Abstract

We numerically investigate the band structure and guided modes within arrays of metallic nanowires. We show that bandgaps appear for a range of array geometries and that these can be used to guide light in these structures. Values of attenuation as low as 1.7dBcm are predicted for arrays of silver wires at communications wavelengths. This is more than 100 times smaller than the attenuation of the surface plasmon polariton modes on a single silver nanowire.

© 2007 Optical Society of America

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References

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  1. P. St.J. Russell, J. Lightwave Technol. 24, 4729 (2006).
    [CrossRef]
  2. B. T. Kuhlmey, K. Pathmanandavel, and R. C. McPhedran, Opt. Express 14, 10851 (2006).
    [CrossRef] [PubMed]
  3. P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, Science 311, 1583 (2006).
    [CrossRef] [PubMed]
  4. M. A. Ordal, L. L. Long, R. J. Bell, S. E. Bell, R. R. Bell, R. W. Alexander, and C. A. Ward, Appl. Opt. 22, 1099 (1983).
    [CrossRef] [PubMed]
  5. I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
    [CrossRef]
  6. G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).
  7. T. P. White, B. T. Kuhlmey, R. C. McPhedran, D. Maystre, G. Renversez, C. M. de Sterke, and L. C. Botten, J. Opt. Soc. Am. B 19, 2322 (2002).
    [CrossRef]
  8. P. St.J. Russell, T. Birks, and F. D. Lloyd-Lucas, Photonic Bloch Waves and Photonic Band Gaps (Plenum, 1995), p. 607.
  9. T. A. Birks, G. J. Pearce, and D. M. Bird, Opt. Express 14, 9483 (2006).
    [CrossRef] [PubMed]
  10. A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984), pp. 473-477.

2006 (4)

P. St.J. Russell, J. Lightwave Technol. 24, 4729 (2006).
[CrossRef]

B. T. Kuhlmey, K. Pathmanandavel, and R. C. McPhedran, Opt. Express 14, 10851 (2006).
[CrossRef] [PubMed]

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, Science 311, 1583 (2006).
[CrossRef] [PubMed]

T. A. Birks, G. J. Pearce, and D. M. Bird, Opt. Express 14, 9483 (2006).
[CrossRef] [PubMed]

2002 (1)

2000 (1)

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

1983 (1)

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

Alexander, R. W.

Amezcua-Correa, A.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, Science 311, 1583 (2006).
[CrossRef] [PubMed]

Badding, J. V.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, Science 311, 1583 (2006).
[CrossRef] [PubMed]

Baril, N. F.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, Science 311, 1583 (2006).
[CrossRef] [PubMed]

Bell, R. J.

Bell, R. R.

Bell, S. E.

Bird, D. M.

Birks, T.

P. St.J. Russell, T. Birks, and F. D. Lloyd-Lucas, Photonic Bloch Waves and Photonic Band Gaps (Plenum, 1995), p. 607.

Birks, T. A.

Biswas, R.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Botten, L. C.

Crespi, V. H.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, Science 311, 1583 (2006).
[CrossRef] [PubMed]

de Sterke, C. M.

El-Kady, I.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Finlayson, C. E.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, Science 311, 1583 (2006).
[CrossRef] [PubMed]

Gopalan, V.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, Science 311, 1583 (2006).
[CrossRef] [PubMed]

Hayes, J. R.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, Science 311, 1583 (2006).
[CrossRef] [PubMed]

Ho, K. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Jackson, B. R.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, Science 311, 1583 (2006).
[CrossRef] [PubMed]

Kuhlmey, B. T.

Lloyd-Lucas, F. D.

P. St.J. Russell, T. Birks, and F. D. Lloyd-Lucas, Photonic Bloch Waves and Photonic Band Gaps (Plenum, 1995), p. 607.

Long, L. L.

Margine, E. R.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, Science 311, 1583 (2006).
[CrossRef] [PubMed]

Maystre, D.

McPhedran, R. C.

Ordal, M. A.

Pathmanandavel, K.

Pearce, G. J.

Renversez, G.

Russell, P. St.J.

P. St.J. Russell, J. Lightwave Technol. 24, 4729 (2006).
[CrossRef]

P. St.J. Russell, T. Birks, and F. D. Lloyd-Lucas, Photonic Bloch Waves and Photonic Band Gaps (Plenum, 1995), p. 607.

Sazio, P. J. A.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, Science 311, 1583 (2006).
[CrossRef] [PubMed]

Scheidemantel, T. J.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, Science 311, 1583 (2006).
[CrossRef] [PubMed]

Sigalas, M. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Soukoulis, C. M.

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Ward, C. A.

White, T. P.

Won, D.-J.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, Science 311, 1583 (2006).
[CrossRef] [PubMed]

Yariv, A.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984), pp. 473-477.

Yeh, P.

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984), pp. 473-477.

Zhang, F.

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, Science 311, 1583 (2006).
[CrossRef] [PubMed]

Appl. Opt. (1)

J. Lightwave Technol. (1)

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

Opt. Express (2)

Phys. Rev. B (1)

I. El-Kady, M. M. Sigalas, R. Biswas, K. M. Ho, and C. M. Soukoulis, Phys. Rev. B 62, 15299 (2000).
[CrossRef]

Science (1)

P. J. A. Sazio, A. Amezcua-Correa, C. E. Finlayson, J. R. Hayes, T. J. Scheidemantel, N. F. Baril, B. R. Jackson, D.-J. Won, F. Zhang, E. R. Margine, V. Gopalan, V. H. Crespi, and J. V. Badding, Science 311, 1583 (2006).
[CrossRef] [PubMed]

Other (3)

G. P. Agrawal, Nonlinear Fiber Optics (Academic, 2001).

A. Yariv and P. Yeh, Optical Waves in Crystals (Wiley, 1984), pp. 473-477.

P. St.J. Russell, T. Birks, and F. D. Lloyd-Lucas, Photonic Bloch Waves and Photonic Band Gaps (Plenum, 1995), p. 607.

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Figures (3)

Fig. 1
Fig. 1

Presence of bandgaps (gray) as a function of normalized frequency k 0 Λ in a silica matrix of refractive index n, for different wire diameters d. All calculations were performed for the optical properties of silver and silica at λ 0 = 1.55 μ m , neglecting material loss. The plasmon modes appear as resonances above the light line. Because of the strong interaction between the plasmon modes, large normalized frequencies ( k 0 Λ > 30 ) are necessary to establish a gap below the light line.

Fig. 2
Fig. 2

(a) Fundamental guided mode and bandgaps (gray regions) of an array of nanowires consisting of silver cylinders in a silica matrix, with d = 1.5 μ m and Λ = 10 μ m . (b) Attenuation in the fundamental guided mode (solid), as compared with the first three plasmon modes of a single wire (dotted). (c) Magnified view of the anticrossing point. The imaginary part of the effective index ( Im [ n eff ] ) is depicted as the shaded region on either side of the mode itself and shows the relative magnitude of the attenuation. (d) Real part of the Poynting vector of the guided mode at the anticrossing point, on the lower branch ( f = 253 THz , λ 0 = 1.18 μ m ). The closeup shows that the fields have a strongly quadrupolar dependence.

Fig. 3
Fig. 3

Total attenuation (top) and comparison of leakage and material loss (bottom) of the fundamental mode in structures possessing one, two, and three rings of wires surrounding the core. The leakage loss decreases rapidly with each successive layer, and the resulting total attenuation is dominated by the material loss.

Equations (2)

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ϵ m = ϵ ω p 2 ω 2 + i ω ω τ ,
ω p = 2 π × 2175 THz , ω τ = 2 π × 4.35 THz ,

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