Abstract

Evolution of the absorption and scattering cross sections, quality-factor (Q-factor), and field enhancement of three-dimensional retardation-based plasmonic resonators being transformed from straight gold nanorod antennas to split-ring resonators by bending is considered. The optical resonances are confirmed to be of plasmonic origin and are specifically shown to be related to the formation of standing waves of short-range surface plasmon polaritons supported by straight and bent nanorods. We verify that by bending nanoantennas it is possible to reduce and ultimately, in the split-ring resonator limit, practically eliminate their scattering at the fundamental resonance, resulting in a substantial increase in the corresponding Q-factors. The decrease in scattering by bending is connected with the attenuation of the electric-dipole response in favor of a magnetic-dipole one, leading to Q-factors exceeding the quasi-static limit by a factor of 1.7. Simultaneously, the structures exhibit local field enhancements of >50.

© 2010 Optical Society of America

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  1. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  2. M. Pelton, J. Aizpurua, and G. Bryant, “Metal-nanoparticle plasmonics,” Laser Photonics Rev. 2, 136–159 (2008).
    [CrossRef]
  3. T. Søndergaard and S. Bozhevolnyi, “Slow-plasmon resonant nanostructures: Scattering and field enhancement,” Phys. Rev. B 75, 073402 (2007).
    [CrossRef]
  4. E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
    [CrossRef]
  5. J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry–Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. 9, 2372–2377 (2009).
    [CrossRef] [PubMed]
  6. T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, “Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration,” Phys. Rev. B 77, 115420 (2008).
    [CrossRef]
  7. S. I. Bozhevolnyi and T. Søndergaard, “General properties of slow-plasmon resonant nanostructures: nano-antennas and resonators,” Opt. Express 15, 10869–10877 (2007).
    [CrossRef] [PubMed]
  8. T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi B 245, 9–19 (2008).
    [CrossRef]
  9. J. Jung and T. Søndergaard, “Gap plasmon-polariton nanoresonators: Scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B 79, 035401 (2009).
    [CrossRef]
  10. H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96, 097401 (2006).
    [CrossRef] [PubMed]
  11. J. Takahara, S. Yamagishi, H. Taki, A. Morimoto, and T. Kobayashi, “Guiding of a one-dimensional optical beam with nanometer diameter,” Opt. Lett. 22, 475–477 (1997).
    [CrossRef] [PubMed]
  12. L. Novotny, “Effective wavelength scaling for optical antennas,” Phys. Rev. Lett. 98, 266802 (2007).
    [CrossRef] [PubMed]
  13. H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
    [CrossRef] [PubMed]
  14. S. D. Liu, Z. S. Zhang, and Q. Q. Wang, “High sensitivity and large field enhancement of symmetry broken Au nanorings: effect of multipolar plasmon resonance and propagation,” Opt. Express 17, 2906–2917 (2009).
    [CrossRef] [PubMed]
  15. C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14, 8827–8836 (2006).
    [CrossRef] [PubMed]
  16. H. Guo, N. Liu, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, “Thickness dependence of the optical properties of split-ring resonator metamaterials,” Phys. Status Solidi B 244, 1256–1261 (2007).
    [CrossRef]
  17. J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic and electric excitations in split ring resonators,” Opt. Express 15, 17881–17890 (2007).
    [CrossRef] [PubMed]
  18. S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic response of metamaterials at 100 terahertz,” Science 306, 1351–1353 (2004).
    [CrossRef] [PubMed]
  19. M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
    [CrossRef]
  20. D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Shultz, “Composite medium with simultaneously negative permeability and permittivity,” Phys. Rev. Lett. 84, 4184–4187 (2000).
    [CrossRef] [PubMed]
  21. A. K. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B 75, 085436 (2007).
    [CrossRef]
  22. G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “Efficient suppression of radiation damping in resonant retardation-based plasmonic structures,” Phys. Rev. B 79, 113410 (2009).
    [CrossRef]
  23. G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “High-Q plasmonic resonators based on metal split nanocylinders,” Phys. Rev. B 80, 235405 (2009).
    [CrossRef]
  24. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  25. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  26. G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “Plasmon-polariton nano-strip resonators: from visible to infra-red,” Opt. Express 16, 6867–6876 (2008).
    [CrossRef] [PubMed]
  27. J. D. Jackson, Classical Electrodynamics (Wiley, 1962).
  28. P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
    [CrossRef] [PubMed]
  29. P. Berini and J. Lu, “Curved long-range surface plasmon-polariton waveguides,” Opt. Express 14, 2365–2371 (2006).
    [CrossRef] [PubMed]
  30. Y. Zeng, C. Dineen, and J. V. Moloney, “Magnetic dipole moments in single and coupled split-ring resonators,” Phys. Rev. B 81, 075116 (2010).
    [CrossRef]
  31. M. Kerker, D. S. Wang, and H. Chew, “Surface enhanced Raman scattering (SERS) by molecules adsorbed at spherical particles: errata,” Appl. Opt. 19, 4159–4174 (1980).
    [CrossRef] [PubMed]
  32. K. Kneipp, R. R. Dasari, and Y. Wang, “Near-infrared surface-enhanced Raman scattering (NIR SERS) on colloidal silver and gold,” Appl. Spectrosc. 48, 951–955 (1994).
    [CrossRef]
  33. F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97, 206806 (2006).
    [CrossRef] [PubMed]
  34. E. Feigenbaum and M. Orenstein, “Ultrasmall volume plasmons, yet with complete retardation effects,” Phys. Rev. Lett. 101, 163902 (2008).
    [CrossRef] [PubMed]

2010

Y. Zeng, C. Dineen, and J. V. Moloney, “Magnetic dipole moments in single and coupled split-ring resonators,” Phys. Rev. B 81, 075116 (2010).
[CrossRef]

2009

G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “Efficient suppression of radiation damping in resonant retardation-based plasmonic structures,” Phys. Rev. B 79, 113410 (2009).
[CrossRef]

G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “High-Q plasmonic resonators based on metal split nanocylinders,” Phys. Rev. B 80, 235405 (2009).
[CrossRef]

J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry–Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. 9, 2372–2377 (2009).
[CrossRef] [PubMed]

J. Jung and T. Søndergaard, “Gap plasmon-polariton nanoresonators: Scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B 79, 035401 (2009).
[CrossRef]

S. D. Liu, Z. S. Zhang, and Q. Q. Wang, “High sensitivity and large field enhancement of symmetry broken Au nanorings: effect of multipolar plasmon resonance and propagation,” Opt. Express 17, 2906–2917 (2009).
[CrossRef] [PubMed]

2008

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi B 245, 9–19 (2008).
[CrossRef]

T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, “Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration,” Phys. Rev. B 77, 115420 (2008).
[CrossRef]

M. Pelton, J. Aizpurua, and G. Bryant, “Metal-nanoparticle plasmonics,” Laser Photonics Rev. 2, 136–159 (2008).
[CrossRef]

G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “Plasmon-polariton nano-strip resonators: from visible to infra-red,” Opt. Express 16, 6867–6876 (2008).
[CrossRef] [PubMed]

E. Feigenbaum and M. Orenstein, “Ultrasmall volume plasmons, yet with complete retardation effects,” Phys. Rev. Lett. 101, 163902 (2008).
[CrossRef] [PubMed]

2007

T. Søndergaard and S. Bozhevolnyi, “Slow-plasmon resonant nanostructures: Scattering and field enhancement,” Phys. Rev. B 75, 073402 (2007).
[CrossRef]

S. I. Bozhevolnyi and T. Søndergaard, “General properties of slow-plasmon resonant nanostructures: nano-antennas and resonators,” Opt. Express 15, 10869–10877 (2007).
[CrossRef] [PubMed]

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

A. K. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B 75, 085436 (2007).
[CrossRef]

H. Guo, N. Liu, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, “Thickness dependence of the optical properties of split-ring resonator metamaterials,” Phys. Status Solidi B 244, 1256–1261 (2007).
[CrossRef]

J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic and electric excitations in split ring resonators,” Opt. Express 15, 17881–17890 (2007).
[CrossRef] [PubMed]

2006

C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14, 8827–8836 (2006).
[CrossRef] [PubMed]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96, 097401 (2006).
[CrossRef] [PubMed]

F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97, 206806 (2006).
[CrossRef] [PubMed]

P. Berini and J. Lu, “Curved long-range surface plasmon-polariton waveguides,” Opt. Express 14, 2365–2371 (2006).
[CrossRef] [PubMed]

2005

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef] [PubMed]

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

2004

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

2000

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

1997

1994

1980

1972

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

1969

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[CrossRef]

Aizpurua, J.

M. Pelton, J. Aizpurua, and G. Bryant, “Metal-nanoparticle plasmonics,” Laser Photonics Rev. 2, 136–159 (2008).
[CrossRef]

Aussenegg, F. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Beermann, J.

T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, “Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration,” Phys. Rev. B 77, 115420 (2008).
[CrossRef]

Berini, P.

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Boltasseva, A.

T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, “Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration,” Phys. Rev. B 77, 115420 (2008).
[CrossRef]

Bozhevolnyi, S.

T. Søndergaard and S. Bozhevolnyi, “Slow-plasmon resonant nanostructures: Scattering and field enhancement,” Phys. Rev. B 75, 073402 (2007).
[CrossRef]

Bozhevolnyi, S. I.

G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “High-Q plasmonic resonators based on metal split nanocylinders,” Phys. Rev. B 80, 235405 (2009).
[CrossRef]

G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “Efficient suppression of radiation damping in resonant retardation-based plasmonic structures,” Phys. Rev. B 79, 113410 (2009).
[CrossRef]

G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “Plasmon-polariton nano-strip resonators: from visible to infra-red,” Opt. Express 16, 6867–6876 (2008).
[CrossRef] [PubMed]

T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, “Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration,” Phys. Rev. B 77, 115420 (2008).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi B 245, 9–19 (2008).
[CrossRef]

S. I. Bozhevolnyi and T. Søndergaard, “General properties of slow-plasmon resonant nanostructures: nano-antennas and resonators,” Opt. Express 15, 10869–10877 (2007).
[CrossRef] [PubMed]

Bryant, G.

M. Pelton, J. Aizpurua, and G. Bryant, “Metal-nanoparticle plasmonics,” Laser Photonics Rev. 2, 136–159 (2008).
[CrossRef]

Busch, K.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

Chew, H.

Christy, R. W.

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

Dasari, R. R.

Dineen, C.

Y. Zeng, C. Dineen, and J. V. Moloney, “Magnetic dipole moments in single and coupled split-ring resonators,” Phys. Rev. B 81, 075116 (2010).
[CrossRef]

Ditlbacher, H.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Dorfmüller, J.

J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry–Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. 9, 2372–2377 (2009).
[CrossRef] [PubMed]

Economou, E. N.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[CrossRef]

Eisler, H. -J.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef] [PubMed]

Enkrich, C.

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

Etrich, C.

J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry–Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. 9, 2372–2377 (2009).
[CrossRef] [PubMed]

C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14, 8827–8836 (2006).
[CrossRef] [PubMed]

Feigenbaum, E.

E. Feigenbaum and M. Orenstein, “Ultrasmall volume plasmons, yet with complete retardation effects,” Phys. Rev. Lett. 101, 163902 (2008).
[CrossRef] [PubMed]

Feth, N.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

Fu, L.

H. Guo, N. Liu, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, “Thickness dependence of the optical properties of split-ring resonator metamaterials,” Phys. Status Solidi B 244, 1256–1261 (2007).
[CrossRef]

Giessen, H.

H. Guo, N. Liu, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, “Thickness dependence of the optical properties of split-ring resonator metamaterials,” Phys. Status Solidi B 244, 1256–1261 (2007).
[CrossRef]

C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14, 8827–8836 (2006).
[CrossRef] [PubMed]

Guo, H.

H. Guo, N. Liu, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, “Thickness dependence of the optical properties of split-ring resonator metamaterials,” Phys. Status Solidi B 244, 1256–1261 (2007).
[CrossRef]

Hecht, B.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef] [PubMed]

Hofer, F.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Hohenau, A.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Husnik, M.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, 1962).

Johnson, P. B.

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

Jung, J.

J. Jung and T. Søndergaard, “Gap plasmon-polariton nanoresonators: Scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B 79, 035401 (2009).
[CrossRef]

Kaiser, S.

H. Guo, N. Liu, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, “Thickness dependence of the optical properties of split-ring resonator metamaterials,” Phys. Status Solidi B 244, 1256–1261 (2007).
[CrossRef]

Kerker, M.

Kern, K.

J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry–Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. 9, 2372–2377 (2009).
[CrossRef] [PubMed]

Klein, M. W.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

Kneipp, K.

Kobayashi, T.

König, M.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

Koschny, T.

J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic and electric excitations in split ring resonators,” Opt. Express 15, 17881–17890 (2007).
[CrossRef] [PubMed]

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

Kreibig, U.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Krenn, J. R.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Kuhl, J.

Kurokawa, Y.

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96, 097401 (2006).
[CrossRef] [PubMed]

Lederer, F.

J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry–Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. 9, 2372–2377 (2009).
[CrossRef] [PubMed]

C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14, 8827–8836 (2006).
[CrossRef] [PubMed]

Linden, S.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

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

Liu, N.

H. Guo, N. Liu, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, “Thickness dependence of the optical properties of split-ring resonator metamaterials,” Phys. Status Solidi B 244, 1256–1261 (2007).
[CrossRef]

Liu, S. D.

Lu, J.

Maier, S. A.

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

Martin, O. J. F.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef] [PubMed]

Miyazaki, H. T.

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96, 097401 (2006).
[CrossRef] [PubMed]

Moloney, J. V.

Y. Zeng, C. Dineen, and J. V. Moloney, “Magnetic dipole moments in single and coupled split-ring resonators,” Phys. Rev. B 81, 075116 (2010).
[CrossRef]

Morimoto, A.

Mühlschlegel, P.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef] [PubMed]

Nemat-Nasser, S. C.

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

Niegemann, J.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

Novotny, L.

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

Orenstein, M.

E. Feigenbaum and M. Orenstein, “Ultrasmall volume plasmons, yet with complete retardation effects,” Phys. Rev. Lett. 101, 163902 (2008).
[CrossRef] [PubMed]

Padilla, W. J.

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

Pelton, M.

M. Pelton, J. Aizpurua, and G. Bryant, “Metal-nanoparticle plasmonics,” Laser Photonics Rev. 2, 136–159 (2008).
[CrossRef]

Pertsch, T.

J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry–Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. 9, 2372–2377 (2009).
[CrossRef] [PubMed]

Pohl, D. W.

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef] [PubMed]

Rockstuhl, C.

J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry–Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. 9, 2372–2377 (2009).
[CrossRef] [PubMed]

C. Rockstuhl, F. Lederer, C. Etrich, T. Zentgraf, J. Kuhl, and H. Giessen, “On the reinterpretation of resonances in split-ring-resonators at normal incidence,” Opt. Express 14, 8827–8836 (2006).
[CrossRef] [PubMed]

Rogers, M.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Sarychev, A. K.

A. K. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B 75, 085436 (2007).
[CrossRef]

Schweizer, H.

H. Guo, N. Liu, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, “Thickness dependence of the optical properties of split-ring resonator metamaterials,” Phys. Status Solidi B 244, 1256–1261 (2007).
[CrossRef]

Shen, Y. R.

F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97, 206806 (2006).
[CrossRef] [PubMed]

Shultz, S.

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

Smith, D. R.

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

Søndergaard, T.

J. Jung and T. Søndergaard, “Gap plasmon-polariton nanoresonators: Scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B 79, 035401 (2009).
[CrossRef]

G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “Efficient suppression of radiation damping in resonant retardation-based plasmonic structures,” Phys. Rev. B 79, 113410 (2009).
[CrossRef]

G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “High-Q plasmonic resonators based on metal split nanocylinders,” Phys. Rev. B 80, 235405 (2009).
[CrossRef]

G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “Plasmon-polariton nano-strip resonators: from visible to infra-red,” Opt. Express 16, 6867–6876 (2008).
[CrossRef] [PubMed]

T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, “Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration,” Phys. Rev. B 77, 115420 (2008).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi B 245, 9–19 (2008).
[CrossRef]

S. I. Bozhevolnyi and T. Søndergaard, “General properties of slow-plasmon resonant nanostructures: nano-antennas and resonators,” Opt. Express 15, 10869–10877 (2007).
[CrossRef] [PubMed]

T. Søndergaard and S. Bozhevolnyi, “Slow-plasmon resonant nanostructures: Scattering and field enhancement,” Phys. Rev. B 75, 073402 (2007).
[CrossRef]

Soukoulis, C. M.

J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic and electric excitations in split ring resonators,” Opt. Express 15, 17881–17890 (2007).
[CrossRef] [PubMed]

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

Takahara, J.

Taki, H.

Tartakovsky, G.

A. K. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B 75, 085436 (2007).
[CrossRef]

Valle, G. D.

G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “Efficient suppression of radiation damping in resonant retardation-based plasmonic structures,” Phys. Rev. B 79, 113410 (2009).
[CrossRef]

G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “High-Q plasmonic resonators based on metal split nanocylinders,” Phys. Rev. B 80, 235405 (2009).
[CrossRef]

G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “Plasmon-polariton nano-strip resonators: from visible to infra-red,” Opt. Express 16, 6867–6876 (2008).
[CrossRef] [PubMed]

Vier, D. C.

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

Vogelgesang, R.

J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry–Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. 9, 2372–2377 (2009).
[CrossRef] [PubMed]

Wagner, D.

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Wang, D. S.

Wang, F.

F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97, 206806 (2006).
[CrossRef] [PubMed]

Wang, Q. Q.

Wang, Y.

Wegener, M.

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

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

Weitz, R. T.

J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry–Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. 9, 2372–2377 (2009).
[CrossRef] [PubMed]

Yamagishi, S.

Zeng, Y.

Y. Zeng, C. Dineen, and J. V. Moloney, “Magnetic dipole moments in single and coupled split-ring resonators,” Phys. Rev. B 81, 075116 (2010).
[CrossRef]

Zentgraf, T.

Zhang, Z. S.

Zhou, J.

J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic and electric excitations in split ring resonators,” Opt. Express 15, 17881–17890 (2007).
[CrossRef] [PubMed]

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

Appl. Opt.

Appl. Spectrosc.

Laser Photonics Rev.

M. Pelton, J. Aizpurua, and G. Bryant, “Metal-nanoparticle plasmonics,” Laser Photonics Rev. 2, 136–159 (2008).
[CrossRef]

Nano Lett.

J. Dorfmüller, R. Vogelgesang, R. T. Weitz, C. Rockstuhl, C. Etrich, T. Pertsch, F. Lederer, and K. Kern, “Fabry–Pérot resonances in one-dimensional plasmonic nanostructures,” Nano Lett. 9, 2372–2377 (2009).
[CrossRef] [PubMed]

Nat. Photonics

M. Husnik, M. W. Klein, N. Feth, M. König, J. Niegemann, K. Busch, S. Linden, and M. Wegener, “Absolute extinction cross-section of individual magnetic split-ring resonators,” Nat. Photonics 2, 614–617 (2008).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev.

E. N. Economou, “Surface plasmons in thin films,” Phys. Rev. 182, 539–554 (1969).
[CrossRef]

Phys. Rev. B

T. Søndergaard and S. Bozhevolnyi, “Slow-plasmon resonant nanostructures: Scattering and field enhancement,” Phys. Rev. B 75, 073402 (2007).
[CrossRef]

T. Søndergaard, J. Beermann, A. Boltasseva, and S. I. Bozhevolnyi, “Slow-plasmon resonant-nanostrip antennas: Analysis and demonstration,” Phys. Rev. B 77, 115420 (2008).
[CrossRef]

J. Jung and T. Søndergaard, “Gap plasmon-polariton nanoresonators: Scattering enhancement and launching of surface plasmon polaritons,” Phys. Rev. B 79, 035401 (2009).
[CrossRef]

Y. Zeng, C. Dineen, and J. V. Moloney, “Magnetic dipole moments in single and coupled split-ring resonators,” Phys. Rev. B 81, 075116 (2010).
[CrossRef]

A. K. Sarychev and G. Tartakovsky, “Magnetic plasmonic metamaterials in actively pumped host medium and plasmonic nanolaser,” Phys. Rev. B 75, 085436 (2007).
[CrossRef]

G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “Efficient suppression of radiation damping in resonant retardation-based plasmonic structures,” Phys. Rev. B 79, 113410 (2009).
[CrossRef]

G. D. Valle, T. Søndergaard, and S. I. Bozhevolnyi, “High-Q plasmonic resonators based on metal split nanocylinders,” Phys. Rev. B 80, 235405 (2009).
[CrossRef]

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

Phys. Rev. Lett.

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

F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanostructures,” Phys. Rev. Lett. 97, 206806 (2006).
[CrossRef] [PubMed]

E. Feigenbaum and M. Orenstein, “Ultrasmall volume plasmons, yet with complete retardation effects,” Phys. Rev. Lett. 101, 163902 (2008).
[CrossRef] [PubMed]

H. T. Miyazaki and Y. Kurokawa, “Squeezing visible light waves into a 3-nm-thick and 55-nm-long plasmon cavity,” Phys. Rev. Lett. 96, 097401 (2006).
[CrossRef] [PubMed]

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

H. Ditlbacher, A. Hohenau, D. Wagner, U. Kreibig, M. Rogers, F. Hofer, F. R. Aussenegg, and J. R. Krenn, “Silver nanowires as surface plasmon resonators,” Phys. Rev. Lett. 95, 257403 (2005).
[CrossRef] [PubMed]

Phys. Status Solidi B

H. Guo, N. Liu, L. Fu, H. Schweizer, S. Kaiser, and H. Giessen, “Thickness dependence of the optical properties of split-ring resonator metamaterials,” Phys. Status Solidi B 244, 1256–1261 (2007).
[CrossRef]

T. Søndergaard and S. I. Bozhevolnyi, “Strip and gap plasmon polariton optical resonators,” Phys. Status Solidi B 245, 9–19 (2008).
[CrossRef]

Science

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

P. Mühlschlegel, H.-J. Eisler, O. J. F. Martin, B. Hecht, and D. W. Pohl, “Resonant optical antennas,” Science 308, 1607–1609 (2005).
[CrossRef] [PubMed]

Other

J. D. Jackson, Classical Electrodynamics (Wiley, 1962).

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).

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Figures (9)

Fig. 1
Fig. 1

(a) Schematic of the modeled straight nanorod with length L, width w, and height h = 50   nm . (b) Bending of the straight nanorod with bending radius a. (c) With regular bending the length of the nanorod is kept constant, while the length is slightly increased with gap terminations making the end facets parallel (definition of split-ring resonator).

Fig. 2
Fig. 2

Effective scattering and absorption cross section (optical cross section divided by the geometrical cross section L × w ) for different dimensions of the straight nanorod and polarizations of the incoming wave (captions are more thoroughly explained in the text).

Fig. 3
Fig. 3

(a) The FE distribution and center line enhancement at resonance for nanorod L × w = 300   nm × 50   nm (first and third modes), (b) L × w = 709   nm × 50   nm (second mode), (c) two nanorods of L × w = 150   nm × 50   nm separated by a gap of 10 nm (first mode). FE close to the corners of the nanorod exceeds the scale bars, and these areas are indicated by a black color.

Fig. 4
Fig. 4

Radiation patterns in the x z -plane under resonant excitation of the first mode for nanorod L × w = 300   nm × 50   nm (solid black curve), second mode of L × w = 709   nm × 50   nm (dotted red curve), and first mode for two nanorods of L × w = 150   nm × 50   nm separated by a gap of 10 nm (dashed-dotted green curve). Angles are in degrees.

Fig. 5
Fig. 5

Effective scattering and absorption cross section for a nanorod of L × w = 300   nm × 50   nm with different bending radii a excited with a z-propagating x-polarized wave. Legends with specific gap-sizes correspond to split-ring resonator structures [Fig. 1c, gap terminations]. The inset drawings schematically show the plasmonic currents (arrows indicate current direction) for the two modes and the polarization of the incident E-field.

Fig. 6
Fig. 6

Effective scattering and absorption cross section for a nanorod of L × w = 300   nm × 50   nm with different bending radii a excited with a z-propagating y-polarized wave. For further details, see caption of Fig. 5.

Fig. 7
Fig. 7

Radiation patterns for three different radii of nanorod L × w = 300   nm × 50   nm . (a) Radiation patterns in x z -plane under resonant excitation of the first mode (x-polarized incident field). Dark yellow short-dashed curve is multiplied by a factor of 40. The inset shows a close-up of the center of the radiation patterns. (b) Radiation patterns in the y z -plane at resonance of the second mode (y-polarized incident field). Angles are in degrees.

Fig. 8
Fig. 8

(a) The distribution of the FE for split-ring resonator with a = 51   nm and gap of 10 nm for the first mode at resonance, (b) second mode at resonance, (c) third mode at resonance. The polarization vector is indicated by arrows. Black areas are positions where the enhancement exceeds the scale bars. (d) FE along the centerline (red dashed circle in inset drawing) as a function of angle for the three modes.

Fig. 9
Fig. 9

The Q-factor and FE as functions of the bending radii a for regular bending of the nanorod with L × w = 300   nm × 50   nm . The triangles connected by a dotted line correspond to Q-factor Q s t for nanostructures in the quasi-static limit calculated for resonance wavelengths of the first mode [Eq. (2)].

Equations (2)

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L 2 π λ n SR-SPP = m π ϕ ,
Q s t = λ 2 ε m d ε m d λ ,

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