Abstract

Gold nanorod has generated great research interest due to its tunable longitudinal plasmon resonance. However, little progress has been made in the understanding of the effect. A major reason is that, except for the metallic spheres and ellipsoids, the interaction between light and nanoparticles is generally insoluble. In this paper, a new scheme has been proposed to study the plasmon resonance of gold nanorod, in which the nanorod is modeled as an LC circuit with an inductance and a capacitance. The obtained resonance wavelength is dependent on not only aspect ratio but also rod radius, suggesting the importance of self-inductance and the breakdown of linear scaling. Moreover, the cross sections for light scattering and absorption have been deduced analytically, giving rise to a Lorentzian line-shape for the extinction spectrum. The result provides us with new insight into the phenomenon.

© 2009 Optical Society of America

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    [CrossRef] [PubMed]
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  7. X. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, "Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods," J. Am. Chem. Soc. 128, 2115-2120 (2006).
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  16. 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).
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    [CrossRef]

2008

L. Qiu, T.A. Larson, D. Smith, E. Vitkin, M. D. Modell, B. A. Korgel, K. V. Sokolov, E. B. Hanlon, I. Itzkan, and L. T. Perelman, "Observation of plasmon line broadening in single gold nanorods," Appl. Phys. Lett. 93, 153106 (2008).
[CrossRef]

2007

P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, "Au nanoparticles target cancer," Nanotoday 2, 18-29 (2007).

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. Stat. Sol. (B) 244, 1256-1261 (2007).
[CrossRef]

2006

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Single-slit split-ring resonators at optical frequencies: limits of size scaling," Opt. Lett. 31, 1259-1261 (2006).
[CrossRef] [PubMed]

E. S. Kooij and B. Poelsema, "Shape and size effects in the optical properties of metallic nanorods," Phys. Chem.Chem. Phys. 8, 3349-3357 (2006).
[CrossRef]

J. Hafner, "Gold nanoparticles are shaped for effect," Laser Focus World 42, 99-101 (2006).

X. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, "Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods," J. Am. Chem. Soc. 128, 2115-2120 (2006).
[CrossRef] [PubMed]

S. W. Prescott and P. Mulvaney, "Gold nanorod extinction spectra," J.Appl.Phys. 99, 123504 (2006).
[CrossRef]

2005

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 (2005).
[CrossRef] [PubMed]

2004

L. M. Liz-Marzan, "Nanometals: formation and color," Materials Today 7, 26-31 (2004).

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]

E. Hutter and J. H. Fendler, "Exploitation of localized surface plasmon resonance," Adv. Mater. 16, 1685-1706 (2004).
[CrossRef]

2003

H. Kuwata, H. Tamaru, K. Esumi, and K. Miyano, "Resonant light scattering from metal nanoparticles: Practical analysis beyond Rayleigh approximation," Appl. Phys. Lett. 83, 4625-4627 (2003).
[CrossRef]

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229- 232 (2003).
[CrossRef] [PubMed]

2002

C. J. Murphy and N. R. Jana, "Controlling the aspect ratio of inorganic nanorods and nanowires," Adv. Mater. 14, 80-82 (2002).
[CrossRef]

1999

S. Link, M. B. Mohamed, and M. A. El-Sayed, "Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant," J. Phys. Chem. B 103, 3073-3077 (1999).
[CrossRef]

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]

Atwater, H. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229- 232 (2003).
[CrossRef] [PubMed]

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]

Economou, E. N.

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 (2005).
[CrossRef] [PubMed]

El-Sayed, I. H.

P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, "Au nanoparticles target cancer," Nanotoday 2, 18-29 (2007).

X. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, "Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods," J. Am. Chem. Soc. 128, 2115-2120 (2006).
[CrossRef] [PubMed]

El-Sayed, M. A.

P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, "Au nanoparticles target cancer," Nanotoday 2, 18-29 (2007).

X. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, "Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods," J. Am. Chem. Soc. 128, 2115-2120 (2006).
[CrossRef] [PubMed]

S. Link, M. B. Mohamed, and M. A. El-Sayed, "Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant," J. Phys. Chem. B 103, 3073-3077 (1999).
[CrossRef]

Enkrich, C.

Esumi, K.

H. Kuwata, H. Tamaru, K. Esumi, and K. Miyano, "Resonant light scattering from metal nanoparticles: Practical analysis beyond Rayleigh approximation," Appl. Phys. Lett. 83, 4625-4627 (2003).
[CrossRef]

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]

Fendler, J. H.

E. Hutter and J. H. Fendler, "Exploitation of localized surface plasmon resonance," Adv. Mater. 16, 1685-1706 (2004).
[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. Stat. Sol. (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. Stat. Sol. (B) 244, 1256-1261 (2007).
[CrossRef]

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. Stat. Sol. (B) 244, 1256-1261 (2007).
[CrossRef]

Hafner, J.

J. Hafner, "Gold nanoparticles are shaped for effect," Laser Focus World 42, 99-101 (2006).

Hanlon, E. B.

L. Qiu, T.A. Larson, D. Smith, E. Vitkin, M. D. Modell, B. A. Korgel, K. V. Sokolov, E. B. Hanlon, I. Itzkan, and L. T. Perelman, "Observation of plasmon line broadening in single gold nanorods," Appl. Phys. Lett. 93, 153106 (2008).
[CrossRef]

Harel, E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229- 232 (2003).
[CrossRef] [PubMed]

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]

Huang, X.

X. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, "Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods," J. Am. Chem. Soc. 128, 2115-2120 (2006).
[CrossRef] [PubMed]

Hutter, E.

E. Hutter and J. H. Fendler, "Exploitation of localized surface plasmon resonance," Adv. Mater. 16, 1685-1706 (2004).
[CrossRef]

Itzkan, I.

L. Qiu, T.A. Larson, D. Smith, E. Vitkin, M. D. Modell, B. A. Korgel, K. V. Sokolov, E. B. Hanlon, I. Itzkan, and L. T. Perelman, "Observation of plasmon line broadening in single gold nanorods," Appl. Phys. Lett. 93, 153106 (2008).
[CrossRef]

Jain, P. K.

P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, "Au nanoparticles target cancer," Nanotoday 2, 18-29 (2007).

Jana, N. R.

C. J. Murphy and N. R. Jana, "Controlling the aspect ratio of inorganic nanorods and nanowires," Adv. Mater. 14, 80-82 (2002).
[CrossRef]

Kafesaki, M.

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 (2005).
[CrossRef] [PubMed]

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. Stat. Sol. (B) 244, 1256-1261 (2007).
[CrossRef]

Kik, P. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229- 232 (2003).
[CrossRef] [PubMed]

Klein, M. W.

Koel, B. E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229- 232 (2003).
[CrossRef] [PubMed]

Kooij, E. S.

E. S. Kooij and B. Poelsema, "Shape and size effects in the optical properties of metallic nanorods," Phys. Chem.Chem. Phys. 8, 3349-3357 (2006).
[CrossRef]

Korgel, B. A.

L. Qiu, T.A. Larson, D. Smith, E. Vitkin, M. D. Modell, B. A. Korgel, K. V. Sokolov, E. B. Hanlon, I. Itzkan, and L. T. Perelman, "Observation of plasmon line broadening in single gold nanorods," Appl. Phys. Lett. 93, 153106 (2008).
[CrossRef]

Koschny, T.

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 (2005).
[CrossRef] [PubMed]

Kuwata, H.

H. Kuwata, H. Tamaru, K. Esumi, and K. Miyano, "Resonant light scattering from metal nanoparticles: Practical analysis beyond Rayleigh approximation," Appl. Phys. Lett. 83, 4625-4627 (2003).
[CrossRef]

Larson, T.A.

L. Qiu, T.A. Larson, D. Smith, E. Vitkin, M. D. Modell, B. A. Korgel, K. V. Sokolov, E. B. Hanlon, I. Itzkan, and L. T. Perelman, "Observation of plasmon line broadening in single gold nanorods," Appl. Phys. Lett. 93, 153106 (2008).
[CrossRef]

Linden, S.

Link, S.

S. Link, M. B. Mohamed, and M. A. El-Sayed, "Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant," J. Phys. Chem. B 103, 3073-3077 (1999).
[CrossRef]

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. Stat. Sol. (B) 244, 1256-1261 (2007).
[CrossRef]

Liz-Marzan, L. M.

L. M. Liz-Marzan, "Nanometals: formation and color," Materials Today 7, 26-31 (2004).

Maier, S. A.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229- 232 (2003).
[CrossRef] [PubMed]

Meltzer, S.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229- 232 (2003).
[CrossRef] [PubMed]

Miyano, K.

H. Kuwata, H. Tamaru, K. Esumi, and K. Miyano, "Resonant light scattering from metal nanoparticles: Practical analysis beyond Rayleigh approximation," Appl. Phys. Lett. 83, 4625-4627 (2003).
[CrossRef]

Modell, M. D.

L. Qiu, T.A. Larson, D. Smith, E. Vitkin, M. D. Modell, B. A. Korgel, K. V. Sokolov, E. B. Hanlon, I. Itzkan, and L. T. Perelman, "Observation of plasmon line broadening in single gold nanorods," Appl. Phys. Lett. 93, 153106 (2008).
[CrossRef]

Mohamed, M. B.

S. Link, M. B. Mohamed, and M. A. El-Sayed, "Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant," J. Phys. Chem. B 103, 3073-3077 (1999).
[CrossRef]

Mulvaney, P.

S. W. Prescott and P. Mulvaney, "Gold nanorod extinction spectra," J.Appl.Phys. 99, 123504 (2006).
[CrossRef]

Murphy, C. J.

C. J. Murphy and N. R. Jana, "Controlling the aspect ratio of inorganic nanorods and nanowires," Adv. Mater. 14, 80-82 (2002).
[CrossRef]

Padilla, W. 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]

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 (2005).
[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]

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]

Perelman, L. T.

L. Qiu, T.A. Larson, D. Smith, E. Vitkin, M. D. Modell, B. A. Korgel, K. V. Sokolov, E. B. Hanlon, I. Itzkan, and L. T. Perelman, "Observation of plasmon line broadening in single gold nanorods," Appl. Phys. Lett. 93, 153106 (2008).
[CrossRef]

Poelsema, B.

E. S. Kooij and B. Poelsema, "Shape and size effects in the optical properties of metallic nanorods," Phys. Chem.Chem. Phys. 8, 3349-3357 (2006).
[CrossRef]

Prescott, S. W.

S. W. Prescott and P. Mulvaney, "Gold nanorod extinction spectra," J.Appl.Phys. 99, 123504 (2006).
[CrossRef]

Qian, W.

X. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, "Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods," J. Am. Chem. Soc. 128, 2115-2120 (2006).
[CrossRef] [PubMed]

Qiu, L.

L. Qiu, T.A. Larson, D. Smith, E. Vitkin, M. D. Modell, B. A. Korgel, K. V. Sokolov, E. B. Hanlon, I. Itzkan, and L. T. Perelman, "Observation of plasmon line broadening in single gold nanorods," Appl. Phys. Lett. 93, 153106 (2008).
[CrossRef]

Requicha, A. A. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229- 232 (2003).
[CrossRef] [PubMed]

Robbins, D. J.

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

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. Stat. Sol. (B) 244, 1256-1261 (2007).
[CrossRef]

Smith, D.

L. Qiu, T.A. Larson, D. Smith, E. Vitkin, M. D. Modell, B. A. Korgel, K. V. Sokolov, E. B. Hanlon, I. Itzkan, and L. T. Perelman, "Observation of plasmon line broadening in single gold nanorods," Appl. Phys. Lett. 93, 153106 (2008).
[CrossRef]

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]

Sokolov, K. V.

L. Qiu, T.A. Larson, D. Smith, E. Vitkin, M. D. Modell, B. A. Korgel, K. V. Sokolov, E. B. Hanlon, I. Itzkan, and L. T. Perelman, "Observation of plasmon line broadening in single gold nanorods," Appl. Phys. Lett. 93, 153106 (2008).
[CrossRef]

Soukoulis, C. M.

M. W. Klein, C. Enkrich, M. Wegener, C. M. Soukoulis, and S. Linden, "Single-slit split-ring resonators at optical frequencies: limits of size scaling," Opt. Lett. 31, 1259-1261 (2006).
[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 (2005).
[CrossRef] [PubMed]

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L. Qiu, T.A. Larson, D. Smith, E. Vitkin, M. D. Modell, B. A. Korgel, K. V. Sokolov, E. B. Hanlon, I. Itzkan, and L. T. Perelman, "Observation of plasmon line broadening in single gold nanorods," Appl. Phys. Lett. 93, 153106 (2008).
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[CrossRef] [PubMed]

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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]

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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 (2005).
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X. Huang, I. H. El-Sayed, W. Qian, and M. A. El-Sayed, "Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods," J. Am. Chem. Soc. 128, 2115-2120 (2006).
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S. Link, M. B. Mohamed, and M. A. El-Sayed, "Simulation of the optical absorption spectra of gold nanorods as a function of their aspect ratio and the effect of the medium dielectric constant," J. Phys. Chem. B 103, 3073-3077 (1999).
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P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, "Au nanoparticles target cancer," Nanotoday 2, 18-29 (2007).

Nat. Mater.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, and A. A. G. Requicha, "Local detection of electromagnetic energy transport below the diffraction limit in metal nanoparticle plasmon waveguides," Nat. Mater. 2, 229- 232 (2003).
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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 (2005).
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Figures (3)

Fig. 1.
Fig. 1.

(a) Schematic view of the structure under study. The subwavelength gold nanorod is embedded in a dielectric, and the incident light is propagating with the electric field along the rod axis, thus exciting the longitudinal plasmon resonance. (b) The magnetic field distribution around the nanorod when a current flow in the rod is excited by the light electric field.

Fig. 2.
Fig. 2.

(a) Dependence of resonance wavelength on the aspect ratio. The squares represent the experimental data [10] and the line gives our calculated values (the rod diameter is fixed as 22nm). (b) Dependence of resonance wavelength on the rod radius. The symbols are obtained by numerical calculations [19] and the lines obtained by our calculation. Here the aspect ratio is set as 3, 5 and 7, respectively (from the bottom to the top).

Fig. 3.
Fig. 3.

(a) Normalized extinction spectra for a single gold nanorod, which has a length of 52.65nm and radius of 8.1nm. The open and solid circles represent, respectively, the theoretical (by equation (5)) and experimental [11] results. The solid line is a numerical fit of experimental data with the Lorentzian line-shape. (b) Calculated extinction spectra for three gold nanorods with different rod sizes, where the rod radius is fixed as 10nm and the length is set as 60, 80, and 100nm, respectively (from the left to the right).

Equations (6)

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L = ( μ 0 l / 2 π ) ln ( l / 2 r 0 ) ,
C = α π ε 0 ε d r 0 .
p = ε 0 A ω 0 2 ω 2 i η ω E ,
λ 0 = π n d 10 κ ( 2 δ 2 + r 0 2 ln κ ) ,
C sca = A 2 6 π c 4 ω 4 ( ω 0 2 ω 2 ) 2 + η 2 ω 2 , C abs = A η n d c ω 2 ( ω 0 2 ω 2 ) 2 + η 2 ω 2 .
λ 0 = π n d 5 l ( 2 π δ 2 + a b ln κ ) a ln ( b / a + 1 + b 2 / a 2 ) + b ln ( a / b + 1 + a 2 / b 2 ) .

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