Abstract

We systematically investigate the resonant behavior of arrays of Ag nano-structures ranging from isolated simple rods, to U-shapes, to single split ring structures. We show that the lowest order plasmonic resonance associated with a rod red shifts as we create a U and SRR into the position normally associated with a simple LC mode. A second mode red shifts and grows in intensity as we extend the arms of the U-shape, and a third mode appears in the spectra as we close the arms and form a split ring structure. We performed simulations of the structures and examine the E-field and current density. The simulations show that the current path is different for these modes. We examine the behavior of the lowest order mode in detail, discuss the effects of skin depth, and present an improved LC model to describe this resonance.

© 2008 Optical Society of America

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2008 (3)

H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: Design, fabrication and characterization,” Opt. Express 10, 7181–7188 (2008).
[Crossref]

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, and E. N. Economou, “The science of negative index materials,” J. Phys.: Condens. Matter 20, 304217 (2008).
[Crossref]

K. Füchsel, U. Schulz, N. Kaiser, and A. Tünnermann, “Low temperature deposition of indium tin oxide films by plasma ion-assisted evaporation,” Appl. Opt. 47, C297–C302 (2008).

2007 (3)

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamatrerials,” Opt. Lett. 3253–55 (2007).
[Crossref]

T. P. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: Optical frequency resonance circuits,” Phys. Rev. B 75, 205102 (2007).

N. Engheta, “Circuits with light at nanoscales: Optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007).
[Crossref] [PubMed]

2006 (2)

2005 (5)

2004 (3)

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[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]

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). Online supplement: http://www.sciencemag.org/cgi/content/full/sci;306/5700/1351/DC1.
[Crossref] [PubMed]

2003 (1)

J. Ederth, G. A. Niklasson, A. Hultaker, P. Heszler, C. G. Granqvist, A. R. van Doom, M. J. Jongerius, and D. Burgard, “Characterization of porous indium tin oxide films using effective medium theory,” J. Appl. Phys. 93, 984–988 (2003).
[Crossref]

2000 (2)

D. R. Smith, Willie J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Science 84, 4184–4187 (2000).

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

1999 (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

1995 (1)

M. A. Bueno and A. K. T. Assis, “A new method for inductance calculations,” J. Phys. D Appl. Phys. 281802–1806 (1995).
[Crossref]

1983 (1)

Alexander, R. W.

Assis, A. K. T.

M. A. Bueno and A. K. T. Assis, “A new method for inductance calculations,” J. Phys. D Appl. Phys. 281802–1806 (1995).
[Crossref]

M. A. Bueno and A. K. T. Assis, Inductance and force calculations in electrical circuits (Nova Science, 2001).

M. A. Bueno and A. K. T. Assis, Inductance and force calculations in electrical circuits (Nova Science, 2001), p. 24, 30. See http://www.ifi.unicamp.br/~assis/wbooks.htm for correction to eq. 3.2.

M. A Bueno and A. K. T. Assis, Inductance and force calculations in electrical circuits (Nova Science, 2001), p. 40.

Averitt, R. D.

H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: Design, fabrication and characterization,” Opt. Express 10, 7181–7188 (2008).
[Crossref]

Bartal, G.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature Lett. (2008), http://www.nature.com/nature/journal/vaop/ncurrent/abs/nature07247.html.
[Crossref]

Basov, D. N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

Bell, R. J.

Bell, R. R.

Bell, S. E.

Bingham, C. M.

H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: Design, fabrication and characterization,” Opt. Express 10, 7181–7188 (2008).
[Crossref]

Brueck, S. R. J.

Bueno, M. A

M. A Bueno and A. K. T. Assis, Inductance and force calculations in electrical circuits (Nova Science, 2001), p. 40.

Bueno, M. A.

M. A. Bueno and A. K. T. Assis, “A new method for inductance calculations,” J. Phys. D Appl. Phys. 281802–1806 (1995).
[Crossref]

M. A. Bueno and A. K. T. Assis, Inductance and force calculations in electrical circuits (Nova Science, 2001), p. 24, 30. See http://www.ifi.unicamp.br/~assis/wbooks.htm for correction to eq. 3.2.

M. A. Bueno and A. K. T. Assis, Inductance and force calculations in electrical circuits (Nova Science, 2001).

Burgard, D.

J. Ederth, G. A. Niklasson, A. Hultaker, P. Heszler, C. G. Granqvist, A. R. van Doom, M. J. Jongerius, and D. Burgard, “Characterization of porous indium tin oxide films using effective medium theory,” J. Appl. Phys. 93, 984–988 (2003).
[Crossref]

Burger, S.

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

Cai, W.

Chettiar, U. K.

Dolling, G.

Doom, A. R. van

J. Ederth, G. A. Niklasson, A. Hultaker, P. Heszler, C. G. Granqvist, A. R. van Doom, M. J. Jongerius, and D. Burgard, “Characterization of porous indium tin oxide films using effective medium theory,” J. Appl. Phys. 93, 984–988 (2003).
[Crossref]

Drachev, V.

Economou, E. N.

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, and E. N. Economou, “The science of negative index materials,” J. Phys.: Condens. Matter 20, 304217 (2008).
[Crossref]

M. Kafesaki, Th. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, “Left-handed metamaterials: detailed numerical studies of the transmission properties,” J. Opt. A:Pure Appl. Opt. 7, S12–S22 (2005).
[Crossref]

N. Katsarakis, G. Konstantininidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, Th. Koschny, and C. M. Soukoulis, “Magnetic response of split-ring resonators in the farinfrared frequency regime,” Opt. Lett. 30, 1348–1350 (2005).
[Crossref] [PubMed]

Ederth, J.

J. Ederth, G. A. Niklasson, A. Hultaker, P. Heszler, C. G. Granqvist, A. R. van Doom, M. J. Jongerius, and D. Burgard, “Characterization of porous indium tin oxide films using effective medium theory,” J. Appl. Phys. 93, 984–988 (2003).
[Crossref]

Engheta, N.

N. Engheta, “Circuits with light at nanoscales: Optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007).
[Crossref] [PubMed]

Enkrich, C.

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

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Response of Metamaterials at 100 Terahertz,” Science 306, 1351–1353 (2004).
[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). Online supplement: http://www.sciencemag.org/cgi/content/full/sci;306/5700/1351/DC1.
[Crossref] [PubMed]

Etrich, C.

Fan, W.

Fang, N.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

Füchsel, K.

Genov, D. A.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature Lett. (2008), http://www.nature.com/nature/journal/vaop/ncurrent/abs/nature07247.html.
[Crossref]

Giessen, H.

T. P. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: Optical frequency resonance circuits,” Phys. Rev. B 75, 205102 (2007).

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

Granqvist, C. G.

J. Ederth, G. A. Niklasson, A. Hultaker, P. Heszler, C. G. Granqvist, A. R. van Doom, M. J. Jongerius, and D. Burgard, “Characterization of porous indium tin oxide films using effective medium theory,” J. Appl. Phys. 93, 984–988 (2003).
[Crossref]

Grover, F. W.

F. W. Grover, Inductance Calculations (Dover, 1973), p. 261.

Gundogdu, T. F.

N. Katsarakis, G. Konstantininidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, Th. Koschny, and C. M. Soukoulis, “Magnetic response of split-ring resonators in the farinfrared frequency regime,” Opt. Lett. 30, 1348–1350 (2005).
[Crossref] [PubMed]

M. Kafesaki, Th. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, “Left-handed metamaterials: detailed numerical studies of the transmission properties,” J. Opt. A:Pure Appl. Opt. 7, S12–S22 (2005).
[Crossref]

Heszler, P.

J. Ederth, G. A. Niklasson, A. Hultaker, P. Heszler, C. G. Granqvist, A. R. van Doom, M. J. Jongerius, and D. Burgard, “Characterization of porous indium tin oxide films using effective medium theory,” J. Appl. Phys. 93, 984–988 (2003).
[Crossref]

Holden, A. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Hultaker, A.

J. Ederth, G. A. Niklasson, A. Hultaker, P. Heszler, C. G. Granqvist, A. R. van Doom, M. J. Jongerius, and D. Burgard, “Characterization of porous indium tin oxide films using effective medium theory,” J. Appl. Phys. 93, 984–988 (2003).
[Crossref]

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics2nd ed. (John Wiley and Sons, 1975). Equation 6 is taken from the general expression δ=c/(2πωσ)1/2 and ε-1=ω2p/ω2=4πiσ/ω.

Jongerius, M. J.

J. Ederth, G. A. Niklasson, A. Hultaker, P. Heszler, C. G. Granqvist, A. R. van Doom, M. J. Jongerius, and D. Burgard, “Characterization of porous indium tin oxide films using effective medium theory,” J. Appl. Phys. 93, 984–988 (2003).
[Crossref]

Kafesaki, M.

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, and E. N. Economou, “The science of negative index materials,” J. Phys.: Condens. Matter 20, 304217 (2008).
[Crossref]

M. Kafesaki, Th. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, “Left-handed metamaterials: detailed numerical studies of the transmission properties,” J. Opt. A:Pure Appl. Opt. 7, S12–S22 (2005).
[Crossref]

N. Katsarakis, G. Konstantininidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, Th. Koschny, and C. M. Soukoulis, “Magnetic response of split-ring resonators in the farinfrared frequency regime,” Opt. Lett. 30, 1348–1350 (2005).
[Crossref] [PubMed]

Kaiser, N.

Katsarakis, N.

Kildishev, A. V.

Konstantininidis, G.

Koschny, T.

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, and E. N. Economou, “The science of negative index materials,” J. Phys.: Condens. Matter 20, 304217 (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]

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). Online supplement: http://www.sciencemag.org/cgi/content/full/sci;306/5700/1351/DC1.
[Crossref] [PubMed]

Koschny, Th.

N. Katsarakis, G. Konstantininidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, Th. Koschny, and C. M. Soukoulis, “Magnetic response of split-ring resonators in the farinfrared frequency regime,” Opt. Lett. 30, 1348–1350 (2005).
[Crossref] [PubMed]

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

M. Kafesaki, Th. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, “Left-handed metamaterials: detailed numerical studies of the transmission properties,” J. Opt. A:Pure Appl. Opt. 7, S12–S22 (2005).
[Crossref]

Kostopoulos, A.

Kreibig, U.

U. Kreibig and M. Vollmer, Optical properties of Metal clusters (Springer-Verlag, 1995).

Kuhl, J.

Landy, N. I.

H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: Design, fabrication and characterization,” Opt. Express 10, 7181–7188 (2008).
[Crossref]

Lederer, F.

Linden, S.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamatrerials,” Opt. Lett. 3253–55 (2007).
[Crossref]

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

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Response of Metamaterials at 100 Terahertz,” Science 306, 1351–1353 (2004).
[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). Online supplement: http://www.sciencemag.org/cgi/content/full/sci;306/5700/1351/DC1.
[Crossref] [PubMed]

Long, L. L.

Malloy, K. J.

Meyrath, T. P.

T. P. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: Optical frequency resonance circuits,” Phys. Rev. B 75, 205102 (2007).

Nemat-Nasser, S. C.

D. R. Smith, Willie J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Science 84, 4184–4187 (2000).

Niklasson, G. A.

J. Ederth, G. A. Niklasson, A. Hultaker, P. Heszler, C. G. Granqvist, A. R. van Doom, M. J. Jongerius, and D. Burgard, “Characterization of porous indium tin oxide films using effective medium theory,” J. Appl. Phys. 93, 984–988 (2003).
[Crossref]

Ordal, M. A.

Osgood, R. M.

Padilla, W. J.

H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: Design, fabrication and characterization,” Opt. Express 10, 7181–7188 (2008).
[Crossref]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

Padilla, Willie J.

D. R. Smith, Willie J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Science 84, 4184–4187 (2000).

Palik, E. D.

E. D. Palik, Handbook of optical constants of solids (Academic, 1985).

Panoiu, N. C.

Penciu, R. S.

N. Katsarakis, G. Konstantininidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, Th. Koschny, and C. M. Soukoulis, “Magnetic response of split-ring resonators in the farinfrared frequency regime,” Opt. Lett. 30, 1348–1350 (2005).
[Crossref] [PubMed]

M. Kafesaki, Th. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, “Left-handed metamaterials: detailed numerical studies of the transmission properties,” J. Opt. A:Pure Appl. Opt. 7, S12–S22 (2005).
[Crossref]

Pendry, J. B.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

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

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Robbins, D. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Rockstuhl, C.

Sarychev, A. K.

Schmidt, F.

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

Schultz, S.

D. R. Smith, Willie J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Science 84, 4184–4187 (2000).

Schulz, U.

Shalaev, V.

Smith, D. R.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

D. R. Smith, Willie J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Science 84, 4184–4187 (2000).

Smythe, W. R.

C. Wasshuber and W. R. Smythe,http://www.iue.tuwien.ac.at/phd/wasshuber/node77.html, Static and Dynamic Electricity2nd ed. (McGraw-Hill, 1950), in § 5.08 p. 118 the capacitance between two spheres is studied.

Soukoulis, C. M.

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, and E. N. Economou, “The science of negative index materials,” J. Phys.: Condens. Matter 20, 304217 (2008).
[Crossref]

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamatrerials,” Opt. Lett. 3253–55 (2007).
[Crossref]

N. Katsarakis, G. Konstantininidis, A. Kostopoulos, R. S. Penciu, T. F. Gundogdu, M. Kafesaki, E. N. Economou, Th. Koschny, and C. M. Soukoulis, “Magnetic response of split-ring resonators in the farinfrared frequency regime,” Opt. Lett. 30, 1348–1350 (2005).
[Crossref] [PubMed]

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

M. Kafesaki, Th. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, “Left-handed metamaterials: detailed numerical studies of the transmission properties,” J. Opt. A:Pure Appl. Opt. 7, S12–S22 (2005).
[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]

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). Online supplement: http://www.sciencemag.org/cgi/content/full/sci;306/5700/1351/DC1.
[Crossref] [PubMed]

Stewart, W. J.

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

Stockman, M. I.

M. I. Stockman, “Does nature allow negative refraction with low losses in optical region?” J. Cond. Mat. 14, 0611350 (2006).

Tao, H.

H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: Design, fabrication and characterization,” Opt. Express 10, 7181–7188 (2008).
[Crossref]

Tünnermann, A.

Ulin-Avila, E.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature Lett. (2008), http://www.nature.com/nature/journal/vaop/ncurrent/abs/nature07247.html.
[Crossref]

Valentine, J.

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature Lett. (2008), http://www.nature.com/nature/journal/vaop/ncurrent/abs/nature07247.html.
[Crossref]

Vier, D. C.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

D. R. Smith, Willie J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Science 84, 4184–4187 (2000).

Vollmer, M.

U. Kreibig and M. Vollmer, Optical properties of Metal clusters (Springer-Verlag, 1995).

Ward, C. A.

Wasshuber, C.

C. Wasshuber and W. R. Smythe,http://www.iue.tuwien.ac.at/phd/wasshuber/node77.html, Static and Dynamic Electricity2nd ed. (McGraw-Hill, 1950), in § 5.08 p. 118 the capacitance between two spheres is studied.

Wegener, M.

G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Cut-wire pairs and plate pairs as magnetic atoms for optical metamatrerials,” Opt. Lett. 3253–55 (2007).
[Crossref]

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

S. Linden, C. Enkrich, M. Wegener, J. Zhou, T. Koschny, and C. M. Soukoulis, “Magnetic Response of Metamaterials at 100 Terahertz,” Science 306, 1351–1353 (2004).
[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). Online supplement: http://www.sciencemag.org/cgi/content/full/sci;306/5700/1351/DC1.
[Crossref] [PubMed]

Yen, T. J.

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

Yuan, H-K

Zentgraf, T.

T. P. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: Optical frequency resonance circuits,” Phys. Rev. B 75, 205102 (2007).

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

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature Lett. (2008), http://www.nature.com/nature/journal/vaop/ncurrent/abs/nature07247.html.
[Crossref]

Zhang, S.

S. Zhang, W. Fan, K. J. Malloy, S. R. J. Brueck, N. C. Panoiu, and R. M. Osgood, “Near-infrared double negative metamaterials,” Opt. Express 13, 4922–4930 (2005).
[Crossref] [PubMed]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature Lett. (2008), http://www.nature.com/nature/journal/vaop/ncurrent/abs/nature07247.html.
[Crossref]

Zhang, X.

H. Tao, N. I. Landy, C. M. Bingham, X. Zhang, R. D. Averitt, and W. J. Padilla, “A metamaterial absorber for the terahertz regime: Design, fabrication and characterization,” Opt. Express 10, 7181–7188 (2008).
[Crossref]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[Crossref] [PubMed]

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature Lett. (2008), http://www.nature.com/nature/journal/vaop/ncurrent/abs/nature07247.html.
[Crossref]

Zhou, J.

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, and E. N. Economou, “The science of negative index materials,” J. Phys.: Condens. Matter 20, 304217 (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]

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). Online supplement: http://www.sciencemag.org/cgi/content/full/sci;306/5700/1351/DC1.
[Crossref] [PubMed]

Zhou, J. F.

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

Zschiedrich, L.

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

Appl. Opt. (2)

IEEE Trans. Microwave Theory Tech. (1)

J. B. Pendry, A. J. Holden, D. J. Robbins, and W. J. Stewart, “Magnetism from conductors and enhanced nonlinear phenomena,” IEEE Trans. Microwave Theory Tech. 47, 2075–2084 (1999).
[Crossref]

J. Appl. Phys. (1)

J. Ederth, G. A. Niklasson, A. Hultaker, P. Heszler, C. G. Granqvist, A. R. van Doom, M. J. Jongerius, and D. Burgard, “Characterization of porous indium tin oxide films using effective medium theory,” J. Appl. Phys. 93, 984–988 (2003).
[Crossref]

J. Cond. Mat. (1)

M. I. Stockman, “Does nature allow negative refraction with low losses in optical region?” J. Cond. Mat. 14, 0611350 (2006).

J. Opt. A:Pure Appl. Opt. (1)

M. Kafesaki, Th. Koschny, R. S. Penciu, T. F. Gundogdu, E. N. Economou, and C. M. Soukoulis, “Left-handed metamaterials: detailed numerical studies of the transmission properties,” J. Opt. A:Pure Appl. Opt. 7, S12–S22 (2005).
[Crossref]

J. Phys. D Appl. Phys. (1)

M. A. Bueno and A. K. T. Assis, “A new method for inductance calculations,” J. Phys. D Appl. Phys. 281802–1806 (1995).
[Crossref]

J. Phys.: Condens. Matter (1)

C. M. Soukoulis, J. Zhou, T. Koschny, M. Kafesaki, and E. N. Economou, “The science of negative index materials,” J. Phys.: Condens. Matter 20, 304217 (2008).
[Crossref]

Opt. Express (3)

Opt. Lett. (3)

Phys. Rev. (1)

T. P. Meyrath, T. Zentgraf, and H. Giessen, “Lorentz model for metamaterials: Optical frequency resonance circuits,” Phys. Rev. B 75, 205102 (2007).

Phys. Rev. Lett. (2)

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

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

Science (5)

N. Engheta, “Circuits with light at nanoscales: Optical nanocircuits inspired by metamaterials,” Science 317, 1698–1702 (2007).
[Crossref] [PubMed]

D. R. Smith, Willie J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity,” Science 84, 4184–4187 (2000).

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]

T. J. Yen, W. J. Padilla, N. Fang, D. C. Vier, D. R. Smith, J. B. Pendry, D. N. Basov, and X. Zhang, “Terahertz Magnetic Response from Artificial Materials,” Science 303, 1494–1496 (2004).
[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). Online supplement: http://www.sciencemag.org/cgi/content/full/sci;306/5700/1351/DC1.
[Crossref] [PubMed]

Other (9)

C. Wasshuber and W. R. Smythe,http://www.iue.tuwien.ac.at/phd/wasshuber/node77.html, Static and Dynamic Electricity2nd ed. (McGraw-Hill, 1950), in § 5.08 p. 118 the capacitance between two spheres is studied.

J. D. Jackson, Classical Electrodynamics2nd ed. (John Wiley and Sons, 1975). Equation 6 is taken from the general expression δ=c/(2πωσ)1/2 and ε-1=ω2p/ω2=4πiσ/ω.

F. W. Grover, Inductance Calculations (Dover, 1973), p. 261.

M. A. Bueno and A. K. T. Assis, Inductance and force calculations in electrical circuits (Nova Science, 2001).

M. A. Bueno and A. K. T. Assis, Inductance and force calculations in electrical circuits (Nova Science, 2001), p. 24, 30. See http://www.ifi.unicamp.br/~assis/wbooks.htm for correction to eq. 3.2.

M. A Bueno and A. K. T. Assis, Inductance and force calculations in electrical circuits (Nova Science, 2001), p. 40.

E. D. Palik, Handbook of optical constants of solids (Academic, 1985).

U. Kreibig and M. Vollmer, Optical properties of Metal clusters (Springer-Verlag, 1995).

J. Valentine, S. Zhang, T. Zentgraf, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang, “Three-dimensional optical metamaterial with a negative refractive index,” Nature Lett. (2008), http://www.nature.com/nature/journal/vaop/ncurrent/abs/nature07247.html.
[Crossref]

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Figures (9)

Fig. 1.
Fig. 1.

Transmission measurements of the a) single split rings with horizontal E-field polarization, b) single split rings with vertical E-field polarization, c) U-shapes and rods with horizontal E-field polarization, and d) U-shapes and rods with vertical E-field polarization. Below the plots are sample SEM images of some of these structures.

Fig. 2.
Fig. 2.

Simulation and experimental transmission curves for the SRRs with gap =55 nm.

Fig. 3.
Fig. 3.

Vector E-field (left) and current density (right) plots for a horizontally polarized field for the (a) rod, and U-shape for (b) mode 1 and (c) mode 2.

Fig. 4.
Fig. 4.

Vector E-field (left) and current density (right) plots for a horizontally polarized field for single split rings for a) mode 1 b) mode 2, and c) mode 3 resonant positions.

Fig. 5.
Fig. 5.

Plots of calculated values of the resonance frequency as a function of gap using a simple LC model (red line), along with the experimental data for mode 1 resonance (black squares). The blue line shows the modified LC resonance model described below.

Fig. 6.
Fig. 6.

The resonant frequency for the 55 nm gap SRR obtained using HFSS simulations of each mode as a function of inverse plasma frequency and normalized to the plasma frequency of silver. The green line shows the prediction of a modified LC model taking into account the skin depth on the inductance.

Fig. 7.
Fig. 7.

Normal incidence transmission measurements with E-field in the horizontal direction showing the comparison of Ag and Al (a) rods, (b) U-shapes, and (c) small gap split rings.

Fig. 8.
Fig. 8.

Illustration of the single split ring resonator used in the model inductance calculations and simulations. A 3D view with relevant parameter definitions is shown in (a). A crosssectional view illustrates the effective height and length modifications used when modeling (b) a perfect conductor and (c) a real material with some skin depth δ. A cross-sectional view of the currents based on simulations for the G55 structure is shown in (d).

Fig. 9.
Fig. 9.

Plots showing the mode 1 resonance shift from 75 nm SRRs as a function of height for (a) a perfect conductor and Ag with and without a substrate, and (b) the simulation data of Ag SRRs with a substrate compared with the modified LC model.

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

f L C = 1 L C = g 2 π ε o μ o 2 w = c 2 π g w
f L C = c 2 π g w ε 0 ε eff
ε e ff ( f ) = α ε ITO ( f ) + ( 1 α ) ε 0
C 4 π ε a ( 1 + a 2 d 2 a 2 + a 4 d 4 3 d 2 a 2 + a 4 )
a = ( 3 r 2 h 4 ) 1 3
δ c ω P
L eff = 4 ( L sheet M pairs )
L SRR 4 ( L sheet M pairs ) ( 2.93 ) μ 0 π ( 3 h ) 1 2 μ 0 π ( 0.934 )
L ring 2 μ o outer π ( ln ( 4 outer h + w ) 0.662 )

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