Abstract

By applying the Maxwell Garnett model to gold nanoparticles in water we deduce a value of Im χi(3)=1.1 ×10-7 esu for the imaginary part of the cubic susceptibility for gold corresponding to a Fermi smearing mechanism. We also demonstrate a sign reversal in the nonlinear absorption for gold particles in 1, 1, 3, 3, 3, 3-hexamethylindotricarbocyanine iodide. Although the imaginary part of χ(3) is positive for each component by itself, remarkably the imaginary part of χ(3) is negative for the colloid as a whole. We show that the nonlinearity of the host must be considered and that the sign reversal in χ(3) is a result of the fact that at the surface plasmon resonance the local field factor has an imaginary component that arises from a phase shift between the applied field and the local field inside the particle.

© 1997 Optical Society of America

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  1. V. K. Mizrahi, K. W. Delong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140 (1989).
    [CrossRef] [PubMed]
  2. K. W. Delong and G. I. Stegeman, “Two-photon absorption as a limitation to all-optical waveguide switching in semiconductors,” Appl. Phys. Lett. 57, 2063 (1990).
    [CrossRef]
  3. F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. A 47, 347 (1988).
    [CrossRef]
  4. J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London 203, 385 (1904); 205, 237 (1906).
  5. D. Ricard, P. Rousignol, and C. Flytzanis, “Surface-mediated enhancement of optical phase conjugation in metal colloids,” Opt. Lett. 10, 511 (1985).
    [CrossRef] [PubMed]
  6. J. W. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnet model,” Phys. Rev. A 46, 1614 (1992).
    [CrossRef] [PubMed]
  7. D. A. G. Bruggeman, “Calculation of various physical constants of heterogeneous substances. Part I. Dielectric constant and conductivity of mixtures of isotropic substances,” Ann. Phys. (Leipzig) 24, 636 (1935).
    [CrossRef]
  8. J. A. A. J. Perenboom, P. Wyder, and F. Meier, “Electronic properties of small metallic particles,” Phys. Rep. 78, 173 (1981).
    [CrossRef]
  9. J. Turkevich, P. C. Stevenson, and J. Hillier, “A study of the nucleation and growth processes in the synthesis of colloidal gold,” Discuss. Faraday Soc. 11, 55 (1951).
    [CrossRef]
  10. L. Sibille, “Study by gravimetry, fluorometry, and calorimetry of crystallizing tetragonal lysozyme solutions,” Ph.D. dissertation (Institut National des Sciences Appliquées des Toulouse, Toulouse, France, 1994).
  11. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
    [CrossRef]
  12. J. A. Giordmaine and J. A. Howe, “Intensity-induced optical absorption cross section in CS2,” Phys. Rev. Lett. 11, 207 (1963).
    [CrossRef]
  13. Y. M. Cheung and S. K. Gayen, “Optical nonlinearities of tea studied by Z-scan and four-wave mixing techniques,” J. Opt. Soc. Am. B 11, 636 (1994).
    [CrossRef]
  14. M. J. Bloemer, J. W. Haus, and P. R. Ashley, “Degenerate four-wave mixing in colloidal gold as a function of particle size,” J. Opt. Soc. Am. B 7, 790 (1990).
    [CrossRef]
  15. H. Fröhlich, Theory of Dielectrics (Oxford U. Press, London, 1958).
  16. S. N. R. Swatton, K. R. Welford, S. J. Till, and J. R. Sambles, “Nonlinear absorption of a carbocyanine dye 1, 1, 3, 3, 3, 3-hexamethylindotricarbocyanine iodide using a Z-scan technique,” Appl. Phys. Lett. 66, 1868 (1995).
    [CrossRef]
  17. L. Onsager, “Electric moments of molecules in liquids,” J. Am. Chem. Soc. 58, 1486 (1936).
    [CrossRef]

1995 (1)

S. N. R. Swatton, K. R. Welford, S. J. Till, and J. R. Sambles, “Nonlinear absorption of a carbocyanine dye 1, 1, 3, 3, 3, 3-hexamethylindotricarbocyanine iodide using a Z-scan technique,” Appl. Phys. Lett. 66, 1868 (1995).
[CrossRef]

1994 (1)

1992 (1)

J. W. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnet model,” Phys. Rev. A 46, 1614 (1992).
[CrossRef] [PubMed]

1990 (3)

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

K. W. Delong and G. I. Stegeman, “Two-photon absorption as a limitation to all-optical waveguide switching in semiconductors,” Appl. Phys. Lett. 57, 2063 (1990).
[CrossRef]

M. J. Bloemer, J. W. Haus, and P. R. Ashley, “Degenerate four-wave mixing in colloidal gold as a function of particle size,” J. Opt. Soc. Am. B 7, 790 (1990).
[CrossRef]

1989 (1)

1988 (1)

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. A 47, 347 (1988).
[CrossRef]

1985 (1)

1981 (1)

J. A. A. J. Perenboom, P. Wyder, and F. Meier, “Electronic properties of small metallic particles,” Phys. Rep. 78, 173 (1981).
[CrossRef]

1963 (1)

J. A. Giordmaine and J. A. Howe, “Intensity-induced optical absorption cross section in CS2,” Phys. Rev. Lett. 11, 207 (1963).
[CrossRef]

1951 (1)

J. Turkevich, P. C. Stevenson, and J. Hillier, “A study of the nucleation and growth processes in the synthesis of colloidal gold,” Discuss. Faraday Soc. 11, 55 (1951).
[CrossRef]

1936 (1)

L. Onsager, “Electric moments of molecules in liquids,” J. Am. Chem. Soc. 58, 1486 (1936).
[CrossRef]

1935 (1)

D. A. G. Bruggeman, “Calculation of various physical constants of heterogeneous substances. Part I. Dielectric constant and conductivity of mixtures of isotropic substances,” Ann. Phys. (Leipzig) 24, 636 (1935).
[CrossRef]

Andrejco, M. J.

Ashley, P. R.

Bloemer, M. J.

Boyd, R. W.

J. W. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnet model,” Phys. Rev. A 46, 1614 (1992).
[CrossRef] [PubMed]

Bruggeman, D. A. G.

D. A. G. Bruggeman, “Calculation of various physical constants of heterogeneous substances. Part I. Dielectric constant and conductivity of mixtures of isotropic substances,” Ann. Phys. (Leipzig) 24, 636 (1935).
[CrossRef]

Cheung, Y. M.

Delong, K. W.

K. W. Delong and G. I. Stegeman, “Two-photon absorption as a limitation to all-optical waveguide switching in semiconductors,” Appl. Phys. Lett. 57, 2063 (1990).
[CrossRef]

V. K. Mizrahi, K. W. Delong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140 (1989).
[CrossRef] [PubMed]

Flytzanis, C.

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. A 47, 347 (1988).
[CrossRef]

D. Ricard, P. Rousignol, and C. Flytzanis, “Surface-mediated enhancement of optical phase conjugation in metal colloids,” Opt. Lett. 10, 511 (1985).
[CrossRef] [PubMed]

Gayen, S. K.

Giordmaine, J. A.

J. A. Giordmaine and J. A. Howe, “Intensity-induced optical absorption cross section in CS2,” Phys. Rev. Lett. 11, 207 (1963).
[CrossRef]

Hache, F.

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. A 47, 347 (1988).
[CrossRef]

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Haus, J. W.

Hillier, J.

J. Turkevich, P. C. Stevenson, and J. Hillier, “A study of the nucleation and growth processes in the synthesis of colloidal gold,” Discuss. Faraday Soc. 11, 55 (1951).
[CrossRef]

Howe, J. A.

J. A. Giordmaine and J. A. Howe, “Intensity-induced optical absorption cross section in CS2,” Phys. Rev. Lett. 11, 207 (1963).
[CrossRef]

Kreibig, U.

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. A 47, 347 (1988).
[CrossRef]

Meier, F.

J. A. A. J. Perenboom, P. Wyder, and F. Meier, “Electronic properties of small metallic particles,” Phys. Rep. 78, 173 (1981).
[CrossRef]

Mizrahi, V. K.

Onsager, L.

L. Onsager, “Electric moments of molecules in liquids,” J. Am. Chem. Soc. 58, 1486 (1936).
[CrossRef]

Perenboom, J. A. A. J.

J. A. A. J. Perenboom, P. Wyder, and F. Meier, “Electronic properties of small metallic particles,” Phys. Rep. 78, 173 (1981).
[CrossRef]

Ricard, D.

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. A 47, 347 (1988).
[CrossRef]

D. Ricard, P. Rousignol, and C. Flytzanis, “Surface-mediated enhancement of optical phase conjugation in metal colloids,” Opt. Lett. 10, 511 (1985).
[CrossRef] [PubMed]

Rousignol, P.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Saifi, M. A.

Sambles, J. R.

S. N. R. Swatton, K. R. Welford, S. J. Till, and J. R. Sambles, “Nonlinear absorption of a carbocyanine dye 1, 1, 3, 3, 3, 3-hexamethylindotricarbocyanine iodide using a Z-scan technique,” Appl. Phys. Lett. 66, 1868 (1995).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Sipe, J. W.

J. W. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnet model,” Phys. Rev. A 46, 1614 (1992).
[CrossRef] [PubMed]

Stegeman, G. I.

K. W. Delong and G. I. Stegeman, “Two-photon absorption as a limitation to all-optical waveguide switching in semiconductors,” Appl. Phys. Lett. 57, 2063 (1990).
[CrossRef]

V. K. Mizrahi, K. W. Delong, G. I. Stegeman, M. A. Saifi, and M. J. Andrejco, “Two-photon absorption as a limitation to all-optical switching,” Opt. Lett. 14, 1140 (1989).
[CrossRef] [PubMed]

Stevenson, P. C.

J. Turkevich, P. C. Stevenson, and J. Hillier, “A study of the nucleation and growth processes in the synthesis of colloidal gold,” Discuss. Faraday Soc. 11, 55 (1951).
[CrossRef]

Swatton, S. N. R.

S. N. R. Swatton, K. R. Welford, S. J. Till, and J. R. Sambles, “Nonlinear absorption of a carbocyanine dye 1, 1, 3, 3, 3, 3-hexamethylindotricarbocyanine iodide using a Z-scan technique,” Appl. Phys. Lett. 66, 1868 (1995).
[CrossRef]

Till, S. J.

S. N. R. Swatton, K. R. Welford, S. J. Till, and J. R. Sambles, “Nonlinear absorption of a carbocyanine dye 1, 1, 3, 3, 3, 3-hexamethylindotricarbocyanine iodide using a Z-scan technique,” Appl. Phys. Lett. 66, 1868 (1995).
[CrossRef]

Turkevich, J.

J. Turkevich, P. C. Stevenson, and J. Hillier, “A study of the nucleation and growth processes in the synthesis of colloidal gold,” Discuss. Faraday Soc. 11, 55 (1951).
[CrossRef]

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Wei, T.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Welford, K. R.

S. N. R. Swatton, K. R. Welford, S. J. Till, and J. R. Sambles, “Nonlinear absorption of a carbocyanine dye 1, 1, 3, 3, 3, 3-hexamethylindotricarbocyanine iodide using a Z-scan technique,” Appl. Phys. Lett. 66, 1868 (1995).
[CrossRef]

Wyder, P.

J. A. A. J. Perenboom, P. Wyder, and F. Meier, “Electronic properties of small metallic particles,” Phys. Rep. 78, 173 (1981).
[CrossRef]

Ann. Phys. (Leipzig) (1)

D. A. G. Bruggeman, “Calculation of various physical constants of heterogeneous substances. Part I. Dielectric constant and conductivity of mixtures of isotropic substances,” Ann. Phys. (Leipzig) 24, 636 (1935).
[CrossRef]

Appl. Phys. A (1)

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, “The optical Kerr effect in small metal particles and metal colloids: the case of gold,” Appl. Phys. A 47, 347 (1988).
[CrossRef]

Appl. Phys. Lett. (2)

S. N. R. Swatton, K. R. Welford, S. J. Till, and J. R. Sambles, “Nonlinear absorption of a carbocyanine dye 1, 1, 3, 3, 3, 3-hexamethylindotricarbocyanine iodide using a Z-scan technique,” Appl. Phys. Lett. 66, 1868 (1995).
[CrossRef]

K. W. Delong and G. I. Stegeman, “Two-photon absorption as a limitation to all-optical waveguide switching in semiconductors,” Appl. Phys. Lett. 57, 2063 (1990).
[CrossRef]

Discuss. Faraday Soc. (1)

J. Turkevich, P. C. Stevenson, and J. Hillier, “A study of the nucleation and growth processes in the synthesis of colloidal gold,” Discuss. Faraday Soc. 11, 55 (1951).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

J. Am. Chem. Soc. (1)

L. Onsager, “Electric moments of molecules in liquids,” J. Am. Chem. Soc. 58, 1486 (1936).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Lett. (2)

Phys. Rep. (1)

J. A. A. J. Perenboom, P. Wyder, and F. Meier, “Electronic properties of small metallic particles,” Phys. Rep. 78, 173 (1981).
[CrossRef]

Phys. Rev. A (1)

J. W. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnet model,” Phys. Rev. A 46, 1614 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

J. A. Giordmaine and J. A. Howe, “Intensity-induced optical absorption cross section in CS2,” Phys. Rev. Lett. 11, 207 (1963).
[CrossRef]

Other (3)

L. Sibille, “Study by gravimetry, fluorometry, and calorimetry of crystallizing tetragonal lysozyme solutions,” Ph.D. dissertation (Institut National des Sciences Appliquées des Toulouse, Toulouse, France, 1994).

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London 203, 385 (1904); 205, 237 (1906).

H. Fröhlich, Theory of Dielectrics (Oxford U. Press, London, 1958).

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Figures (4)

Fig. 1
Fig. 1

Z-scan experimental arrangement.10

Fig. 2
Fig. 2

Open-aperture Z scans at 532 nm and Pi=0.46 MW for a gold colloid stock solution and for solutions fractionally diluted by 1/2, 1/4, and 1/16 from the stock.

Fig. 3
Fig. 3

Nonlinear absorption of the gold colloid. The solid curve is a fit from the Maxwell Garnett theory, where Im χi(3) is a fitting parameter.

Fig. 4
Fig. 4

Nonlinear absorption of various concentrations of gold in HITCI. The nonlinear absorption is canceled near curve 6.

Tables (2)

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Table 1 Change in Nonlinear Absorption with Concentration

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Table 2 Component Proportions for HITCI–Au Composite

Equations (14)

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=h 1+2ηf1-ηf,
ηi-hi+2h.
χ(3)=fqi2|qi|2χi(3)+qh2|qh|2[(1-f)+xf]χh(3),
x85η2|η|2+65η|η|2+25η3+185(|η|2+η2).
qi=+2hi+2h,
qh=+2h3h.
χ(3)=fqi2|qi|2χi(3)+χh(3).
i(ωs)=-2h,
tan-1 ϕ=ih-ihih+ih+2(h2+h2),
tan-1 ϕ=-(h/h).
tan-1 ϕ=-ii+2h.
T(z)=m=0 -βI0Leff1+z2/z02m(m+1)3/2,
α0=ωn0c=ωn0cf|qi2|i.
Im χ(3)=λcn02β640π3,

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