Abstract

We demonstrate an efficient eigendecomposition method for analyzing the guided modes in metal nanoparticle chains. The proposed method has the advantage of simultaneously showing the dispersion relation and the mode quality. It can also separate the material properties from the geometrical properties. Its efficiency therefore does not depend on the complexity of the material polarizability. We used the method to analyze the guided modes of a single and a pair of metal nanoparticle chains. The rigorous dynamic dipole polarizability typically gives a redshift compared with the results obtained from the broadly used quasi-static dipole polarizability with radiation correction.

© 2007 Optical Society of America

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  1. M. Quinten, A. Leitner, J. R. Krenn, and F. R. Aussenegg, Opt. Lett. 23, 1331 (1998).
    [CrossRef]
  2. M. L. Brongersma, J. W. Hartman, and H. A. Atwater, Phys. Rev. B 62, R16356 (2000).
    [CrossRef]
  3. S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, Adv. Mater. (Weinheim, Ger.) 13, 1501 (2001).
    [CrossRef]
  4. S. A. Maier and H. A. Atwater, J. Appl. Phys. 98, 011101 (2005).
    [CrossRef]
  5. See, e.g., C. Girard, Rep. Prog. Phys. 68, 1883 (2005), and references cited therein.
    [CrossRef]
  6. S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. G. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
    [CrossRef] [PubMed]
  7. S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, Appl. Phys. Lett. 84, 3990 (2004).
    [CrossRef]
  8. R. Quidant, C. Girard, J. C. Weeber, and A. Dereux, Phys. Rev. B 69, 085407 (2004).
    [CrossRef]
  9. R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, Europhys. Lett. 57, 191 (2002).
    [CrossRef]
  10. D. S. Citrin, Opt. Lett. 31, 98 (2006).
    [CrossRef] [PubMed]
  11. M. Sukharev and T. Seideman, Nano Lett. 6, 715 (2006).
    [CrossRef] [PubMed]
  12. S. Zou and G. C. Schatz, Phys. Rev. B 74, 125111 (2006).
    [CrossRef]
  13. W. H. Weber and G. W. Ford, Phys. Rev. B 70, 125429 (2004).
    [CrossRef]
  14. A. F. Koenderink and A. Polman, Phys. Rev. B 74, 033402 (2006).
    [CrossRef]
  15. S. Y. Park and D. Stroud, Phys. Rev. B 69, 125418 (2004).
    [CrossRef]
  16. C. R. Simovski, A. J. Viitanen, and S. A. Tretyakov, Phys. Rev. E 72, 066606 (2005).
    [CrossRef]
  17. D. S. Citrin, Nano Lett. 4, 1561 (2004).
    [CrossRef]
  18. R. A. Shore and A. D. Yaghjian, Electron. Lett. 41, 578 (2005).
    [CrossRef]
  19. A comparison with the generalized Mie theory can show this.
  20. V. A. Markel and V. M. Shalaev, in Computational Studies of New Materials, D.A.Jelski and T.F.George, eds. (World Scientific, 1999), pp. 210-243.
  21. L. Zhou and S. T. Chui, Phys. Rev. B 74, 035419 (2006).
    [CrossRef]
  22. C. E. Dungey and C. F. Bohren, J. Opt. Soc. Am. A 8, 81 (1991).
    [CrossRef]
  23. V. A. Markel, J. Phys. B 38, L115 (2005).
    [CrossRef]
  24. See, e.g., C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  25. The eigenvectors, forming a complete set, are "normalized" in the sense that ⟨p̂kσ∣p̂k′σ′⟩=δσ,σ′∑n=−∞∞δ(k−k′+2nπ/a).

2006 (5)

M. Sukharev and T. Seideman, Nano Lett. 6, 715 (2006).
[CrossRef] [PubMed]

S. Zou and G. C. Schatz, Phys. Rev. B 74, 125111 (2006).
[CrossRef]

A. F. Koenderink and A. Polman, Phys. Rev. B 74, 033402 (2006).
[CrossRef]

L. Zhou and S. T. Chui, Phys. Rev. B 74, 035419 (2006).
[CrossRef]

D. S. Citrin, Opt. Lett. 31, 98 (2006).
[CrossRef] [PubMed]

2005 (5)

V. A. Markel, J. Phys. B 38, L115 (2005).
[CrossRef]

R. A. Shore and A. D. Yaghjian, Electron. Lett. 41, 578 (2005).
[CrossRef]

C. R. Simovski, A. J. Viitanen, and S. A. Tretyakov, Phys. Rev. E 72, 066606 (2005).
[CrossRef]

S. A. Maier and H. A. Atwater, J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

See, e.g., C. Girard, Rep. Prog. Phys. 68, 1883 (2005), and references cited therein.
[CrossRef]

2004 (5)

W. H. Weber and G. W. Ford, Phys. Rev. B 70, 125429 (2004).
[CrossRef]

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, Appl. Phys. Lett. 84, 3990 (2004).
[CrossRef]

R. Quidant, C. Girard, J. C. Weeber, and A. Dereux, Phys. Rev. B 69, 085407 (2004).
[CrossRef]

D. S. Citrin, Nano Lett. 4, 1561 (2004).
[CrossRef]

S. Y. Park and D. Stroud, Phys. Rev. B 69, 125418 (2004).
[CrossRef]

2003 (1)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. G. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

2002 (1)

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, Europhys. Lett. 57, 191 (2002).
[CrossRef]

2001 (1)

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, Adv. Mater. (Weinheim, Ger.) 13, 1501 (2001).
[CrossRef]

2000 (1)

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, Phys. Rev. B 62, R16356 (2000).
[CrossRef]

1998 (1)

1991 (1)

Atwater, H. A.

S. A. Maier and H. A. Atwater, J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. G. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, Adv. Mater. (Weinheim, Ger.) 13, 1501 (2001).
[CrossRef]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, Phys. Rev. B 62, R16356 (2000).
[CrossRef]

Aussenegg, F. R.

Barclay, P. E.

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, Appl. Phys. Lett. 84, 3990 (2004).
[CrossRef]

Bohren, C. F.

C. E. Dungey and C. F. Bohren, J. Opt. Soc. Am. A 8, 81 (1991).
[CrossRef]

See, e.g., C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Brongersma, M. L.

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, Adv. Mater. (Weinheim, Ger.) 13, 1501 (2001).
[CrossRef]

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, Phys. Rev. B 62, R16356 (2000).
[CrossRef]

Chen, Y.

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, Europhys. Lett. 57, 191 (2002).
[CrossRef]

Chui, S. T.

L. Zhou and S. T. Chui, Phys. Rev. B 74, 035419 (2006).
[CrossRef]

Citrin, D. S.

Dereux, A.

R. Quidant, C. Girard, J. C. Weeber, and A. Dereux, Phys. Rev. B 69, 085407 (2004).
[CrossRef]

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, Europhys. Lett. 57, 191 (2002).
[CrossRef]

Dungey, C. E.

Ford, G. W.

W. H. Weber and G. W. Ford, Phys. Rev. B 70, 125429 (2004).
[CrossRef]

Friedman, M. D.

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, Appl. Phys. Lett. 84, 3990 (2004).
[CrossRef]

Girard, C.

See, e.g., C. Girard, Rep. Prog. Phys. 68, 1883 (2005), and references cited therein.
[CrossRef]

R. Quidant, C. Girard, J. C. Weeber, and A. Dereux, Phys. Rev. B 69, 085407 (2004).
[CrossRef]

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, Europhys. Lett. 57, 191 (2002).
[CrossRef]

Harel, E.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. G. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

Hartman, J. W.

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, Phys. Rev. B 62, R16356 (2000).
[CrossRef]

Huffman, D. R.

See, e.g., C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Johnson, T. J.

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, Appl. Phys. Lett. 84, 3990 (2004).
[CrossRef]

Kik, P. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. G. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, Adv. Mater. (Weinheim, Ger.) 13, 1501 (2001).
[CrossRef]

Koel, B. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. G. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

Koenderink, A. F.

A. F. Koenderink and A. Polman, Phys. Rev. B 74, 033402 (2006).
[CrossRef]

Krenn, J. R.

Leitner, A.

Maier, S. A.

S. A. Maier and H. A. Atwater, J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, Appl. Phys. Lett. 84, 3990 (2004).
[CrossRef]

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. G. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, Adv. Mater. (Weinheim, Ger.) 13, 1501 (2001).
[CrossRef]

Markel, V. A.

V. A. Markel, J. Phys. B 38, L115 (2005).
[CrossRef]

V. A. Markel and V. M. Shalaev, in Computational Studies of New Materials, D.A.Jelski and T.F.George, eds. (World Scientific, 1999), pp. 210-243.

Meltzer, S.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. G. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, Adv. Mater. (Weinheim, Ger.) 13, 1501 (2001).
[CrossRef]

Painter, O.

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, Appl. Phys. Lett. 84, 3990 (2004).
[CrossRef]

Park, S. Y.

S. Y. Park and D. Stroud, Phys. Rev. B 69, 125418 (2004).
[CrossRef]

Peyrade, D.

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, Europhys. Lett. 57, 191 (2002).
[CrossRef]

Polman, A.

A. F. Koenderink and A. Polman, Phys. Rev. B 74, 033402 (2006).
[CrossRef]

Quidant, R.

R. Quidant, C. Girard, J. C. Weeber, and A. Dereux, Phys. Rev. B 69, 085407 (2004).
[CrossRef]

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, Europhys. Lett. 57, 191 (2002).
[CrossRef]

Quinten, M.

Requicha, A. A. G.

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. G. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, Adv. Mater. (Weinheim, Ger.) 13, 1501 (2001).
[CrossRef]

Schatz, G. C.

S. Zou and G. C. Schatz, Phys. Rev. B 74, 125111 (2006).
[CrossRef]

Seideman, T.

M. Sukharev and T. Seideman, Nano Lett. 6, 715 (2006).
[CrossRef] [PubMed]

Shalaev, V. M.

V. A. Markel and V. M. Shalaev, in Computational Studies of New Materials, D.A.Jelski and T.F.George, eds. (World Scientific, 1999), pp. 210-243.

Shore, R. A.

R. A. Shore and A. D. Yaghjian, Electron. Lett. 41, 578 (2005).
[CrossRef]

Simovski, C. R.

C. R. Simovski, A. J. Viitanen, and S. A. Tretyakov, Phys. Rev. E 72, 066606 (2005).
[CrossRef]

Stroud, D.

S. Y. Park and D. Stroud, Phys. Rev. B 69, 125418 (2004).
[CrossRef]

Sukharev, M.

M. Sukharev and T. Seideman, Nano Lett. 6, 715 (2006).
[CrossRef] [PubMed]

Tretyakov, S. A.

C. R. Simovski, A. J. Viitanen, and S. A. Tretyakov, Phys. Rev. E 72, 066606 (2005).
[CrossRef]

Viitanen, A. J.

C. R. Simovski, A. J. Viitanen, and S. A. Tretyakov, Phys. Rev. E 72, 066606 (2005).
[CrossRef]

Weber, W. H.

W. H. Weber and G. W. Ford, Phys. Rev. B 70, 125429 (2004).
[CrossRef]

Weeber, J. C.

R. Quidant, C. Girard, J. C. Weeber, and A. Dereux, Phys. Rev. B 69, 085407 (2004).
[CrossRef]

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, Europhys. Lett. 57, 191 (2002).
[CrossRef]

Yaghjian, A. D.

R. A. Shore and A. D. Yaghjian, Electron. Lett. 41, 578 (2005).
[CrossRef]

Zhou, L.

L. Zhou and S. T. Chui, Phys. Rev. B 74, 035419 (2006).
[CrossRef]

Zou, S.

S. Zou and G. C. Schatz, Phys. Rev. B 74, 125111 (2006).
[CrossRef]

Adv. Mater. (Weinheim, Ger.) (1)

S. A. Maier, M. L. Brongersma, P. G. Kik, S. Meltzer, A. A. G. Requicha, and H. A. Atwater, Adv. Mater. (Weinheim, Ger.) 13, 1501 (2001).
[CrossRef]

Appl. Phys. Lett. (1)

S. A. Maier, P. E. Barclay, T. J. Johnson, M. D. Friedman, and O. Painter, Appl. Phys. Lett. 84, 3990 (2004).
[CrossRef]

Electron. Lett. (1)

R. A. Shore and A. D. Yaghjian, Electron. Lett. 41, 578 (2005).
[CrossRef]

Europhys. Lett. (1)

R. Quidant, J. C. Weeber, A. Dereux, D. Peyrade, Y. Chen, and C. Girard, Europhys. Lett. 57, 191 (2002).
[CrossRef]

J. Appl. Phys. (1)

S. A. Maier and H. A. Atwater, J. Appl. Phys. 98, 011101 (2005).
[CrossRef]

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

J. Phys. B (1)

V. A. Markel, J. Phys. B 38, L115 (2005).
[CrossRef]

Nano Lett. (2)

D. S. Citrin, Nano Lett. 4, 1561 (2004).
[CrossRef]

M. Sukharev and T. Seideman, Nano Lett. 6, 715 (2006).
[CrossRef] [PubMed]

Nat. Mater. (1)

S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. G. Koel, and A. A. G. Requicha, Nat. Mater. 2, 229 (2003).
[CrossRef] [PubMed]

Opt. Lett. (2)

Phys. Rev. B (7)

M. L. Brongersma, J. W. Hartman, and H. A. Atwater, Phys. Rev. B 62, R16356 (2000).
[CrossRef]

S. Zou and G. C. Schatz, Phys. Rev. B 74, 125111 (2006).
[CrossRef]

W. H. Weber and G. W. Ford, Phys. Rev. B 70, 125429 (2004).
[CrossRef]

A. F. Koenderink and A. Polman, Phys. Rev. B 74, 033402 (2006).
[CrossRef]

S. Y. Park and D. Stroud, Phys. Rev. B 69, 125418 (2004).
[CrossRef]

L. Zhou and S. T. Chui, Phys. Rev. B 74, 035419 (2006).
[CrossRef]

R. Quidant, C. Girard, J. C. Weeber, and A. Dereux, Phys. Rev. B 69, 085407 (2004).
[CrossRef]

Phys. Rev. E (1)

C. R. Simovski, A. J. Viitanen, and S. A. Tretyakov, Phys. Rev. E 72, 066606 (2005).
[CrossRef]

Rep. Prog. Phys. (1)

See, e.g., C. Girard, Rep. Prog. Phys. 68, 1883 (2005), and references cited therein.
[CrossRef]

Other (4)

A comparison with the generalized Mie theory can show this.

V. A. Markel and V. M. Shalaev, in Computational Studies of New Materials, D.A.Jelski and T.F.George, eds. (World Scientific, 1999), pp. 210-243.

See, e.g., C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

The eigenvectors, forming a complete set, are "normalized" in the sense that ⟨p̂kσ∣p̂k′σ′⟩=δσ,σ′∑n=−∞∞δ(k−k′+2nπ/a).

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Figures (3)

Fig. 1
Fig. 1

Intensity plot of Im [ α k σ ( ω ) ] d 3 for the dispersion relation of an MNP chain with γ = 0.7 eV . T (L) indicates the transverse (longitudinal) mode. (a) and (b) Quasi-static DA with radiation correction. (c) and (d) Dynamic DA. The squares connected by dashed lines are calculated by the root searching method using quasi-static DA with radiation correction.

Fig. 2
Fig. 2

Same as Fig. 1 but for dynamic DA. (a) and (b) γ = 0.1 eV . (c) and (d) γ = 0.02 eV .

Fig. 3
Fig. 3

Same as Fig. 2 but for a parallel pair of MNP chains with γ = 0.1 eV . ST (AT) indicates the symmetric (antisymmetric) T mode. (a) and (b) b = a = 75 nm . (c) and (d) b = 5 a = 375 nm .

Equations (3)

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

p m = α ( ω ) [ m m g ( r m r m ) p m + E m drive ] ,
α ( ω ) = i 3 2 c 3 ω 3 a 1 ( ω ) ,
M ( ω ) p = E drive ,

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