Abstract

We apply the plasmon hybridization (PH) method to a general metallic nanowire/double-shell structure, providing a simple and intuitive description of the plasmon excitations of the system. In special cases, we find explicit forms of surface plasmon oscillations, in terms of interaction between the bare plasmon modes of the individual surfaces of the coated metallic core. In particular, we show that when the longitudinal wave vector is zero (q=0), the PH of core/double-nanotubes has a behavior similar to coated metallic nanospheres. We present numerical results displaying how the plasmon excitations of the system depend on the dielectric difference between the metallic core and metallic shell.

© 2012 Optical Society of America

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References

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  1. L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).
  2. S. A. Maier, Plasmonics: Fundamentals and Applications (Springer, 2007).
  3. I. Villo-Perez, Z. L. Miskovic, and N. R. Arista, “Plasmon spectra of nano-structures: a hydrodynamic model,” in A. Aldea and V. Barsan, eds., Trends in Nanophysics (Springer, 2010), pp. 217–254.
  4. E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
    [CrossRef]
  5. E. Prodan and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys 120, 5444–5454 (2004).
    [CrossRef]
  6. A. Moradi, “Plasmon hybridization in metallic nanotubes,” J. Phys. Chem. Sol. 69, 2936–2938 (2008).
    [CrossRef]
  7. A. Moradi, “Plasmon hybridization in metallic nanotubes with a nonconcentric core,” Opt. Commun. 282, 3368–3370 (2009).
    [CrossRef]
  8. A. Moradi, “Plasmon hybridization in parallel nano-wire systems,” Phys. Plasmas 18, 064508 (2011).
    [CrossRef]
  9. M. D. Turner, Md. M. Hossain, and M. Gu, “The effects of retardation on plasmon hybridization within metallic nanostructures,” New J. Phys. 12, 083062 (2010).
    [CrossRef]
  10. R. M. Abraham Ekeroth, M. Lester, L. B. Scaffardi, and D. C. Schinca, “Metallic nanotubes characterization via surface plasmon excitation,” Plasmonics 6, 435–444 (2011).
    [CrossRef]
  11. F. Tam, A. L. Chen, J. Kundu, H. Wang, and N. J. Halas, “Mesoscopic nanoshells: geometry-dependent plasmon resonances beyond the quasistatic limit,” J. Chem. Phys. 127, 204703 (2007).
    [CrossRef]
  12. A. Passian, R. H. Ritchie, A. L. Lereu, T. Thundat, and T. L. Ferrell, “Curvature effects in surface plasmon dispersion and coupling,” Phys. Rev. B 71, 115425 (2005).
    [CrossRef]
  13. K. Bao, H. Sobhani, and P. Nordlander, “Plasmon hybridization for real metals,” Chin. Sci. Bull. 55, 2629–2634 (2010).
    [CrossRef]
  14. Y. Zhang, G. T. Fei, and L. D. Zhang, “Plasmon hybridization in coated metallic nanosphere,” J. Appl. Phys. 109, 054315 (2011).
    [CrossRef]
  15. H. Xu, H. Li, Zh. Liu, S. Xie, X. Zhou, X. Peng, and X. Xu, “Effects of symmetry breaking on plasmon resonance in a noncoaxial nanotube and nanotube dimer,” J. Opt. Soc. Am. A 28, 1662–1667 (2011).
    [CrossRef]
  16. H. Xu, H. Li, Zh. Liu, S. Xie, X. Zhou, and J. Wu, “Adjustable plasmon resonance in the coaxial gold nanotubes,” Solid State Commun. 151, 759–762 (2011).
    [CrossRef]
  17. D. J. Mowbray, Z. L. Miskovic, F. O. Goodman, and Y.-N. Wang, “Interactions of fast ions with carbon nanotubes: two-fluid model,” Phys. Rev. B 70, 195418 (2004).
    [CrossRef]
  18. D. J. Mowbray, Z. L. Miskovic, and F. O. Goodman, “Ion interactions with carbon nanotubes in dielectric media,” Phys. Rev. B 74, 195435 (2006).
    [CrossRef]
  19. S. Kawata, Near-Field Optics and Surface Plasmon Polaritons (Springer, 2001).

2011 (5)

A. Moradi, “Plasmon hybridization in parallel nano-wire systems,” Phys. Plasmas 18, 064508 (2011).
[CrossRef]

R. M. Abraham Ekeroth, M. Lester, L. B. Scaffardi, and D. C. Schinca, “Metallic nanotubes characterization via surface plasmon excitation,” Plasmonics 6, 435–444 (2011).
[CrossRef]

Y. Zhang, G. T. Fei, and L. D. Zhang, “Plasmon hybridization in coated metallic nanosphere,” J. Appl. Phys. 109, 054315 (2011).
[CrossRef]

H. Xu, H. Li, Zh. Liu, S. Xie, X. Zhou, and J. Wu, “Adjustable plasmon resonance in the coaxial gold nanotubes,” Solid State Commun. 151, 759–762 (2011).
[CrossRef]

H. Xu, H. Li, Zh. Liu, S. Xie, X. Zhou, X. Peng, and X. Xu, “Effects of symmetry breaking on plasmon resonance in a noncoaxial nanotube and nanotube dimer,” J. Opt. Soc. Am. A 28, 1662–1667 (2011).
[CrossRef]

2010 (2)

K. Bao, H. Sobhani, and P. Nordlander, “Plasmon hybridization for real metals,” Chin. Sci. Bull. 55, 2629–2634 (2010).
[CrossRef]

M. D. Turner, Md. M. Hossain, and M. Gu, “The effects of retardation on plasmon hybridization within metallic nanostructures,” New J. Phys. 12, 083062 (2010).
[CrossRef]

2009 (1)

A. Moradi, “Plasmon hybridization in metallic nanotubes with a nonconcentric core,” Opt. Commun. 282, 3368–3370 (2009).
[CrossRef]

2008 (1)

A. Moradi, “Plasmon hybridization in metallic nanotubes,” J. Phys. Chem. Sol. 69, 2936–2938 (2008).
[CrossRef]

2007 (1)

F. Tam, A. L. Chen, J. Kundu, H. Wang, and N. J. Halas, “Mesoscopic nanoshells: geometry-dependent plasmon resonances beyond the quasistatic limit,” J. Chem. Phys. 127, 204703 (2007).
[CrossRef]

2006 (1)

D. J. Mowbray, Z. L. Miskovic, and F. O. Goodman, “Ion interactions with carbon nanotubes in dielectric media,” Phys. Rev. B 74, 195435 (2006).
[CrossRef]

2005 (1)

A. Passian, R. H. Ritchie, A. L. Lereu, T. Thundat, and T. L. Ferrell, “Curvature effects in surface plasmon dispersion and coupling,” Phys. Rev. B 71, 115425 (2005).
[CrossRef]

2004 (2)

E. Prodan and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys 120, 5444–5454 (2004).
[CrossRef]

D. J. Mowbray, Z. L. Miskovic, F. O. Goodman, and Y.-N. Wang, “Interactions of fast ions with carbon nanotubes: two-fluid model,” Phys. Rev. B 70, 195418 (2004).
[CrossRef]

2003 (1)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[CrossRef]

Abraham Ekeroth, R. M.

R. M. Abraham Ekeroth, M. Lester, L. B. Scaffardi, and D. C. Schinca, “Metallic nanotubes characterization via surface plasmon excitation,” Plasmonics 6, 435–444 (2011).
[CrossRef]

Arista, N. R.

I. Villo-Perez, Z. L. Miskovic, and N. R. Arista, “Plasmon spectra of nano-structures: a hydrodynamic model,” in A. Aldea and V. Barsan, eds., Trends in Nanophysics (Springer, 2010), pp. 217–254.

Bao, K.

K. Bao, H. Sobhani, and P. Nordlander, “Plasmon hybridization for real metals,” Chin. Sci. Bull. 55, 2629–2634 (2010).
[CrossRef]

Chen, A. L.

F. Tam, A. L. Chen, J. Kundu, H. Wang, and N. J. Halas, “Mesoscopic nanoshells: geometry-dependent plasmon resonances beyond the quasistatic limit,” J. Chem. Phys. 127, 204703 (2007).
[CrossRef]

Fei, G. T.

Y. Zhang, G. T. Fei, and L. D. Zhang, “Plasmon hybridization in coated metallic nanosphere,” J. Appl. Phys. 109, 054315 (2011).
[CrossRef]

Ferrell, T. L.

A. Passian, R. H. Ritchie, A. L. Lereu, T. Thundat, and T. L. Ferrell, “Curvature effects in surface plasmon dispersion and coupling,” Phys. Rev. B 71, 115425 (2005).
[CrossRef]

Goodman, F. O.

D. J. Mowbray, Z. L. Miskovic, and F. O. Goodman, “Ion interactions with carbon nanotubes in dielectric media,” Phys. Rev. B 74, 195435 (2006).
[CrossRef]

D. J. Mowbray, Z. L. Miskovic, F. O. Goodman, and Y.-N. Wang, “Interactions of fast ions with carbon nanotubes: two-fluid model,” Phys. Rev. B 70, 195418 (2004).
[CrossRef]

Gu, M.

M. D. Turner, Md. M. Hossain, and M. Gu, “The effects of retardation on plasmon hybridization within metallic nanostructures,” New J. Phys. 12, 083062 (2010).
[CrossRef]

Halas, N. J.

F. Tam, A. L. Chen, J. Kundu, H. Wang, and N. J. Halas, “Mesoscopic nanoshells: geometry-dependent plasmon resonances beyond the quasistatic limit,” J. Chem. Phys. 127, 204703 (2007).
[CrossRef]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[CrossRef]

Hecht, B.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

Kawata, S.

S. Kawata, Near-Field Optics and Surface Plasmon Polaritons (Springer, 2001).

Kundu, J.

F. Tam, A. L. Chen, J. Kundu, H. Wang, and N. J. Halas, “Mesoscopic nanoshells: geometry-dependent plasmon resonances beyond the quasistatic limit,” J. Chem. Phys. 127, 204703 (2007).
[CrossRef]

Lereu, A. L.

A. Passian, R. H. Ritchie, A. L. Lereu, T. Thundat, and T. L. Ferrell, “Curvature effects in surface plasmon dispersion and coupling,” Phys. Rev. B 71, 115425 (2005).
[CrossRef]

Lester, M.

R. M. Abraham Ekeroth, M. Lester, L. B. Scaffardi, and D. C. Schinca, “Metallic nanotubes characterization via surface plasmon excitation,” Plasmonics 6, 435–444 (2011).
[CrossRef]

Li, H.

H. Xu, H. Li, Zh. Liu, S. Xie, X. Zhou, X. Peng, and X. Xu, “Effects of symmetry breaking on plasmon resonance in a noncoaxial nanotube and nanotube dimer,” J. Opt. Soc. Am. A 28, 1662–1667 (2011).
[CrossRef]

H. Xu, H. Li, Zh. Liu, S. Xie, X. Zhou, and J. Wu, “Adjustable plasmon resonance in the coaxial gold nanotubes,” Solid State Commun. 151, 759–762 (2011).
[CrossRef]

Liu, Zh.

H. Xu, H. Li, Zh. Liu, S. Xie, X. Zhou, and J. Wu, “Adjustable plasmon resonance in the coaxial gold nanotubes,” Solid State Commun. 151, 759–762 (2011).
[CrossRef]

H. Xu, H. Li, Zh. Liu, S. Xie, X. Zhou, X. Peng, and X. Xu, “Effects of symmetry breaking on plasmon resonance in a noncoaxial nanotube and nanotube dimer,” J. Opt. Soc. Am. A 28, 1662–1667 (2011).
[CrossRef]

M. Hossain, Md.

M. D. Turner, Md. M. Hossain, and M. Gu, “The effects of retardation on plasmon hybridization within metallic nanostructures,” New J. Phys. 12, 083062 (2010).
[CrossRef]

Maier, S. A.

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

Miskovic, Z. L.

D. J. Mowbray, Z. L. Miskovic, and F. O. Goodman, “Ion interactions with carbon nanotubes in dielectric media,” Phys. Rev. B 74, 195435 (2006).
[CrossRef]

D. J. Mowbray, Z. L. Miskovic, F. O. Goodman, and Y.-N. Wang, “Interactions of fast ions with carbon nanotubes: two-fluid model,” Phys. Rev. B 70, 195418 (2004).
[CrossRef]

I. Villo-Perez, Z. L. Miskovic, and N. R. Arista, “Plasmon spectra of nano-structures: a hydrodynamic model,” in A. Aldea and V. Barsan, eds., Trends in Nanophysics (Springer, 2010), pp. 217–254.

Moradi, A.

A. Moradi, “Plasmon hybridization in parallel nano-wire systems,” Phys. Plasmas 18, 064508 (2011).
[CrossRef]

A. Moradi, “Plasmon hybridization in metallic nanotubes with a nonconcentric core,” Opt. Commun. 282, 3368–3370 (2009).
[CrossRef]

A. Moradi, “Plasmon hybridization in metallic nanotubes,” J. Phys. Chem. Sol. 69, 2936–2938 (2008).
[CrossRef]

Mowbray, D. J.

D. J. Mowbray, Z. L. Miskovic, and F. O. Goodman, “Ion interactions with carbon nanotubes in dielectric media,” Phys. Rev. B 74, 195435 (2006).
[CrossRef]

D. J. Mowbray, Z. L. Miskovic, F. O. Goodman, and Y.-N. Wang, “Interactions of fast ions with carbon nanotubes: two-fluid model,” Phys. Rev. B 70, 195418 (2004).
[CrossRef]

Nordlander, P.

K. Bao, H. Sobhani, and P. Nordlander, “Plasmon hybridization for real metals,” Chin. Sci. Bull. 55, 2629–2634 (2010).
[CrossRef]

E. Prodan and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys 120, 5444–5454 (2004).
[CrossRef]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[CrossRef]

Novotny, L.

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

Passian, A.

A. Passian, R. H. Ritchie, A. L. Lereu, T. Thundat, and T. L. Ferrell, “Curvature effects in surface plasmon dispersion and coupling,” Phys. Rev. B 71, 115425 (2005).
[CrossRef]

Peng, X.

Prodan, E.

E. Prodan and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys 120, 5444–5454 (2004).
[CrossRef]

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[CrossRef]

Radloff, C.

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[CrossRef]

Ritchie, R. H.

A. Passian, R. H. Ritchie, A. L. Lereu, T. Thundat, and T. L. Ferrell, “Curvature effects in surface plasmon dispersion and coupling,” Phys. Rev. B 71, 115425 (2005).
[CrossRef]

Scaffardi, L. B.

R. M. Abraham Ekeroth, M. Lester, L. B. Scaffardi, and D. C. Schinca, “Metallic nanotubes characterization via surface plasmon excitation,” Plasmonics 6, 435–444 (2011).
[CrossRef]

Schinca, D. C.

R. M. Abraham Ekeroth, M. Lester, L. B. Scaffardi, and D. C. Schinca, “Metallic nanotubes characterization via surface plasmon excitation,” Plasmonics 6, 435–444 (2011).
[CrossRef]

Sobhani, H.

K. Bao, H. Sobhani, and P. Nordlander, “Plasmon hybridization for real metals,” Chin. Sci. Bull. 55, 2629–2634 (2010).
[CrossRef]

Tam, F.

F. Tam, A. L. Chen, J. Kundu, H. Wang, and N. J. Halas, “Mesoscopic nanoshells: geometry-dependent plasmon resonances beyond the quasistatic limit,” J. Chem. Phys. 127, 204703 (2007).
[CrossRef]

Thundat, T.

A. Passian, R. H. Ritchie, A. L. Lereu, T. Thundat, and T. L. Ferrell, “Curvature effects in surface plasmon dispersion and coupling,” Phys. Rev. B 71, 115425 (2005).
[CrossRef]

Turner, M. D.

M. D. Turner, Md. M. Hossain, and M. Gu, “The effects of retardation on plasmon hybridization within metallic nanostructures,” New J. Phys. 12, 083062 (2010).
[CrossRef]

Villo-Perez, I.

I. Villo-Perez, Z. L. Miskovic, and N. R. Arista, “Plasmon spectra of nano-structures: a hydrodynamic model,” in A. Aldea and V. Barsan, eds., Trends in Nanophysics (Springer, 2010), pp. 217–254.

Wang, H.

F. Tam, A. L. Chen, J. Kundu, H. Wang, and N. J. Halas, “Mesoscopic nanoshells: geometry-dependent plasmon resonances beyond the quasistatic limit,” J. Chem. Phys. 127, 204703 (2007).
[CrossRef]

Wang, Y.-N.

D. J. Mowbray, Z. L. Miskovic, F. O. Goodman, and Y.-N. Wang, “Interactions of fast ions with carbon nanotubes: two-fluid model,” Phys. Rev. B 70, 195418 (2004).
[CrossRef]

Wu, J.

H. Xu, H. Li, Zh. Liu, S. Xie, X. Zhou, and J. Wu, “Adjustable plasmon resonance in the coaxial gold nanotubes,” Solid State Commun. 151, 759–762 (2011).
[CrossRef]

Xie, S.

H. Xu, H. Li, Zh. Liu, S. Xie, X. Zhou, and J. Wu, “Adjustable plasmon resonance in the coaxial gold nanotubes,” Solid State Commun. 151, 759–762 (2011).
[CrossRef]

H. Xu, H. Li, Zh. Liu, S. Xie, X. Zhou, X. Peng, and X. Xu, “Effects of symmetry breaking on plasmon resonance in a noncoaxial nanotube and nanotube dimer,” J. Opt. Soc. Am. A 28, 1662–1667 (2011).
[CrossRef]

Xu, H.

H. Xu, H. Li, Zh. Liu, S. Xie, X. Zhou, X. Peng, and X. Xu, “Effects of symmetry breaking on plasmon resonance in a noncoaxial nanotube and nanotube dimer,” J. Opt. Soc. Am. A 28, 1662–1667 (2011).
[CrossRef]

H. Xu, H. Li, Zh. Liu, S. Xie, X. Zhou, and J. Wu, “Adjustable plasmon resonance in the coaxial gold nanotubes,” Solid State Commun. 151, 759–762 (2011).
[CrossRef]

Xu, X.

Zhang, L. D.

Y. Zhang, G. T. Fei, and L. D. Zhang, “Plasmon hybridization in coated metallic nanosphere,” J. Appl. Phys. 109, 054315 (2011).
[CrossRef]

Zhang, Y.

Y. Zhang, G. T. Fei, and L. D. Zhang, “Plasmon hybridization in coated metallic nanosphere,” J. Appl. Phys. 109, 054315 (2011).
[CrossRef]

Zhou, X.

H. Xu, H. Li, Zh. Liu, S. Xie, X. Zhou, X. Peng, and X. Xu, “Effects of symmetry breaking on plasmon resonance in a noncoaxial nanotube and nanotube dimer,” J. Opt. Soc. Am. A 28, 1662–1667 (2011).
[CrossRef]

H. Xu, H. Li, Zh. Liu, S. Xie, X. Zhou, and J. Wu, “Adjustable plasmon resonance in the coaxial gold nanotubes,” Solid State Commun. 151, 759–762 (2011).
[CrossRef]

Chin. Sci. Bull. (1)

K. Bao, H. Sobhani, and P. Nordlander, “Plasmon hybridization for real metals,” Chin. Sci. Bull. 55, 2629–2634 (2010).
[CrossRef]

J. Appl. Phys. (1)

Y. Zhang, G. T. Fei, and L. D. Zhang, “Plasmon hybridization in coated metallic nanosphere,” J. Appl. Phys. 109, 054315 (2011).
[CrossRef]

J. Chem. Phys (1)

E. Prodan and P. Nordlander, “Plasmon hybridization in spherical nanoparticles,” J. Chem. Phys 120, 5444–5454 (2004).
[CrossRef]

J. Chem. Phys. (1)

F. Tam, A. L. Chen, J. Kundu, H. Wang, and N. J. Halas, “Mesoscopic nanoshells: geometry-dependent plasmon resonances beyond the quasistatic limit,” J. Chem. Phys. 127, 204703 (2007).
[CrossRef]

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

J. Phys. Chem. Sol. (1)

A. Moradi, “Plasmon hybridization in metallic nanotubes,” J. Phys. Chem. Sol. 69, 2936–2938 (2008).
[CrossRef]

New J. Phys. (1)

M. D. Turner, Md. M. Hossain, and M. Gu, “The effects of retardation on plasmon hybridization within metallic nanostructures,” New J. Phys. 12, 083062 (2010).
[CrossRef]

Opt. Commun. (1)

A. Moradi, “Plasmon hybridization in metallic nanotubes with a nonconcentric core,” Opt. Commun. 282, 3368–3370 (2009).
[CrossRef]

Phys. Plasmas (1)

A. Moradi, “Plasmon hybridization in parallel nano-wire systems,” Phys. Plasmas 18, 064508 (2011).
[CrossRef]

Phys. Rev. B (3)

D. J. Mowbray, Z. L. Miskovic, F. O. Goodman, and Y.-N. Wang, “Interactions of fast ions with carbon nanotubes: two-fluid model,” Phys. Rev. B 70, 195418 (2004).
[CrossRef]

D. J. Mowbray, Z. L. Miskovic, and F. O. Goodman, “Ion interactions with carbon nanotubes in dielectric media,” Phys. Rev. B 74, 195435 (2006).
[CrossRef]

A. Passian, R. H. Ritchie, A. L. Lereu, T. Thundat, and T. L. Ferrell, “Curvature effects in surface plasmon dispersion and coupling,” Phys. Rev. B 71, 115425 (2005).
[CrossRef]

Plasmonics (1)

R. M. Abraham Ekeroth, M. Lester, L. B. Scaffardi, and D. C. Schinca, “Metallic nanotubes characterization via surface plasmon excitation,” Plasmonics 6, 435–444 (2011).
[CrossRef]

Science (1)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science 302, 419–422 (2003).
[CrossRef]

Solid State Commun. (1)

H. Xu, H. Li, Zh. Liu, S. Xie, X. Zhou, and J. Wu, “Adjustable plasmon resonance in the coaxial gold nanotubes,” Solid State Commun. 151, 759–762 (2011).
[CrossRef]

Other (4)

S. Kawata, Near-Field Optics and Surface Plasmon Polaritons (Springer, 2001).

L. Novotny and B. Hecht, Principles of Nano-Optics (Cambridge University, 2006).

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

I. Villo-Perez, Z. L. Miskovic, and N. R. Arista, “Plasmon spectra of nano-structures: a hydrodynamic model,” in A. Aldea and V. Barsan, eds., Trends in Nanophysics (Springer, 2010), pp. 217–254.

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Figures (7)

Fig. 1.
Fig. 1.

Top view of an infinitely long nanowire/double-shell structure. The radius from inner to outer is a1, a2, and a3, respectively. d=a3a2 is the metallic tube thickness, and δ=a2a1 is the separation between the core and metal tubes.

Fig. 2.
Fig. 2.

Energy-level diagram describing PH in a composite metal core/metal NT system. Stage 1: (left) interaction between the capillary and wire plasmons of the metallic NT, yielding a HF (antisymmetric) and a LF (symmetric) plasmon. Stage 2: (right) interaction between the HF-NT plasmon and the metal core plasmon branches, yielding symmetrically coupled core-(HF-NT) plasmons. Stage 3: interaction between the metal core plasmon and the LF-NT plasmon, yielding antisymmetrically coupled and symmetrically coupled core-(LF-NT) plasmons.

Fig. 3.
Fig. 3.

Plasmon energy ω in electron volts of a gold NT of radii a2=8nm and a3=9nm (black solid lines), a gold nanowire of radius a1=7nm (red solid line) and the composite gold NT and gold core system (brown solid lines), (a) for m=0 and (b) for m=1, using ωgold=1.37×1016Hz plotted versus q in 1/nm.

Fig. 4.
Fig. 4.

Plasmon energy ω in electron volts of a metal NT of radii a2=8nm and a3=9nm (black solid lines), a metal nanowire of radius a1=7nm (red solid line), and the composite metal NT and metal core system (brown solid lines), for m=0 (a) when ωp1=ωsilver, ωp3=ωgold and (b) when ωp1=ωgold, ωp3=ωsilver, using ωgold=1.37×1016Hz and ωsilver=1.22×1016Hz plotted versus q in 1/nm.

Fig. 5.
Fig. 5.

Plasmon energy ω in electron volts of a composite gold NT and gold core system, for q=0 and m=2, using ωp=1.37×1016Hz, plotted versus x=a1/a2 and y=a2/a3.

Fig. 6.
Fig. 6.

Plasmon energy ω in electron volts of a composite gold NT and gold core system, for q=0 and m=2, using ωp=1.37×1016Hz, plotted versus δ and d, when a1=7nm.

Fig. 7.
Fig. 7.

Plasmon energy ω in electron volts of a composite gold NT and gold core system, for m=0, using ωp=1.37×1016Hz, when ε2=1, ε4=1 (brown solid lines) and ε2=3.9, ε4=1 (black solid lines) plotted versus q in 1/nm.

Equations (15)

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

εj(ω)=1ωpj2ω2+γj2+iωpj2γjω(ω2+γj2),
ω2[(ω2Ω+2)(ω2Ω2)Ωcore2ω2+Ωcore2(ΓΩw2+ΞΩc2)+Ωw2Ωc2]=ΞΘΩw2Ωc2Ωcore2,
Γ=1Im(qa1)Km(qa3)Im(qa3)Km(qa1),
Ξ=1Im(qa1)Km(qa2)Im(qa2)Km(qa1),
Θ=1Im(qa2)Km(qa3)Im(qa3)Km(qa2),
Ωcore2=ωp12(qa1)Im(qa1)Km(qa1)
Ωc2=ωp32(qa2)Im(qa2)Km(qa2)
Ωw2=ωp32(qa3)Im(qa3)Km(qa3)
Ω±2=Ωw2+Ωc22±(Ωw2Ωc22)2+ΩcΩw(1Θ)
ω0=ωp2,
ω±(q=0,m0)=ωp21±(a1a2)2m+(a2a3)2m(a1a3)2m,
ω±2=Ω+2+Ω2+Ωcore22±(Ω+2+Ω2+Ωcore22)2Δ,
Δ=Ω+2Ω2+Ωw2Ωc2+ΓΩw2Ωcore2,
ω±(q=0,m0)=12ωp12+2ωp32±ωp14+4ωp32(ωp32ωp12)(a2a3)2m.
|Im(qa1)(ε1ε2)ε1Im(qa1)Km(qa1)Im(qa1)ε2Km(qa1)0ε2Im(qa2)ε3Im(qa2)Km(qa2)Km(qa2)Km(qa2)(ε2ε3)ε3(qa2)Km(qa2)Im(qa2)Km(qa3)Km(qa2)(ε3ε4)Km(qa3)(ε3ε4)ϒ+Im(qa2)Km(qa3)Km(qa2)(ε4ε3)|=0,

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