Abstract

Metamaterials acquire their functionality from the structuring of the small building blocks, “artificial atoms”. Our paper provides a study of the resonant behaviour for a variety of metallic nanoparticles in the region of hundreds of THz. Resonant modes for nanorods of rectangular cross section are investigated numerically for different types of excitation and the set of resonant frequencies (fundamental and higher order) are determined for rods of various length. From that the dispersion relationship for surface plasmon-polaritons propagating along the rod is deduced. We analyse resonant-mode near-field distribution of the electric field, including the field lines, to emphasise the underlying physics. Resonant frequencies are also found and field distributions analysed when the rods are combined to form particles of L, U and O shapes. The similarities and differences between those particles, both in the values and in the number of resonances, are discussed. The results of this study may aid the design of nanostructured metamaterials with required properties in the IR and optical domain.

© 2009 Optical Society of America

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    [CrossRef]

2008 (2)

2007 (4)

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

K. Busch, G von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007).
[CrossRef]

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

S. Tretyakov, "On geometrical scaling of split-ring and double bar resonators at optical frequencies," Metamaterials 1, 40-43 (2007).
[CrossRef]

2006 (1)

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

2005 (9)

A. Ishikawa, T. Tanaka, and S. Kawata, "Negative magnetic permeability in the visible light region," Phys. Rev. Lett. 95, 273401-273404 (2005).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring-resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223905 (2005).
[CrossRef] [PubMed]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, and E. N. Economou, "Experimental demonstration of negative magnetic permeability in the far infrared frequency region," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, "Characterization of long-range surface-plasmon-polariton waveguides," J. Appl. Phys. 98, 043109-043120 (2005).
[CrossRef]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137407 (2005).
[CrossRef] [PubMed]

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, 32-37 (2005).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95. 203901-203904 (2005).
[CrossRef] [PubMed]

J. S. Shumaker-Parry, H. Rochholz, and M. Kreiter, "Fabrication of crescent-shaped optical antennas," Adv. Mater. 17, 2131-2134 (2005).
[CrossRef]

2004 (2)

S. J. Al-Bader, "Optical transmission on metallic wires-fundamental modes," IEEE J. Quantum Electron. 28, 325-329 (2004).
[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]

2003 (1)

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, amd F. J. García de Abajo, "Optical Properties of Gold Nanorings," Phys. Rev. Lett. 90, 057401-057404 (2003).
[CrossRef] [PubMed]

2002 (2)

V. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, "Optomagnetic composite medium with conducting nanoelements," Phys. Rev. B 66, 155411-155427 (2002).
[CrossRef]

2001 (2)

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, "Imaging, compression and Poynting vector streamlines with negative permittivity materials," Electron. Lett. 37, 1243-1244 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Non-regularly shaped plasmon resonant nanoparticle as localised light source for near-field microscopy," J. Microscopy 202, 60-65 (2001).
[CrossRef]

2000 (2)

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

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Field polarization and polarization charge distributions in plasmon resonant nanoparticles," New J. Phys. 2, 271-279 (2000).
[CrossRef]

1999 (1)

1981 (1)

D. Sarid, "Long range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

1972 (1)

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

1969 (1)

E. N. Economou, "Surface plasmas in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

1962 (1)

A. A. Oliner and T. Tamir, "Backward waves on isotropic plasma slabs," J. Appl. Phys. 33, 231-233 (1962).
[CrossRef]

1950 (1)

W. O. Schumann, "Ausbreitung elektrischer Wellen langs geschichteter und langs kontinuierlich veranderlicher Plasmen, " Z. Naturforsch. A 5, 612-617 (1950).

1941 (1)

1899 (1)

A. Sommerfeld, "Uber die Fortpflanzung elektrodynamischer Wellen langs eines Drahtes," Ann. Phys. Chem. 303, 233-290 (1899).
[CrossRef]

Aizpurua, J.

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, amd F. J. García de Abajo, "Optical Properties of Gold Nanorings," Phys. Rev. Lett. 90, 057401-057404 (2003).
[CrossRef] [PubMed]

Al-Bader, S. J.

S. J. Al-Bader, "Optical transmission on metallic wires-fundamental modes," IEEE J. Quantum Electron. 28, 325-329 (2004).
[CrossRef]

Berini, P.

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, "Characterization of long-range surface-plasmon-polariton waveguides," J. Appl. Phys. 98, 043109-043120 (2005).
[CrossRef]

P. Berini, "Plasmon-polariton modes guided by a metal film of finite width," Opt. Lett. 24, 1011-1013 (1999).
[CrossRef]

Boltasseva, A.

A. Boltasseva and V. M. Shalaev, "Fabrication of optical negative-index metamaterials: Recent advances and outlook," Metamaterials 2, 1-17 (2008).
[CrossRef]

Brueck, S. R. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137407 (2005).
[CrossRef] [PubMed]

Bryant, G. W.

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, amd F. J. García de Abajo, "Optical Properties of Gold Nanorings," Phys. Rev. Lett. 90, 057401-057404 (2003).
[CrossRef] [PubMed]

Burger, S.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95. 203901-203904 (2005).
[CrossRef] [PubMed]

Busch, K.

K. Busch, G von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007).
[CrossRef]

Cai, W.

Charbonneau, R.

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, "Characterization of long-range surface-plasmon-polariton waveguides," J. Appl. Phys. 98, 043109-043120 (2005).
[CrossRef]

Chettiar, U. K.

Christy, R. W.

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

Dolling, G.

Drachev, V. P.

Economou, E. N.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, and E. N. Economou, "Experimental demonstration of negative magnetic permeability in the far infrared frequency region," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring-resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223905 (2005).
[CrossRef] [PubMed]

E. N. Economou, "Surface plasmas in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Enkrich, C.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95. 203901-203904 (2005).
[CrossRef] [PubMed]

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

Etrich, C.

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

Fan, W.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137407 (2005).
[CrossRef] [PubMed]

Fano, U.

Garcia-Pomar, J. L.

Giessen, H.

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

Grigorenko, A. N.

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, "Optomagnetic composite medium with conducting nanoelements," Phys. Rev. B 66, 155411-155427 (2002).
[CrossRef]

Gundogdu, T. F.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, and E. N. Economou, "Experimental demonstration of negative magnetic permeability in the far infrared frequency region," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

Guo, H.

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

Hanarp, P.

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, amd F. J. García de Abajo, "Optical Properties of Gold Nanorings," Phys. Rev. Lett. 90, 057401-057404 (2003).
[CrossRef] [PubMed]

Ishikawa, A.

A. Ishikawa, T. Tanaka, and S. Kawata, "Negative magnetic permeability in the visible light region," Phys. Rev. Lett. 95, 273401-273404 (2005).
[CrossRef]

Johnson, P. B.

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

Kafesaki, M.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, and E. N. Economou, "Experimental demonstration of negative magnetic permeability in the far infrared frequency region," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring-resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223905 (2005).
[CrossRef] [PubMed]

Kalinin, V. A.

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, "Imaging, compression and Poynting vector streamlines with negative permittivity materials," Electron. Lett. 37, 1243-1244 (2001).
[CrossRef]

Käll, M.

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, amd F. J. García de Abajo, "Optical Properties of Gold Nanorings," Phys. Rev. Lett. 90, 057401-057404 (2003).
[CrossRef] [PubMed]

Kawata, S.

A. Ishikawa, T. Tanaka, and S. Kawata, "Negative magnetic permeability in the visible light region," Phys. Rev. Lett. 95, 273401-273404 (2005).
[CrossRef]

Kildishev, A. V.

Koschny, T.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, and E. N. Economou, "Experimental demonstration of negative magnetic permeability in the far infrared frequency region," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95. 203901-203904 (2005).
[CrossRef] [PubMed]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring-resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223905 (2005).
[CrossRef] [PubMed]

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

Kottmann, J. P.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Non-regularly shaped plasmon resonant nanoparticle as localised light source for near-field microscopy," J. Microscopy 202, 60-65 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Field polarization and polarization charge distributions in plasmon resonant nanoparticles," New J. Phys. 2, 271-279 (2000).
[CrossRef]

Kreiter, M.

J. S. Shumaker-Parry, H. Rochholz, and M. Kreiter, "Fabrication of crescent-shaped optical antennas," Adv. Mater. 17, 2131-2134 (2005).
[CrossRef]

Kuhl, J.

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

Lahoud, N.

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, "Characterization of long-range surface-plasmon-polariton waveguides," J. Appl. Phys. 98, 043109-043120 (2005).
[CrossRef]

Lederer, F.

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

Linden, S.

M. Wegener, J. L. Garcia-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, and S. Linden, "Toy model for plasmonic metamaterial resonances coupled to two-level system gain," Opt. Express 16, 19785-19798 (2008).
[CrossRef] [PubMed]

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

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95. 203901-203904 (2005).
[CrossRef] [PubMed]

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

Liu, N.

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

Loa, I.

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

Makhnovskiy, D. P.

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, "Optomagnetic composite medium with conducting nanoelements," Phys. Rev. B 66, 155411-155427 (2002).
[CrossRef]

Malloy, K. J.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137407 (2005).
[CrossRef] [PubMed]

Martin, O. J. F.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Non-regularly shaped plasmon resonant nanoparticle as localised light source for near-field microscopy," J. Microscopy 202, 60-65 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Field polarization and polarization charge distributions in plasmon resonant nanoparticles," New J. Phys. 2, 271-279 (2000).
[CrossRef]

Mattiussi, G.

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, "Characterization of long-range surface-plasmon-polariton waveguides," J. Appl. Phys. 98, 043109-043120 (2005).
[CrossRef]

Meinzer, N.

Narimanov, E. E.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, 32-37 (2005).
[CrossRef]

Oliner, A. A.

A. A. Oliner and T. Tamir, "Backward waves on isotropic plasma slabs," J. Appl. Phys. 33, 231-233 (1962).
[CrossRef]

Osgood, R. M.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137407 (2005).
[CrossRef] [PubMed]

Panina, L. V.

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, "Optomagnetic composite medium with conducting nanoelements," Phys. Rev. B 66, 155411-155427 (2002).
[CrossRef]

Panoiu, N. C.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137407 (2005).
[CrossRef] [PubMed]

Penciu, R. S.

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, and E. N. Economou, "Experimental demonstration of negative magnetic permeability in the far infrared frequency region," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

Pendry, J. B.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring-resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223905 (2005).
[CrossRef] [PubMed]

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

Podolskiy, V.

V. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

Podolskiy, V. A.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, 32-37 (2005).
[CrossRef]

Ringhofer, K. H.

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, "Imaging, compression and Poynting vector streamlines with negative permittivity materials," Electron. Lett. 37, 1243-1244 (2001).
[CrossRef]

Rochholz, H.

J. S. Shumaker-Parry, H. Rochholz, and M. Kreiter, "Fabrication of crescent-shaped optical antennas," Adv. Mater. 17, 2131-2134 (2005).
[CrossRef]

Rockstuhl, C.

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

Ruther, M.

Sarid, D.

D. Sarid, "Long range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

Sarychev, A. K.

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, 32-37 (2005).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

V. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

Schmidt, F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95. 203901-203904 (2005).
[CrossRef] [PubMed]

Schultz, S.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Non-regularly shaped plasmon resonant nanoparticle as localised light source for near-field microscopy," J. Microscopy 202, 60-65 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Field polarization and polarization charge distributions in plasmon resonant nanoparticles," New J. Phys. 2, 271-279 (2000).
[CrossRef]

Schumann, W. O.

W. O. Schumann, "Ausbreitung elektrischer Wellen langs geschichteter und langs kontinuierlich veranderlicher Plasmen, " Z. Naturforsch. A 5, 612-617 (1950).

Shalaev, V. M.

A. Boltasseva and V. M. Shalaev, "Fabrication of optical negative-index metamaterials: Recent advances and outlook," Metamaterials 2, 1-17 (2008).
[CrossRef]

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

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, 32-37 (2005).
[CrossRef]

V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P. Drachev, and A. V. Kildishev, "Negative index of refraction in optical metamaterials," Opt. Lett. 30, 3356-3358 (2005).
[CrossRef]

V. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

Shamonina, E.

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, "Imaging, compression and Poynting vector streamlines with negative permittivity materials," Electron. Lett. 37, 1243-1244 (2001).
[CrossRef]

Shumaker-Parry, J. S.

J. S. Shumaker-Parry, H. Rochholz, and M. Kreiter, "Fabrication of crescent-shaped optical antennas," Adv. Mater. 17, 2131-2134 (2005).
[CrossRef]

Smith, D. R.

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Non-regularly shaped plasmon resonant nanoparticle as localised light source for near-field microscopy," J. Microscopy 202, 60-65 (2001).
[CrossRef]

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Field polarization and polarization charge distributions in plasmon resonant nanoparticles," New J. Phys. 2, 271-279 (2000).
[CrossRef]

Solymar, L.

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, "Imaging, compression and Poynting vector streamlines with negative permittivity materials," Electron. Lett. 37, 1243-1244 (2001).
[CrossRef]

Sommerfeld, A.

A. Sommerfeld, "Uber die Fortpflanzung elektrodynamischer Wellen langs eines Drahtes," Ann. Phys. Chem. 303, 233-290 (1899).
[CrossRef]

Soukoulis, C. M.

M. Wegener, J. L. Garcia-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, and S. Linden, "Toy model for plasmonic metamaterial resonances coupled to two-level system gain," Opt. Express 16, 19785-19798 (2008).
[CrossRef] [PubMed]

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

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring-resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223905 (2005).
[CrossRef] [PubMed]

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95. 203901-203904 (2005).
[CrossRef] [PubMed]

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

Sutherland, D. S.

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, amd F. J. García de Abajo, "Optical Properties of Gold Nanorings," Phys. Rev. Lett. 90, 057401-057404 (2003).
[CrossRef] [PubMed]

Szassen, K.

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

Tamir, T.

A. A. Oliner and T. Tamir, "Backward waves on isotropic plasma slabs," J. Appl. Phys. 33, 231-233 (1962).
[CrossRef]

Tanaka, T.

A. Ishikawa, T. Tanaka, and S. Kawata, "Negative magnetic permeability in the visible light region," Phys. Rev. Lett. 95, 273401-273404 (2005).
[CrossRef]

Tretyakov, S.

S. Tretyakov, "On geometrical scaling of split-ring and double bar resonators at optical frequencies," Metamaterials 1, 40-43 (2007).
[CrossRef]

Wegener, M.

M. Wegener, J. L. Garcia-Pomar, C. M. Soukoulis, N. Meinzer, M. Ruther, and S. Linden, "Toy model for plasmonic metamaterial resonances coupled to two-level system gain," Opt. Express 16, 19785-19798 (2008).
[CrossRef] [PubMed]

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

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95. 203901-203904 (2005).
[CrossRef] [PubMed]

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

Yuan, H.-K.

Zentgraf, T.

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

Zhang, S.

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137407 (2005).
[CrossRef] [PubMed]

Zhou, J.

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring-resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223905 (2005).
[CrossRef] [PubMed]

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

Zhou, J. F.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95. 203901-203904 (2005).
[CrossRef] [PubMed]

Zschiedrich, L.

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95. 203901-203904 (2005).
[CrossRef] [PubMed]

Adv. Mater. (1)

J. S. Shumaker-Parry, H. Rochholz, and M. Kreiter, "Fabrication of crescent-shaped optical antennas," Adv. Mater. 17, 2131-2134 (2005).
[CrossRef]

Ann. Phys. Chem. (1)

A. Sommerfeld, "Uber die Fortpflanzung elektrodynamischer Wellen langs eines Drahtes," Ann. Phys. Chem. 303, 233-290 (1899).
[CrossRef]

Appl. Phys. B (1)

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

Electron. Lett. (1)

E. Shamonina, V. A. Kalinin, K. H. Ringhofer, and L. Solymar, "Imaging, compression and Poynting vector streamlines with negative permittivity materials," Electron. Lett. 37, 1243-1244 (2001).
[CrossRef]

IEEE J. Quantum Electron. (1)

S. J. Al-Bader, "Optical transmission on metallic wires-fundamental modes," IEEE J. Quantum Electron. 28, 325-329 (2004).
[CrossRef]

J. Appl. Phys. (2)

A. A. Oliner and T. Tamir, "Backward waves on isotropic plasma slabs," J. Appl. Phys. 33, 231-233 (1962).
[CrossRef]

P. Berini, R. Charbonneau, N. Lahoud, and G. Mattiussi, "Characterization of long-range surface-plasmon-polariton waveguides," J. Appl. Phys. 98, 043109-043120 (2005).
[CrossRef]

J. Microscopy (1)

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Non-regularly shaped plasmon resonant nanoparticle as localised light source for near-field microscopy," J. Microscopy 202, 60-65 (2001).
[CrossRef]

J. Nonlinear Opt. Phys. Mater. (1)

V. Podolskiy, A. K. Sarychev, and V. M. Shalaev, "Plasmon modes in metal nanowires and left-handed materials," J. Nonlinear Opt. Phys. Mater. 11, 65-74 (2002).
[CrossRef]

J. Opt. A: Pure Appl. Opt. (2)

V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, "Resonant light interaction with plasmonic nanowire systems," J. Opt. A: Pure Appl. Opt. 7, 32-37 (2005).
[CrossRef]

M. Kafesaki, T. Koschny, R. S. Penciu, T. F. Gundogdu, and E. N. Economou, "Experimental demonstration of negative magnetic permeability in the far infrared frequency region," J. Opt. A: Pure Appl. Opt. 7, S12-S22 (2005).
[CrossRef]

J. Opt. Soc. Am. (1)

Metamaterials (2)

A. Boltasseva and V. M. Shalaev, "Fabrication of optical negative-index metamaterials: Recent advances and outlook," Metamaterials 2, 1-17 (2008).
[CrossRef]

S. Tretyakov, "On geometrical scaling of split-ring and double bar resonators at optical frequencies," Metamaterials 1, 40-43 (2007).
[CrossRef]

Nature Photonics (1)

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

New J. Phys. (1)

J. P. Kottmann, O. J. F. Martin, D. R. Smith, and S. Schultz, "Field polarization and polarization charge distributions in plasmon resonant nanoparticles," New J. Phys. 2, 271-279 (2000).
[CrossRef]

Opt. Express (1)

Opt. Lett. (3)

Phys Rev. B (1)

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

Phys. Rep. (1)

K. Busch, G von Freymann, S. Linden, S. F. Mingaleev, L. Tkeshelashvili, and M. Wegener, "Periodic nanostructures for photonics," Phys. Rep. 444, 101-202 (2007).
[CrossRef]

Phys. Rev. (1)

E. N. Economou, "Surface plasmas in thin films," Phys. Rev. 182, 539-554 (1969).
[CrossRef]

Phys. Rev. B (1)

L. V. Panina, A. N. Grigorenko, and D. P. Makhnovskiy, "Optomagnetic composite medium with conducting nanoelements," Phys. Rev. B 66, 155411-155427 (2002).
[CrossRef]

Phys. Rev. Lett. (7)

C. Enkrich, M. Wegener, S. Linden, S. Burger, L. Zschiedrich, F. Schmidt, J. F. Zhou, T. Koschny, and C. M. Soukoulis, "Magnetic metamaterials at telecommunication and visible frequencies," Phys. Rev. Lett. 95. 203901-203904 (2005).
[CrossRef] [PubMed]

J. Aizpurua, P. Hanarp, D. S. Sutherland, M. Käll, G. W. Bryant, amd F. J. García de Abajo, "Optical Properties of Gold Nanorings," Phys. Rev. Lett. 90, 057401-057404 (2003).
[CrossRef] [PubMed]

D. Sarid, "Long range surface-plasma waves on very thin metal films," Phys. Rev. Lett. 47, 1927-1930 (1981).
[CrossRef]

S. Zhang, W. Fan, N. C. Panoiu, K. J. Malloy, R. M. Osgood, and S. R. J. Brueck, "Experimental demonstration of near-infrared negative-index metamaterials," Phys. Rev. Lett. 95, 137404-137407 (2005).
[CrossRef] [PubMed]

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

A. Ishikawa, T. Tanaka, and S. Kawata, "Negative magnetic permeability in the visible light region," Phys. Rev. Lett. 95, 273401-273404 (2005).
[CrossRef]

J. Zhou, T. Koschny, M. Kafesaki, E. N. Economou, J. B. Pendry, and C. M. Soukoulis, "Saturation of the magnetic response of split-ring-resonators at optical frequencies," Phys. Rev. Lett. 95, 223902-223905 (2005).
[CrossRef] [PubMed]

Science (1)

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]

Z. Naturforsch. A (1)

W. O. Schumann, "Ausbreitung elektrischer Wellen langs geschichteter und langs kontinuierlich veranderlicher Plasmen, " Z. Naturforsch. A 5, 612-617 (1950).

Other (2)

R. Marques and M. Freire, "On the usefulness of split ring resonators for magnetic metamaterial design at infrared and optical frequencies," IEEE MELECON, Benaldamena (Malaga), Spain, 222-224 (2005).

H. Jasik, ed., Antenna Engineering Handbook (McGraw-Hill, 1961).

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Figures (19)

Fig. 1.
Fig. 1.

Schematic representation of the studied nanorod. The y component of the electric field measured 4 nm above the top of the rod on the rod axis (red arrow) is used in the plot of the resonance curve.

Fig. 2.
Fig. 2.

Resonance curve of the 150 nm long rod normalized to the amplitude of the incident wave. Inset shows the geometry and the polarization of the excitation.

Fig. 3.
Fig. 3.

Electric field patterns of the nanorod at 220 THz (a), 541 THz (b) and 749 THz (c). Field strength plotted on a logarithmic scale (normalized to the respective field maximum).

Fig. 4.
Fig. 4.

Electric field components (maxima normalized to unity) along the rod at 220 THz. Inset shows a sketch of the electric field in the vicinity of a corner.

Fig. 5.
Fig. 5.

Electric field components (maxima normalized to unity) across the rod at 220 THz.

Fig. 6.
Fig. 6.

Electric field components (maxima normalized to unity) along the rod at 541 THz.

Fig. 7.
Fig. 7.

Electric field components (maxima normalized to unity) along the rod at 749 THz.

Fig. 8.
Fig. 8.

Comparison of the dispersion curves of a metal-air interface (dashed curve), a 10 nm thick metal slab (dashed-dotted curve) and the retrieved dispersion of the 10 nm × 10 nm thick rod (open circles). Solid curve is the light line.

Fig. 9.
Fig. 9.

Resonant length of the rod at its lowest resonance.

Fig. 10.
Fig. 10.

Schematic representation of the L, U and O particles. The y component of the electric field measured 4 nm above the left vertical rod on its axis (red arrow) is used in the plot of the resonance curves.

Fig. 11.
Fig. 11.

Resonance curve of the 150 nm long L particle normalized to the amplitude of the incident wave. Inset shows the geometry and the polarization of the excitation.

Fig. 12.
Fig. 12.

Electric field patterns of the L particle at 226 THz (a), 406 THz (b) and 545 THz (c). Field strength plotted on a logarithmic scale (normalized to the respective field maximum).

Fig. 13.
Fig. 13.

Resonance curve of the 220 nm long U particle normalized to the amplitude of the incident wave. Inset shows the geometry and the polarization of the excitation.

Fig. 14.
Fig. 14.

Electric field patterns of the U particle at 162 THz (a), 308 THz (b) and 418 THz (c). Field strength plotted on a logarithmic scale (normalized to the respective field maximum).

Fig. 15.
Fig. 15.

Resonance curve of the U particle normalized to the amplitude of the incident wave. Inset shows the geometry and the polarization of the excitation.

Fig. 16.
Fig. 16.

Resonance curve of the U particle normalized to the amplitude of the incident wave. Inset shows the geometry and the polarization of the excitation.

Fig. 17.
Fig. 17.

Resonance curve of the U particle normalized to the amplitude of the incident wave. Inset shows the geometry and the polarization of the excitation.

Fig. 18.
Fig. 18.

Resonance curves of the 280 nm long O particle normalized to the amplitude of the incident wave, for two different polarizations of the excitation.

Fig. 19.
Fig. 19.

Electric field patterns of the O particle at 279 THz (a), 463 THz (b) and 601 THz (c). Field strength plotted on a logarithmic scale (normalized to the respective field maximum).

Equations (2)

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εp=ε0[1ωp2ω2iγω],
εairEy,air=εp Ey,p ,

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