mode and C a pure lattice mode. The inset shows the simulation volume with embedded SRR-structure and periodic boundaries on the sides (red). (color online)

Fig. 4.
Fig. 4.

(a) Average in-plane power flow shown for weak (A-mode) and strong radiative coupling (B-mode) as well as for the (0,1) lattice mode (C-mode). (b) Evolution of the simulated transmission spectrum from the weak to the strong coupling regime (A to B see Fig. 3(c)) (Media 3). The spectra are vertically offset for clarity. (c) Corresponding Q-factors of the plasmonic resonances. (color online)

Equations (1)

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k 2 = i 2 ( 2 π g x ) 2 + j 2 ( 2 π g y ) 2 ,

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