Abstract

Using terahertz near-field imaging we experimentally investigate the interaction between split-ring resonators (SRRs) in metamaterial arrays. Depending on the inter-SRR spacing two regimes can be distinguished for which strong coupling between SRRs occurs. For dense arrays SRRs couple via their electric and magnetic near-fields. In this case distinct deformations of the SRRs’ characteristic near-field patterns are observed as a signature of their strong interaction. For larger separations with a periodicity matching the resonance wavelength, the SRRs become diffractively coupled via their radiated fields. In this regime hybridization between plasmonic and lattice modes can be clearly identified in the experimentally obtained near-field maps.

© 2011 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  36. H. C. Guo, N. Liu, L. W. Fu, T. P. Meyrath, T. Zentgraf, H. Schweizer, and H. Giessen, “Resonance hybridization in double split-ring resonator metamaterials,” Opt. Express 15(19), 12095–12101 (2007).
    [CrossRef] [PubMed]

2011 (4)

M. T. Reiten, D. R. Chowdhury, J. Zhou, A. J. Taylor, J. F. O’Hara, and A. K. Azad, “Resonance tuning behavior in closely spaced inhomogeneous bilayer metamaterials,” Appl. Phys. Lett. 98, 131105 (2011).
[CrossRef]

M. Walther and A. Bitzer, “Electromagnetic wave propagation close to microstructures studied by time and phase-resolved THz near-field imaging,” J. Infrared Milli. Terahz. Waves (2011) DOI:.
[CrossRef]

A. Bitzer, A. Ortner, H. Merbold, T. Feurer, and M. Walther, “Terahertz near-field microscopy of complementary planar metamaterials: Babinet’s principle,” Opt. Express 19(3), 2537–2545 (2011).
[CrossRef] [PubMed]

R. Mueckstein and O. Mitrofanov, “Imaging of terahertz surface plasmon waves excited on a gold surface by a focused beam,” Opt. Express 19(4), 3212–3217 (2011).
[CrossRef] [PubMed]

2010 (7)

N. Feth, M. Konig, M. Husnik, K. Stannigel, J. Niegemann, K. Busch, M. Wegener, and S. Linden, “Electromagnetic interaction of split-ring resonators: The role of separation and relative orientation,” Opt. Express 18(7), 6545–6554 (2010).
[CrossRef] [PubMed]

A. Bitzer, A. Ortner, and M. Walther, “Terahertz near-field microscopy with subwavelength spatial resolution based on photoconductive antennas,” Appl. Opt. 49(19), E1–E6 (2010).
[CrossRef] [PubMed]

D. Diessel, M. Decker, S. Linden, and M. Wegener, “Near-field optical experiments on low-symmetry split-ring-resonator arrays,” Opt. Lett. 35(21), 3661–3663 (2010).
[CrossRef] [PubMed]

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104(22), 223901 (2010).
[CrossRef] [PubMed]

M. Burresi, D. Diessel, D. van Oosten, S. Linden, M. Wegener, and L. Kuipers, “Negative-index metamaterials: looking into the unit cell,” Nano Lett. 10(7), 2480–2483 (2010).
[CrossRef] [PubMed]

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

R. Singh, C. Rockstuhl, and W. L. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97(24), 241108 (2010).
[CrossRef]

2009 (8)

N. Liu, H. Liu, S. N. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009).
[CrossRef]

G. Vecchi, V. Giannini, and J. G. Rivas, “Shaping the fluorescent emission by lattice resonances in plasmonic crystals of nanoantennas,” Phys. Rev. Lett. 102(14), 146807 (2009).
[CrossRef] [PubMed]

G. Vecchi, V. Giannini, and J. G. Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009).
[CrossRef]

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(8), 085111 (2009).
[CrossRef]

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]

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(5), 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(17), 15072–15086 (2009).
[CrossRef] [PubMed]

A. Bitzer, J. Wallauer, H. Helm, H. Merbold, T. Feurer, and M. Walther, “Lattice modes mediate radiative coupling in metamaterial arrays,” Opt. Express 17(24), 22108–22113 (2009).
[CrossRef] [PubMed]

2008 (8)

T. Zentgraf, J. Dorfmuller, C. Rockstuhl, C. Etrich, R. Vogelgesang, K. Kern, T. Pertsch, F. Lederer, and H. Giessen, “Amplitude-and phase-resolved optical near fields of split-ring-resonator-based metamaterials,” Opt. Lett. 33(8), 848–850 (2008).
[CrossRef] [PubMed]

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(10), 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(23), 18745–18751 (2008).
[CrossRef]

N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and electroinductive coupling in plasmonic metamaterial molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
[CrossRef]

A. Bitzer and M. Walther, “Terahertz near-field imaging of metallic subwavelength holes and hole arrays,” Appl. Phys. Lett. 92(23), 231101 (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(1), 31–37 (2008).
[CrossRef]

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(8), 087403 (2008).
[CrossRef] [PubMed]

B. Auguie and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008).
[CrossRef] [PubMed]

2007 (4)

2006 (1)

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1–2), 219–227 (2006).
[CrossRef]

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(20), 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(11), 2075–2084 (1999).
[CrossRef]

1990 (1)

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(14), 143902 (2008).
[CrossRef] [PubMed]

Azad, A. K.

M. T. Reiten, D. R. Chowdhury, J. Zhou, A. J. Taylor, J. F. O’Hara, and A. K. Azad, “Resonance tuning behavior in closely spaced inhomogeneous bilayer metamaterials,” Appl. Phys. Lett. 98, 131105 (2011).
[CrossRef]

Barnes, W. L.

B. Auguie and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008).
[CrossRef] [PubMed]

Bitzer, A.

Boudarham, G.

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

Brok, J. M.

Burresi, M.

M. Burresi, D. Diessel, D. van Oosten, S. Linden, M. Wegener, and L. Kuipers, “Negative-index metamaterials: looking into the unit cell,” Nano Lett. 10(7), 2480–2483 (2010).
[CrossRef] [PubMed]

Busch, K.

Chen, H. T.

Chowdhury, D. R.

M. T. Reiten, D. R. Chowdhury, J. Zhou, A. J. Taylor, J. F. O’Hara, and A. K. Azad, “Resonance tuning behavior in closely spaced inhomogeneous bilayer metamaterials,” Appl. Phys. Lett. 98, 131105 (2011).
[CrossRef]

Dahmen, C.

C. Dahmen, B. Schmidt, and G. von Plessen, “Radiation damping in metal nanoparticle pairs,” Nano Lett. 7(2), 318–322 (2007).
[CrossRef] [PubMed]

de Abajo, F. J. G.

F. J. G. de Abajo, “Colloquium: light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[CrossRef]

de Abajo, J. G.

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

Decker, M.

Diessel, D.

D. Diessel, M. Decker, S. Linden, and M. Wegener, “Near-field optical experiments on low-symmetry split-ring-resonator arrays,” Opt. Lett. 35(21), 3661–3663 (2010).
[CrossRef] [PubMed]

M. Burresi, D. Diessel, D. van Oosten, S. Linden, M. Wegener, and L. Kuipers, “Negative-index metamaterials: looking into the unit cell,” Nano Lett. 10(7), 2480–2483 (2010).
[CrossRef] [PubMed]

Dorfmuller, J.

Etrich, C.

T. Zentgraf, J. Dorfmuller, C. Rockstuhl, C. Etrich, R. Vogelgesang, K. Kern, T. Pertsch, F. Lederer, and H. Giessen, “Amplitude-and phase-resolved optical near fields of split-ring-resonator-based metamaterials,” Opt. Lett. 33(8), 848–850 (2008).
[CrossRef] [PubMed]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1–2), 219–227 (2006).
[CrossRef]

Fattinger, C.

Fedotov, V. A.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104(22), 223901 (2010).
[CrossRef] [PubMed]

Feth, N.

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

N. Feth, M. Konig, M. Husnik, K. Stannigel, J. Niegemann, K. Busch, M. Wegener, and S. Linden, “Electromagnetic interaction of split-ring resonators: The role of separation and relative orientation,” Opt. Express 18(7), 6545–6554 (2010).
[CrossRef] [PubMed]

Feurer, T.

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]

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(1), 31–37 (2008).
[CrossRef]

H. C. Guo, N. Liu, L. W. Fu, T. P. Meyrath, T. Zentgraf, H. Schweizer, and H. Giessen, “Resonance hybridization in double split-ring resonator metamaterials,” Opt. Express 15(19), 12095–12101 (2007).
[CrossRef] [PubMed]

Giannini, V.

G. Vecchi, V. Giannini, and J. G. Rivas, “Shaping the fluorescent emission by lattice resonances in plasmonic crystals of nanoantennas,” Phys. Rev. Lett. 102(14), 146807 (2009).
[CrossRef] [PubMed]

G. Vecchi, V. Giannini, and J. G. Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009).
[CrossRef]

Giessen, H.

N. Liu, H. Liu, S. N. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009).
[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(1), 31–37 (2008).
[CrossRef]

T. Zentgraf, J. Dorfmuller, C. Rockstuhl, C. Etrich, R. Vogelgesang, K. Kern, T. Pertsch, F. Lederer, and H. Giessen, “Amplitude-and phase-resolved optical near fields of split-ring-resonator-based metamaterials,” Opt. Lett. 33(8), 848–850 (2008).
[CrossRef] [PubMed]

N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and electroinductive coupling in plasmonic metamaterial molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
[CrossRef]

H. C. Guo, N. Liu, L. W. Fu, T. P. Meyrath, T. Zentgraf, H. Schweizer, and H. Giessen, “Resonance hybridization in double split-ring resonator metamaterials,” Opt. Express 15(19), 12095–12101 (2007).
[CrossRef] [PubMed]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1–2), 219–227 (2006).
[CrossRef]

S. Linden, J. Kuhl, and H. Giessen, “Controlling the interaction between light and gold nanoparticles: Selective suppression of extinction,” Phys. Rev. Lett. 86(20), 4688–4691 (2001).
[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(8), 087403 (2008).
[CrossRef] [PubMed]

Grischkowsky, D.

Guo, H.

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1–2), 219–227 (2006).
[CrossRef]

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(1), 31–37 (2008).
[CrossRef]

H. C. Guo, N. Liu, L. W. Fu, T. P. Meyrath, T. Zentgraf, H. Schweizer, and H. Giessen, “Resonance hybridization in double split-ring resonator metamaterials,” Opt. Express 15(19), 12095–12101 (2007).
[CrossRef] [PubMed]

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(11), 2075–2084 (1999).
[CrossRef]

Husnik, M.

Jeoung, S. C.

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(1), 31–37 (2008).
[CrossRef]

N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and electroinductive coupling in plasmonic metamaterial molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
[CrossRef]

Kang, J. H.

Keiding, S.

Kern, K.

Kersting, R.

Kim, D. S.

Knab, J. R.

Kociak, M.

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

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]

Konig, M.

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(8), 087403 (2008).
[CrossRef] [PubMed]

Kuchler, F.

Kuhl, J.

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1–2), 219–227 (2006).
[CrossRef]

S. Linden, J. Kuhl, and H. Giessen, “Controlling the interaction between light and gold nanoparticles: Selective suppression of extinction,” Phys. Rev. Lett. 86(20), 4688–4691 (2001).
[CrossRef] [PubMed]

Kuipers, L.

M. Burresi, D. Diessel, D. van Oosten, S. Linden, M. Wegener, and L. Kuipers, “Negative-index metamaterials: looking into the unit cell,” Nano Lett. 10(7), 2480–2483 (2010).
[CrossRef] [PubMed]

Kuo, P.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104(22), 223901 (2010).
[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(8), 085111 (2009).
[CrossRef]

T. Zentgraf, J. Dorfmuller, C. Rockstuhl, C. Etrich, R. Vogelgesang, K. Kern, T. Pertsch, F. Lederer, and H. Giessen, “Amplitude-and phase-resolved optical near fields of split-ring-resonator-based metamaterials,” Opt. Lett. 33(8), 848–850 (2008).
[CrossRef] [PubMed]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1–2), 219–227 (2006).
[CrossRef]

Lee, J. W.

Linden, S.

N. Feth, M. Konig, M. Husnik, K. Stannigel, J. Niegemann, K. Busch, M. Wegener, and S. Linden, “Electromagnetic interaction of split-ring resonators: The role of separation and relative orientation,” Opt. Express 18(7), 6545–6554 (2010).
[CrossRef] [PubMed]

D. Diessel, M. Decker, S. Linden, and M. Wegener, “Near-field optical experiments on low-symmetry split-ring-resonator arrays,” Opt. Lett. 35(21), 3661–3663 (2010).
[CrossRef] [PubMed]

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

M. Burresi, D. Diessel, D. van Oosten, S. Linden, M. Wegener, and L. Kuipers, “Negative-index metamaterials: looking into the unit cell,” Nano Lett. 10(7), 2480–2483 (2010).
[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(20), 4688–4691 (2001).
[CrossRef] [PubMed]

Liu, H.

N. Liu, H. Liu, S. N. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009).
[CrossRef]

Liu, N.

N. Liu, H. Liu, S. N. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009).
[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(1), 31–37 (2008).
[CrossRef]

N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and electroinductive coupling in plasmonic metamaterial molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
[CrossRef]

H. C. Guo, N. Liu, L. W. Fu, T. P. Meyrath, T. Zentgraf, H. Schweizer, and H. Giessen, “Resonance hybridization in double split-ring resonator metamaterials,” Opt. Express 15(19), 12095–12101 (2007).
[CrossRef] [PubMed]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1–2), 219–227 (2006).
[CrossRef]

Loa, I.

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1–2), 219–227 (2006).
[CrossRef]

Merbold, H.

Meyrath, T. P.

Mitrofanov, O.

Mueckstein, R.

Myroshnychenko, V.

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

Nagel, M.

Niegemann, J.

O’Hara, J. F.

M. T. Reiten, D. R. Chowdhury, J. Zhou, A. J. Taylor, J. F. O’Hara, and A. K. Azad, “Resonance tuning behavior in closely spaced inhomogeneous bilayer metamaterials,” Appl. Phys. Lett. 98, 131105 (2011).
[CrossRef]

Ortner, A.

Papasimakis, N.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104(22), 223901 (2010).
[CrossRef] [PubMed]

Park, Q. H.

Pendry, J. B.

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(11), 2075–2084 (1999).
[CrossRef]

Pertsch, T.

Planken, P. C. M.

Plum, E.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104(22), 223901 (2010).
[CrossRef] [PubMed]

Reiten, M. T.

M. T. Reiten, D. R. Chowdhury, J. Zhou, A. J. Taylor, J. F. O’Hara, and A. K. Azad, “Resonance tuning behavior in closely spaced inhomogeneous bilayer metamaterials,” Appl. Phys. Lett. 98, 131105 (2011).
[CrossRef]

Rivas, J. G.

G. Vecchi, V. Giannini, and J. G. Rivas, “Shaping the fluorescent emission by lattice resonances in plasmonic crystals of nanoantennas,” Phys. Rev. Lett. 102(14), 146807 (2009).
[CrossRef] [PubMed]

G. Vecchi, V. Giannini, and J. G. Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009).
[CrossRef]

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(11), 2075–2084 (1999).
[CrossRef]

Rockstuhl, C.

R. Singh, C. Rockstuhl, and W. L. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97(24), 241108 (2010).
[CrossRef]

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(8), 085111 (2009).
[CrossRef]

T. Zentgraf, J. Dorfmuller, C. Rockstuhl, C. Etrich, R. Vogelgesang, K. Kern, T. Pertsch, F. Lederer, and H. Giessen, “Amplitude-and phase-resolved optical near fields of split-ring-resonator-based metamaterials,” Opt. Lett. 33(8), 848–850 (2008).
[CrossRef] [PubMed]

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1–2), 219–227 (2006).
[CrossRef]

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(8), 087403 (2008).
[CrossRef] [PubMed]

Schmidt, B.

C. Dahmen, B. Schmidt, and G. von Plessen, “Radiation damping in metal nanoparticle pairs,” Nano Lett. 7(2), 318–322 (2007).
[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(1), 31–37 (2008).
[CrossRef]

H. C. Guo, N. Liu, L. W. Fu, T. P. Meyrath, T. Zentgraf, H. Schweizer, and H. Giessen, “Resonance hybridization in double split-ring resonator metamaterials,” Opt. Express 15(19), 12095–12101 (2007).
[CrossRef] [PubMed]

Seo, M. A.

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]

Shaner, E.

Singh, R.

R. Singh, C. Rockstuhl, and W. L. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97(24), 241108 (2010).
[CrossRef]

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(8), 085111 (2009).
[CrossRef]

Stannigel, K.

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(11), 2075–2084 (1999).
[CrossRef]

Syassen, K.

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1–2), 219–227 (2006).
[CrossRef]

Taylor, A. J.

M. T. Reiten, D. R. Chowdhury, J. Zhou, A. J. Taylor, J. F. O’Hara, and A. K. Azad, “Resonance tuning behavior in closely spaced inhomogeneous bilayer metamaterials,” Appl. Phys. Lett. 98, 131105 (2011).
[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(23), 18745–18751 (2008).
[CrossRef]

Thoman, A.

Tsai, D. P.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104(22), 223901 (2010).
[CrossRef] [PubMed]

van Oosten, D.

M. Burresi, D. Diessel, D. van Oosten, S. Linden, M. Wegener, and L. Kuipers, “Negative-index metamaterials: looking into the unit cell,” Nano Lett. 10(7), 2480–2483 (2010).
[CrossRef] [PubMed]

Vanexter, M.

Vecchi, G.

G. Vecchi, V. Giannini, and J. G. Rivas, “Shaping the fluorescent emission by lattice resonances in plasmonic crystals of nanoantennas,” Phys. Rev. Lett. 102(14), 146807 (2009).
[CrossRef] [PubMed]

G. Vecchi, V. Giannini, and J. G. Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009).
[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]

Vogelgesang, R.

von Plessen, G.

C. Dahmen, B. Schmidt, and G. von Plessen, “Radiation damping in metal nanoparticle pairs,” Nano Lett. 7(2), 318–322 (2007).
[CrossRef] [PubMed]

Wallauer, J.

Walther, M.

Wegener, M.

N. Feth, M. Konig, M. Husnik, K. Stannigel, J. Niegemann, K. Busch, M. Wegener, and S. Linden, “Electromagnetic interaction of split-ring resonators: The role of separation and relative orientation,” Opt. Express 18(7), 6545–6554 (2010).
[CrossRef] [PubMed]

D. Diessel, M. Decker, S. Linden, and M. Wegener, “Near-field optical experiments on low-symmetry split-ring-resonator arrays,” Opt. Lett. 35(21), 3661–3663 (2010).
[CrossRef] [PubMed]

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

M. Burresi, D. Diessel, D. van Oosten, S. Linden, M. Wegener, and L. Kuipers, “Negative-index metamaterials: looking into the unit cell,” Nano Lett. 10(7), 2480–2483 (2010).
[CrossRef] [PubMed]

Wood, R. W.

R. W. Wood, “Anomalous diffraction gratings,” Phys. Rev. 48, 928–936 (1935).
[CrossRef]

Zentgraf, T.

Zhang, W. L.

R. Singh, C. Rockstuhl, and W. L. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97(24), 241108 (2010).
[CrossRef]

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(8), 085111 (2009).
[CrossRef]

Zheludev, N. I.

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104(22), 223901 (2010).
[CrossRef] [PubMed]

Zhou, J.

M. T. Reiten, D. R. Chowdhury, J. Zhou, A. J. Taylor, J. F. O’Hara, and A. K. Azad, “Resonance tuning behavior in closely spaced inhomogeneous bilayer metamaterials,” Appl. Phys. Lett. 98, 131105 (2011).
[CrossRef]

Zhu, S. N.

N. Liu, H. Liu, S. N. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009).
[CrossRef]

Adv. Mater. (1)

N. Liu, S. Kaiser, and H. Giessen, “Magnetoinductive and electroinductive coupling in plasmonic metamaterial molecules,” Adv. Mater. 20(23), 4521–4525 (2008).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

C. Rockstuhl, T. Zentgraf, H. Guo, N. Liu, C. Etrich, I. Loa, K. Syassen, J. Kuhl, F. Lederer, and H. Giessen, “Resonances of split-ring resonator metamaterials in the near infrared,” Appl. Phys. B 84(1–2), 219–227 (2006).
[CrossRef]

Appl. Phys. Lett. (3)

R. Singh, C. Rockstuhl, and W. L. Zhang, “Strong influence of packing density in terahertz metamaterials,” Appl. Phys. Lett. 97(24), 241108 (2010).
[CrossRef]

M. T. Reiten, D. R. Chowdhury, J. Zhou, A. J. Taylor, J. F. O’Hara, and A. K. Azad, “Resonance tuning behavior in closely spaced inhomogeneous bilayer metamaterials,” Appl. Phys. Lett. 98, 131105 (2011).
[CrossRef]

A. Bitzer and M. Walther, “Terahertz near-field imaging of metallic subwavelength holes and hole arrays,” Appl. Phys. Lett. 92(23), 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(11), 2075–2084 (1999).
[CrossRef]

J. Infrared Milli. Terahz. Waves (1)

M. Walther and A. Bitzer, “Electromagnetic wave propagation close to microstructures studied by time and phase-resolved THz near-field imaging,” J. Infrared Milli. Terahz. Waves (2011) DOI:.
[CrossRef]

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

Nano Lett. (2)

C. Dahmen, B. Schmidt, and G. von Plessen, “Radiation damping in metal nanoparticle pairs,” Nano Lett. 7(2), 318–322 (2007).
[CrossRef] [PubMed]

M. Burresi, D. Diessel, D. van Oosten, S. Linden, M. Wegener, and L. Kuipers, “Negative-index metamaterials: looking into the unit cell,” Nano Lett. 10(7), 2480–2483 (2010).
[CrossRef] [PubMed]

Nat. Mater. (1)

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(1), 31–37 (2008).
[CrossRef]

Nat. Photonics (1)

N. Liu, H. Liu, S. N. Zhu, and H. Giessen, “Stereometamaterials,” Nat. Photonics 3(3), 157–162 (2009).
[CrossRef]

Opt. Express (10)

M. A. Seo, A. J. L. Adam, J. H. Kang, J. W. Lee, S. C. Jeoung, Q. H. Park, P. C. M. Planken, and D. S. Kim, “Fourier-transform terahertz near-field imaging of one-dimensional slit arrays: mapping of electric-field-, magnetic-field-, and Poynting vectors,” Opt. Express 15(19), 11781–11789 (2007).
[CrossRef] [PubMed]

H. C. Guo, N. Liu, L. W. Fu, T. P. Meyrath, T. Zentgraf, H. Schweizer, and H. Giessen, “Resonance hybridization in double split-ring resonator metamaterials,” Opt. Express 15(19), 12095–12101 (2007).
[CrossRef] [PubMed]

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(10), 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(23), 18745–18751 (2008).
[CrossRef]

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(5), 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(17), 15072–15086 (2009).
[CrossRef] [PubMed]

A. Bitzer, J. Wallauer, H. Helm, H. Merbold, T. Feurer, and M. Walther, “Lattice modes mediate radiative coupling in metamaterial arrays,” Opt. Express 17(24), 22108–22113 (2009).
[CrossRef] [PubMed]

N. Feth, M. Konig, M. Husnik, K. Stannigel, J. Niegemann, K. Busch, M. Wegener, and S. Linden, “Electromagnetic interaction of split-ring resonators: The role of separation and relative orientation,” Opt. Express 18(7), 6545–6554 (2010).
[CrossRef] [PubMed]

A. Bitzer, A. Ortner, H. Merbold, T. Feurer, and M. Walther, “Terahertz near-field microscopy of complementary planar metamaterials: Babinet’s principle,” Opt. Express 19(3), 2537–2545 (2011).
[CrossRef] [PubMed]

R. Mueckstein and O. Mitrofanov, “Imaging of terahertz surface plasmon waves excited on a gold surface by a focused beam,” Opt. Express 19(4), 3212–3217 (2011).
[CrossRef] [PubMed]

Opt. Lett. (2)

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(8), 085111 (2009).
[CrossRef]

G. Vecchi, V. Giannini, and J. G. Rivas, “Surface modes in plasmonic crystals induced by diffractive coupling of nanoantennas,” Phys. Rev. B 80(20), 201401 (2009).
[CrossRef]

Phys. Rev. Lett. (7)

V. A. Fedotov, N. Papasimakis, E. Plum, A. Bitzer, M. Walther, P. Kuo, D. P. Tsai, and N. I. Zheludev, “Spectral collapse in ensembles of metamolecules,” Phys. Rev. Lett. 104(22), 223901 (2010).
[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(20), 4688–4691 (2001).
[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(8), 087403 (2008).
[CrossRef] [PubMed]

B. Auguie and W. L. Barnes, “Collective resonances in gold nanoparticle arrays,” Phys. Rev. Lett. 101(14), 143902 (2008).
[CrossRef] [PubMed]

G. Vecchi, V. Giannini, and J. G. Rivas, “Shaping the fluorescent emission by lattice resonances in plasmonic crystals of nanoantennas,” Phys. Rev. Lett. 102(14), 146807 (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]

G. Boudarham, N. Feth, V. Myroshnychenko, S. Linden, J. G. de Abajo, M. Wegener, and M. Kociak, “Spectral imaging of individual split-ring resonators,” Phys. Rev. Lett. 105(25), 255501 (2010).
[CrossRef]

Rev. Mod. Phys. (1)

F. J. G. de Abajo, “Colloquium: light scattering by particle and hole arrays,” Rev. Mod. Phys. 79(4), 1267–1290 (2007).
[CrossRef]

Supplementary Material (2)

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Figures (6)

Fig. 1
Fig. 1

(a) Microscope image of a section of a SRR array. The sidelength of an individual SRR structure is l = 300 μm and the width w = 30 μm. Lattice periodicities were varied in steps from 380–1200 μm in x- and y-directions separately. (b) THz transmission spectrum of an array with gx = gy = 500 μm with the electric field of the incident wave polarized along the x-axis. Vertical lines indicate expected spectral positions of plasmonic resonances and lattice modes according to Eqs. (1) and (2).

Fig. 2
Fig. 2

(a) THz near-field scan 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. (b) Simulated near-fields in a plane 60 μm behind the SRR. The insets show the currents and charge distributions associated with each resonance.

Fig. 3
Fig. 3

(a) Measured transmission spectra of SRR square arrays as a function of periodicity (gx = gy ). Resonance frequencies of the plasmonic eigenmodes n=1 and n=3 according to Eq. (1) are indicated by vertical dashed lines and the lowest order lattice modes by solid curves. Circles (A1–A3,B1–B3) mark periodicities and frequencies for which THz near-field maps are shown in Fig. 4. (b) Quality factor versus lattice periodicity gx = gy (solid dots) and gy (open squares) for the two lowest plasmonic eigenmodes (n=1 blue, n=3 red).

Fig. 4
Fig. 4

Measured in-plane electric (vectors) and out-of-plane magnetic near-fields (colors) of SRR arrays (field of view: 1.4 × 1.4 mm) with different lattice periodicities at the plasmonic eigenresonances n=1 (top row) and n=3 (bottom row). A whole oscillation cycle can be seen in Media 1. The near-field maps correlate to the corresponding frequencies and lattice periods, A1–A3 and B1–B3, indicated in Fig. 3(a).

Fig. 5
Fig. 5

(a) Measured transmission spectra of SRR arrays as a function of y-periodicity for constant periodicity in x-direction (gx = 380 μm). Resonance frequencies of plasmonic modes n=1, 3 and 5, calculated according to Eq. (1), are indicated by vertical dashed lines. Lattice modes, calculated according to Eq. (2), are shown as solid green and blue curves. Circles mark periodicities and frequencies for which THz near-field maps are shown in Fig. 6. (b) Quality factors of the plasmonic eigenmodes.

Fig. 6
Fig. 6

Measured THz near-field maps at the resonance frequencies of SRR arrays (field of view: 1.4 × 1.4 mm) with two selected lattice periodicities, gy = 487μm (A) and gy = 700 μm (B); gx = 380 μm in both cases (Media 2). Insets show the corresponding spatial 2D Fourier-transforms of the magnetic field maps.

Equations (2)

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ν n c * 2 L , n = 1 , 3 , 5
ν 2 = i 2 ( c * g x ) 2 + j 2 ( c * g y ) 2 ,

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