Abstract

We study the scattering and absorption of an H-polarized plane electromagnetic wave by a circular silver nanotube in the visible range of wavelengths using the separation of variables. The computed spectra of the extinction cross section display several hybrid localized surface-plasmon resonances of the dipole and multipole type. Analytical equations are derived for their resonance wavelengths. Bulk refractive-index sensitivities of nanotube-based sensors are determined, showing higher values for multipole resonances.

© 2013 Optical Society of America

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  1. J. McPhillips, A. Murphy, M. P. Jonsson, W. R. Hendren, R. Atkinson, F. Hook, A. V. Zayats, and R. J. Pollard, ACS Nano 4, 2210 (2010).
    [CrossRef]
  2. A. Murphy, Y. Sonnefraud, A. V. Krasavin, P. Ginzburg, F. Morgan, J. McPhillips, G. Wurtz, S. A. Maier, A. V. Zayats, and R. Pollard, Appl. Phys. Lett. 102, 103103 (2013).
    [CrossRef]
  3. O. J. F. Martin, in Optical Nanotechnologies, Topics in Applied Physics, J. Tominaga and D. P. Tsai, eds. (Springer, 2003), pp. 183–210.
  4. J. Zhu, Mater. Sci. Eng. 454–455, 685 (2007).
    [CrossRef]
  5. H.-Y. She, L.-W. Li, O. J. F. Martin, and J. R. Mosig, Opt. Express 16, 1007 (2008).
    [CrossRef]
  6. J. M. McMahon, S. K. Gray, and G. C. Schatz, J. Phys. Chem. 114, 15903 (2010).
    [CrossRef]
  7. H. Xu, H. Li, Z. Liu, S. Xie, X. Zhou, and J. Wu, Solid State Commun. 151, 759 (2011).
    [CrossRef]
  8. C. Radloff and N. J. Halas, Nano Lett. 4, 1323 (2004).
    [CrossRef]
  9. Y. Wu and P. Nordlander, J. Chem. Phys. 125, 124708 (2006).
    [CrossRef]
  10. F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
    [CrossRef]
  11. Rayleigh, Philos. Mag. 12(73), 81 (1881).
    [CrossRef]
  12. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  13. E. I. Smotrova, T. M. Benson, P. Sewell, J. Ctyroky, and A. I. Nosich, J. Opt. Soc. Am. A 25, 2884 (2008).
    [CrossRef]
  14. G. Toscano, S. Raza, A.-P. Jauho, N. A. Mortensen, and M. Wubs, Opt. Express 20, 4176 (2012).
    [CrossRef]

2013 (1)

A. Murphy, Y. Sonnefraud, A. V. Krasavin, P. Ginzburg, F. Morgan, J. McPhillips, G. Wurtz, S. A. Maier, A. V. Zayats, and R. Pollard, Appl. Phys. Lett. 102, 103103 (2013).
[CrossRef]

2012 (1)

2011 (1)

H. Xu, H. Li, Z. Liu, S. Xie, X. Zhou, and J. Wu, Solid State Commun. 151, 759 (2011).
[CrossRef]

2010 (2)

J. M. McMahon, S. K. Gray, and G. C. Schatz, J. Phys. Chem. 114, 15903 (2010).
[CrossRef]

J. McPhillips, A. Murphy, M. P. Jonsson, W. R. Hendren, R. Atkinson, F. Hook, A. V. Zayats, and R. J. Pollard, ACS Nano 4, 2210 (2010).
[CrossRef]

2008 (3)

2007 (1)

J. Zhu, Mater. Sci. Eng. 454–455, 685 (2007).
[CrossRef]

2006 (1)

Y. Wu and P. Nordlander, J. Chem. Phys. 125, 124708 (2006).
[CrossRef]

2004 (1)

C. Radloff and N. J. Halas, Nano Lett. 4, 1323 (2004).
[CrossRef]

1972 (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

1881 (1)

Rayleigh, Philos. Mag. 12(73), 81 (1881).
[CrossRef]

Atkinson, R.

J. McPhillips, A. Murphy, M. P. Jonsson, W. R. Hendren, R. Atkinson, F. Hook, A. V. Zayats, and R. J. Pollard, ACS Nano 4, 2210 (2010).
[CrossRef]

Benson, T. M.

Christy, R. W.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Ctyroky, J.

Dorpe, P. V.

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
[CrossRef]

Ginzburg, P.

A. Murphy, Y. Sonnefraud, A. V. Krasavin, P. Ginzburg, F. Morgan, J. McPhillips, G. Wurtz, S. A. Maier, A. V. Zayats, and R. Pollard, Appl. Phys. Lett. 102, 103103 (2013).
[CrossRef]

Gray, S. K.

J. M. McMahon, S. K. Gray, and G. C. Schatz, J. Phys. Chem. 114, 15903 (2010).
[CrossRef]

Halas, N. J.

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
[CrossRef]

C. Radloff and N. J. Halas, Nano Lett. 4, 1323 (2004).
[CrossRef]

Hao, F.

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
[CrossRef]

Hendren, W. R.

J. McPhillips, A. Murphy, M. P. Jonsson, W. R. Hendren, R. Atkinson, F. Hook, A. V. Zayats, and R. J. Pollard, ACS Nano 4, 2210 (2010).
[CrossRef]

Hook, F.

J. McPhillips, A. Murphy, M. P. Jonsson, W. R. Hendren, R. Atkinson, F. Hook, A. V. Zayats, and R. J. Pollard, ACS Nano 4, 2210 (2010).
[CrossRef]

Jauho, A.-P.

Johnson, P. B.

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Jonsson, M. P.

J. McPhillips, A. Murphy, M. P. Jonsson, W. R. Hendren, R. Atkinson, F. Hook, A. V. Zayats, and R. J. Pollard, ACS Nano 4, 2210 (2010).
[CrossRef]

Krasavin, A. V.

A. Murphy, Y. Sonnefraud, A. V. Krasavin, P. Ginzburg, F. Morgan, J. McPhillips, G. Wurtz, S. A. Maier, A. V. Zayats, and R. Pollard, Appl. Phys. Lett. 102, 103103 (2013).
[CrossRef]

Li, H.

H. Xu, H. Li, Z. Liu, S. Xie, X. Zhou, and J. Wu, Solid State Commun. 151, 759 (2011).
[CrossRef]

Li, L.-W.

Liu, Z.

H. Xu, H. Li, Z. Liu, S. Xie, X. Zhou, and J. Wu, Solid State Commun. 151, 759 (2011).
[CrossRef]

Maier, S. A.

A. Murphy, Y. Sonnefraud, A. V. Krasavin, P. Ginzburg, F. Morgan, J. McPhillips, G. Wurtz, S. A. Maier, A. V. Zayats, and R. Pollard, Appl. Phys. Lett. 102, 103103 (2013).
[CrossRef]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
[CrossRef]

Martin, O. J. F.

H.-Y. She, L.-W. Li, O. J. F. Martin, and J. R. Mosig, Opt. Express 16, 1007 (2008).
[CrossRef]

O. J. F. Martin, in Optical Nanotechnologies, Topics in Applied Physics, J. Tominaga and D. P. Tsai, eds. (Springer, 2003), pp. 183–210.

McMahon, J. M.

J. M. McMahon, S. K. Gray, and G. C. Schatz, J. Phys. Chem. 114, 15903 (2010).
[CrossRef]

McPhillips, J.

A. Murphy, Y. Sonnefraud, A. V. Krasavin, P. Ginzburg, F. Morgan, J. McPhillips, G. Wurtz, S. A. Maier, A. V. Zayats, and R. Pollard, Appl. Phys. Lett. 102, 103103 (2013).
[CrossRef]

J. McPhillips, A. Murphy, M. P. Jonsson, W. R. Hendren, R. Atkinson, F. Hook, A. V. Zayats, and R. J. Pollard, ACS Nano 4, 2210 (2010).
[CrossRef]

Morgan, F.

A. Murphy, Y. Sonnefraud, A. V. Krasavin, P. Ginzburg, F. Morgan, J. McPhillips, G. Wurtz, S. A. Maier, A. V. Zayats, and R. Pollard, Appl. Phys. Lett. 102, 103103 (2013).
[CrossRef]

Mortensen, N. A.

Mosig, J. R.

Murphy, A.

A. Murphy, Y. Sonnefraud, A. V. Krasavin, P. Ginzburg, F. Morgan, J. McPhillips, G. Wurtz, S. A. Maier, A. V. Zayats, and R. Pollard, Appl. Phys. Lett. 102, 103103 (2013).
[CrossRef]

J. McPhillips, A. Murphy, M. P. Jonsson, W. R. Hendren, R. Atkinson, F. Hook, A. V. Zayats, and R. J. Pollard, ACS Nano 4, 2210 (2010).
[CrossRef]

Nordlander, P.

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
[CrossRef]

Y. Wu and P. Nordlander, J. Chem. Phys. 125, 124708 (2006).
[CrossRef]

Nosich, A. I.

Pollard, R.

A. Murphy, Y. Sonnefraud, A. V. Krasavin, P. Ginzburg, F. Morgan, J. McPhillips, G. Wurtz, S. A. Maier, A. V. Zayats, and R. Pollard, Appl. Phys. Lett. 102, 103103 (2013).
[CrossRef]

Pollard, R. J.

J. McPhillips, A. Murphy, M. P. Jonsson, W. R. Hendren, R. Atkinson, F. Hook, A. V. Zayats, and R. J. Pollard, ACS Nano 4, 2210 (2010).
[CrossRef]

Radloff, C.

C. Radloff and N. J. Halas, Nano Lett. 4, 1323 (2004).
[CrossRef]

Rayleigh,

Rayleigh, Philos. Mag. 12(73), 81 (1881).
[CrossRef]

Raza, S.

Schatz, G. C.

J. M. McMahon, S. K. Gray, and G. C. Schatz, J. Phys. Chem. 114, 15903 (2010).
[CrossRef]

Sewell, P.

She, H.-Y.

Smotrova, E. I.

Sonnefraud, Y.

A. Murphy, Y. Sonnefraud, A. V. Krasavin, P. Ginzburg, F. Morgan, J. McPhillips, G. Wurtz, S. A. Maier, A. V. Zayats, and R. Pollard, Appl. Phys. Lett. 102, 103103 (2013).
[CrossRef]

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
[CrossRef]

Toscano, G.

Wu, J.

H. Xu, H. Li, Z. Liu, S. Xie, X. Zhou, and J. Wu, Solid State Commun. 151, 759 (2011).
[CrossRef]

Wu, Y.

Y. Wu and P. Nordlander, J. Chem. Phys. 125, 124708 (2006).
[CrossRef]

Wubs, M.

Wurtz, G.

A. Murphy, Y. Sonnefraud, A. V. Krasavin, P. Ginzburg, F. Morgan, J. McPhillips, G. Wurtz, S. A. Maier, A. V. Zayats, and R. Pollard, Appl. Phys. Lett. 102, 103103 (2013).
[CrossRef]

Xie, S.

H. Xu, H. Li, Z. Liu, S. Xie, X. Zhou, and J. Wu, Solid State Commun. 151, 759 (2011).
[CrossRef]

Xu, H.

H. Xu, H. Li, Z. Liu, S. Xie, X. Zhou, and J. Wu, Solid State Commun. 151, 759 (2011).
[CrossRef]

Zayats, A. V.

A. Murphy, Y. Sonnefraud, A. V. Krasavin, P. Ginzburg, F. Morgan, J. McPhillips, G. Wurtz, S. A. Maier, A. V. Zayats, and R. Pollard, Appl. Phys. Lett. 102, 103103 (2013).
[CrossRef]

J. McPhillips, A. Murphy, M. P. Jonsson, W. R. Hendren, R. Atkinson, F. Hook, A. V. Zayats, and R. J. Pollard, ACS Nano 4, 2210 (2010).
[CrossRef]

Zhou, X.

H. Xu, H. Li, Z. Liu, S. Xie, X. Zhou, and J. Wu, Solid State Commun. 151, 759 (2011).
[CrossRef]

Zhu, J.

J. Zhu, Mater. Sci. Eng. 454–455, 685 (2007).
[CrossRef]

ACS Nano (1)

J. McPhillips, A. Murphy, M. P. Jonsson, W. R. Hendren, R. Atkinson, F. Hook, A. V. Zayats, and R. J. Pollard, ACS Nano 4, 2210 (2010).
[CrossRef]

Appl. Phys. Lett. (1)

A. Murphy, Y. Sonnefraud, A. V. Krasavin, P. Ginzburg, F. Morgan, J. McPhillips, G. Wurtz, S. A. Maier, A. V. Zayats, and R. Pollard, Appl. Phys. Lett. 102, 103103 (2013).
[CrossRef]

J. Chem. Phys. (1)

Y. Wu and P. Nordlander, J. Chem. Phys. 125, 124708 (2006).
[CrossRef]

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

J. Phys. Chem. (1)

J. M. McMahon, S. K. Gray, and G. C. Schatz, J. Phys. Chem. 114, 15903 (2010).
[CrossRef]

Mater. Sci. Eng. (1)

J. Zhu, Mater. Sci. Eng. 454–455, 685 (2007).
[CrossRef]

Nano Lett. (2)

F. Hao, Y. Sonnefraud, P. V. Dorpe, S. A. Maier, N. J. Halas, and P. Nordlander, Nano Lett. 8, 3983 (2008).
[CrossRef]

C. Radloff and N. J. Halas, Nano Lett. 4, 1323 (2004).
[CrossRef]

Opt. Express (2)

Philos. Mag. (1)

Rayleigh, Philos. Mag. 12(73), 81 (1881).
[CrossRef]

Phys. Rev. B (1)

P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
[CrossRef]

Solid State Commun. (1)

H. Xu, H. Li, Z. Liu, S. Xie, X. Zhou, and J. Wu, Solid State Commun. 151, 759 (2011).
[CrossRef]

Other (1)

O. J. F. Martin, in Optical Nanotechnologies, Topics in Applied Physics, J. Tominaga and D. P. Tsai, eds. (Springer, 2003), pp. 183–210.

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Figures (6)

Fig. 1.
Fig. 1.

(a) TSCSs and (b) ACSs versus the wavelength, for an Ag tube of the inner radius a=50nm in free space. For the thickness h see the inset. Inset shows cross section of the tube.

Fig. 2.
Fig. 2.

In-resonance near-zone magnetic field patterns for an Ag tube with a=50nm and h=10nm located in free space, at the wavelengths of (a) λ=545, (b) 437, (c) 392, and (d) 327 nm.

Fig. 3.
Fig. 3.

Reliefs of (a) TSCS and (b) ACS as a function of the wavelength and the nanotube thickness for an Ag tube of the inner radius a=50nm.

Fig. 4.
Fig. 4.

Reliefs of (a) TSCS and (b) ACS as a function of the wavelength and the nanotube inner radius for an Ag tube of the wall thickness h=10nm.

Fig. 5.
Fig. 5.

Reliefs of ECS (a) as a function of the wavelength and the wall thickness, for a nanotube with a=50nm, and (b) as a function of the wavelength and the inner radius, for a nanotube with h=10nm. Silver nanotube has a glass core and is immersed in water, as explained in text.

Fig. 6.
Fig. 6.

Reliefs of ECS as a function of λ and the outer medium refractive index, for a nanotube having the wall thickness h=10nm and the inner radius (a) a=80, (b) 50, and (c) 20 nm.

Tables (1)

Tables Icon

Table 1. Sensitivities of Hybrid LSPs

Equations (3)

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

(aa+h)2m+(εout+εAg)(εAg+εin)(εoutεAg)(εAgεin)+O[k2(a+h)2ε]=0,
εAg(λPm(±))ε±2ε[(1+h/a)m±1]1,m=1,2,
εAg(λPm(±))(εin+εout)2ξm±[(εin+εout)24ξm2εinεout]1/2,

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