Abstract

A differential interference contrast microscopy technique that employs a photonic crystal fiber as a white-light source is used to measure both the real and the imaginary part of the complex dielectric constant of single 10 and 15nm gold nanoparticles over a wavelength range of 480to610nm. Noticeable deviations from bulk gold measurements are observed at short wavelengths and for individual particles even after taking into account finite-size surface damping effects.

© 2006 Optical Society of America

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References

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  1. U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).
  2. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).
  3. G. Mie, Ann. Phys. 26, 329 (1908).
  4. R. H. Doremus, J. Chem. Phys. 40, 2389 (1964).
    [CrossRef]
  5. C. G. Granqvist and O. Hunderi, Phys. Rev. B 16, 3513 (1977).
    [CrossRef]
  6. Z. Gu, R. Mu, A. Ueda, M. H. Wu, S. Morgan, W. E. Collins, C. I. Muntele, D. Ila, and B. Vlahovic, Surf. Coat. Technol. 196, 89 (2005).
    [CrossRef]
  7. K. Lindfors, T. Kalkbrenner, P. Stoller, and V. Sandoghdar, Phys. Rev. Lett. 93, 037401 (2004).
    [CrossRef] [PubMed]
  8. S. Berciaud, L. Cognet, P. Tamart, and B. Lounis, Nano Lett. 5, 515 (2005).
    [CrossRef] [PubMed]
  9. O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, Appl. Phys. Lett. 88, 063109 (2006).
    [CrossRef]
  10. J. S. Batchelder and M. A. Taubenblatt, Appl. Phys. Lett. 55, 215 (1989).
    [CrossRef]
  11. M. A. Taubenblatt and J. S. Batchelder, Appl. Opt. 30, 4972 (1991).
    [CrossRef] [PubMed]
  12. Y. Matsuo and K. Sasaki, J. Acoust. Soc. Jpn. 40, 6143 (2001).
  13. E. Hecht and A. Zajac, Optics (Addison-Wesley, 1979).
  14. P. B. Johnson and R. W. Christy, Phys. Rev. B 6, 4370 (1972).
    [CrossRef]
  15. R. A. Innes and J. R. Sambles, J. Phys. F: Met. Phys. 17, 277 (1987).
    [CrossRef]
  16. C. Hendrich, J. Bosbach, F. Stietz, F. Hubenthal, T. Vartanyan, and F. Träger, Appl. Phys. B 76, 869 (2003).
    [CrossRef]
  17. U. Kreibig, H. Bönnemann, and J. Hormes, in Handbook of Surfaces and Interfaces of Materials, H.S.Nalwa, ed. (Academic, 2001).

2006 (1)

O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, Appl. Phys. Lett. 88, 063109 (2006).
[CrossRef]

2005 (2)

S. Berciaud, L. Cognet, P. Tamart, and B. Lounis, Nano Lett. 5, 515 (2005).
[CrossRef] [PubMed]

Z. Gu, R. Mu, A. Ueda, M. H. Wu, S. Morgan, W. E. Collins, C. I. Muntele, D. Ila, and B. Vlahovic, Surf. Coat. Technol. 196, 89 (2005).
[CrossRef]

2004 (1)

K. Lindfors, T. Kalkbrenner, P. Stoller, and V. Sandoghdar, Phys. Rev. Lett. 93, 037401 (2004).
[CrossRef] [PubMed]

2003 (1)

C. Hendrich, J. Bosbach, F. Stietz, F. Hubenthal, T. Vartanyan, and F. Träger, Appl. Phys. B 76, 869 (2003).
[CrossRef]

2001 (1)

Y. Matsuo and K. Sasaki, J. Acoust. Soc. Jpn. 40, 6143 (2001).

1991 (1)

1989 (1)

J. S. Batchelder and M. A. Taubenblatt, Appl. Phys. Lett. 55, 215 (1989).
[CrossRef]

1987 (1)

R. A. Innes and J. R. Sambles, J. Phys. F: Met. Phys. 17, 277 (1987).
[CrossRef]

1977 (1)

C. G. Granqvist and O. Hunderi, Phys. Rev. B 16, 3513 (1977).
[CrossRef]

1972 (1)

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

1964 (1)

R. H. Doremus, J. Chem. Phys. 40, 2389 (1964).
[CrossRef]

1908 (1)

G. Mie, Ann. Phys. 26, 329 (1908).

Batchelder, J. S.

M. A. Taubenblatt and J. S. Batchelder, Appl. Opt. 30, 4972 (1991).
[CrossRef] [PubMed]

J. S. Batchelder and M. A. Taubenblatt, Appl. Phys. Lett. 55, 215 (1989).
[CrossRef]

Berciaud, S.

S. Berciaud, L. Cognet, P. Tamart, and B. Lounis, Nano Lett. 5, 515 (2005).
[CrossRef] [PubMed]

Billaud, P.

O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, Appl. Phys. Lett. 88, 063109 (2006).
[CrossRef]

Bohren, C. F.

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

Bönnemann, H.

U. Kreibig, H. Bönnemann, and J. Hormes, in Handbook of Surfaces and Interfaces of Materials, H.S.Nalwa, ed. (Academic, 2001).

Bosbach, J.

C. Hendrich, J. Bosbach, F. Stietz, F. Hubenthal, T. Vartanyan, and F. Träger, Appl. Phys. B 76, 869 (2003).
[CrossRef]

Boyer, M.

O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, Appl. Phys. Lett. 88, 063109 (2006).
[CrossRef]

Christy, R. W.

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

Cognet, L.

S. Berciaud, L. Cognet, P. Tamart, and B. Lounis, Nano Lett. 5, 515 (2005).
[CrossRef] [PubMed]

Collins, W. E.

Z. Gu, R. Mu, A. Ueda, M. H. Wu, S. Morgan, W. E. Collins, C. I. Muntele, D. Ila, and B. Vlahovic, Surf. Coat. Technol. 196, 89 (2005).
[CrossRef]

Del Fatti, N.

O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, Appl. Phys. Lett. 88, 063109 (2006).
[CrossRef]

Doremus, R. H.

R. H. Doremus, J. Chem. Phys. 40, 2389 (1964).
[CrossRef]

Granqvist, C. G.

C. G. Granqvist and O. Hunderi, Phys. Rev. B 16, 3513 (1977).
[CrossRef]

Gu, Z.

Z. Gu, R. Mu, A. Ueda, M. H. Wu, S. Morgan, W. E. Collins, C. I. Muntele, D. Ila, and B. Vlahovic, Surf. Coat. Technol. 196, 89 (2005).
[CrossRef]

Hecht, E.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1979).

Hendrich, C.

C. Hendrich, J. Bosbach, F. Stietz, F. Hubenthal, T. Vartanyan, and F. Träger, Appl. Phys. B 76, 869 (2003).
[CrossRef]

Hormes, J.

U. Kreibig, H. Bönnemann, and J. Hormes, in Handbook of Surfaces and Interfaces of Materials, H.S.Nalwa, ed. (Academic, 2001).

Hubenthal, F.

C. Hendrich, J. Bosbach, F. Stietz, F. Hubenthal, T. Vartanyan, and F. Träger, Appl. Phys. B 76, 869 (2003).
[CrossRef]

Huffman, D. R.

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

Hunderi, O.

C. G. Granqvist and O. Hunderi, Phys. Rev. B 16, 3513 (1977).
[CrossRef]

Huntzinger, J. R.

O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, Appl. Phys. Lett. 88, 063109 (2006).
[CrossRef]

Ila, D.

Z. Gu, R. Mu, A. Ueda, M. H. Wu, S. Morgan, W. E. Collins, C. I. Muntele, D. Ila, and B. Vlahovic, Surf. Coat. Technol. 196, 89 (2005).
[CrossRef]

Innes, R. A.

R. A. Innes and J. R. Sambles, J. Phys. F: Met. Phys. 17, 277 (1987).
[CrossRef]

Johnson, P. B.

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

Kalkbrenner, T.

K. Lindfors, T. Kalkbrenner, P. Stoller, and V. Sandoghdar, Phys. Rev. Lett. 93, 037401 (2004).
[CrossRef] [PubMed]

Kreibig, U.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

U. Kreibig, H. Bönnemann, and J. Hormes, in Handbook of Surfaces and Interfaces of Materials, H.S.Nalwa, ed. (Academic, 2001).

Lindfors, K.

K. Lindfors, T. Kalkbrenner, P. Stoller, and V. Sandoghdar, Phys. Rev. Lett. 93, 037401 (2004).
[CrossRef] [PubMed]

Lounis, B.

S. Berciaud, L. Cognet, P. Tamart, and B. Lounis, Nano Lett. 5, 515 (2005).
[CrossRef] [PubMed]

Matsuo, Y.

Y. Matsuo and K. Sasaki, J. Acoust. Soc. Jpn. 40, 6143 (2001).

Mie, G.

G. Mie, Ann. Phys. 26, 329 (1908).

Morgan, S.

Z. Gu, R. Mu, A. Ueda, M. H. Wu, S. Morgan, W. E. Collins, C. I. Muntele, D. Ila, and B. Vlahovic, Surf. Coat. Technol. 196, 89 (2005).
[CrossRef]

Mu, R.

Z. Gu, R. Mu, A. Ueda, M. H. Wu, S. Morgan, W. E. Collins, C. I. Muntele, D. Ila, and B. Vlahovic, Surf. Coat. Technol. 196, 89 (2005).
[CrossRef]

Muntele, C. I.

Z. Gu, R. Mu, A. Ueda, M. H. Wu, S. Morgan, W. E. Collins, C. I. Muntele, D. Ila, and B. Vlahovic, Surf. Coat. Technol. 196, 89 (2005).
[CrossRef]

Muskens, O.

O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, Appl. Phys. Lett. 88, 063109 (2006).
[CrossRef]

Sambles, J. R.

R. A. Innes and J. R. Sambles, J. Phys. F: Met. Phys. 17, 277 (1987).
[CrossRef]

Sandoghdar, V.

K. Lindfors, T. Kalkbrenner, P. Stoller, and V. Sandoghdar, Phys. Rev. Lett. 93, 037401 (2004).
[CrossRef] [PubMed]

Sasaki, K.

Y. Matsuo and K. Sasaki, J. Acoust. Soc. Jpn. 40, 6143 (2001).

Stietz, F.

C. Hendrich, J. Bosbach, F. Stietz, F. Hubenthal, T. Vartanyan, and F. Träger, Appl. Phys. B 76, 869 (2003).
[CrossRef]

Stoller, P.

K. Lindfors, T. Kalkbrenner, P. Stoller, and V. Sandoghdar, Phys. Rev. Lett. 93, 037401 (2004).
[CrossRef] [PubMed]

Tamart, P.

S. Berciaud, L. Cognet, P. Tamart, and B. Lounis, Nano Lett. 5, 515 (2005).
[CrossRef] [PubMed]

Taubenblatt, M. A.

M. A. Taubenblatt and J. S. Batchelder, Appl. Opt. 30, 4972 (1991).
[CrossRef] [PubMed]

J. S. Batchelder and M. A. Taubenblatt, Appl. Phys. Lett. 55, 215 (1989).
[CrossRef]

Träger, F.

C. Hendrich, J. Bosbach, F. Stietz, F. Hubenthal, T. Vartanyan, and F. Träger, Appl. Phys. B 76, 869 (2003).
[CrossRef]

Ueda, A.

Z. Gu, R. Mu, A. Ueda, M. H. Wu, S. Morgan, W. E. Collins, C. I. Muntele, D. Ila, and B. Vlahovic, Surf. Coat. Technol. 196, 89 (2005).
[CrossRef]

Vallee, F.

O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, Appl. Phys. Lett. 88, 063109 (2006).
[CrossRef]

Vartanyan, T.

C. Hendrich, J. Bosbach, F. Stietz, F. Hubenthal, T. Vartanyan, and F. Träger, Appl. Phys. B 76, 869 (2003).
[CrossRef]

Vlahovic, B.

Z. Gu, R. Mu, A. Ueda, M. H. Wu, S. Morgan, W. E. Collins, C. I. Muntele, D. Ila, and B. Vlahovic, Surf. Coat. Technol. 196, 89 (2005).
[CrossRef]

Vollmer, M.

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

Wu, M. H.

Z. Gu, R. Mu, A. Ueda, M. H. Wu, S. Morgan, W. E. Collins, C. I. Muntele, D. Ila, and B. Vlahovic, Surf. Coat. Technol. 196, 89 (2005).
[CrossRef]

Zajac, A.

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1979).

Ann. Phys. (1)

G. Mie, Ann. Phys. 26, 329 (1908).

Appl. Opt. (1)

Appl. Phys. B (1)

C. Hendrich, J. Bosbach, F. Stietz, F. Hubenthal, T. Vartanyan, and F. Träger, Appl. Phys. B 76, 869 (2003).
[CrossRef]

Appl. Phys. Lett. (2)

O. Muskens, N. Del Fatti, F. Vallee, J. R. Huntzinger, P. Billaud, and M. Boyer, Appl. Phys. Lett. 88, 063109 (2006).
[CrossRef]

J. S. Batchelder and M. A. Taubenblatt, Appl. Phys. Lett. 55, 215 (1989).
[CrossRef]

J. Acoust. Soc. Jpn. (1)

Y. Matsuo and K. Sasaki, J. Acoust. Soc. Jpn. 40, 6143 (2001).

J. Chem. Phys. (1)

R. H. Doremus, J. Chem. Phys. 40, 2389 (1964).
[CrossRef]

J. Phys. F: Met. Phys. (1)

R. A. Innes and J. R. Sambles, J. Phys. F: Met. Phys. 17, 277 (1987).
[CrossRef]

Nano Lett. (1)

S. Berciaud, L. Cognet, P. Tamart, and B. Lounis, Nano Lett. 5, 515 (2005).
[CrossRef] [PubMed]

Phys. Rev. B (2)

C. G. Granqvist and O. Hunderi, Phys. Rev. B 16, 3513 (1977).
[CrossRef]

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

Phys. Rev. Lett. (1)

K. Lindfors, T. Kalkbrenner, P. Stoller, and V. Sandoghdar, Phys. Rev. Lett. 93, 037401 (2004).
[CrossRef] [PubMed]

Surf. Coat. Technol. (1)

Z. Gu, R. Mu, A. Ueda, M. H. Wu, S. Morgan, W. E. Collins, C. I. Muntele, D. Ila, and B. Vlahovic, Surf. Coat. Technol. 196, 89 (2005).
[CrossRef]

Other (4)

U. Kreibig and M. Vollmer, Optical Properties of Metal Clusters (Springer, 1995).

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

U. Kreibig, H. Bönnemann, and J. Hormes, in Handbook of Surfaces and Interfaces of Materials, H.S.Nalwa, ed. (Academic, 2001).

E. Hecht and A. Zajac, Optics (Addison-Wesley, 1979).

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Figures (3)

Fig. 1
Fig. 1

Illustration of the phase-sensitive detection principle. The polarization angles are specified next to each beam. See text for details.

Fig. 2
Fig. 2

(a) X re and (b) X im as a function of wavelength for a single 15 nm gold nanoparticle. The solid curve shows the calculated value for a spherical particle in the quasi-static approximation using the bulk dielectric constant of gold. (c) Real and (d) imaginary parts of the dielectric constant calculated from (a) and (b). The solid curve shows the bulk dielectric constant, and the dashed curve shows this quantity corrected for the size-limited mean free conduction electron path.

Fig. 3
Fig. 3

(a) Real and (b) imaginary parts of the dielectric constant calculated by averaging over fifteen 10 nm particles (blue) and thirteen 15 nm particles (red). The solid curve shows the bulk dielectric constant, and the dashed curves show the same quantity corrected for the size-limited mean free conduction electron path in 10 and 15 nm particles.

Equations (5)

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

X ( ω ) 2 π ϵ m d 3 α ( ω ) = ϵ p ( ω ) ϵ m ϵ p ( ω ) + 2 ϵ m ,
X re = λ 2 C d 3 ( A B ) ,
X im = λ C d 3 [ 1 A + B 1 1 4 ( A B ) 2 ] ,
ϵ re = 1 2 X im 2 + X re 2 X re 2 X im 2 + ( 1 X im ) 2 ϵ m ,
ϵ im = 3 X im X im 2 + ( 1 X re ) 2 ϵ m .

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