Abstract

We study the intensity-dependent absorption coefficient of gold-silica composites as a function of fill fraction at frequencies near the plasmon resonance. The samples we have studied act as saturable absorbers at all wavelengths and all fill fractions, whereas pure gold is an optical limiter. We provide an explanation based on the intensity-dependent damping of the surface plasmon for this reversal of the sign of the nonlinear absorption.

© 2008 Optical Society of America

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  1. J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London, Ser. A 203, 385-420 (1904).
    [CrossRef]
  2. R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, “Optical properties of granular silver and gold films,” Phys. Rev. B 8, 3689-3701 (1973).
    [CrossRef]
  3. C. G. Granqvist and O. Hunderi, “Optical properties of Ag-SiO2 cermet films: a comparison of effective-medium theories,” Phys. Rev. B 18, 2897-2906 (1978).
    [CrossRef]
  4. D. Ricard, P. Roussignol, and C. Flytzanis, “Surface-mediated enhancement of optical phase conjugation in metal colloids,” Opt. Lett. 10, 511-513 (1985).
    [CrossRef] [PubMed]
  5. J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46, 1614-1629 (1992).
    [CrossRef] [PubMed]
  6. D. A. G. Bruggeman, “Berechung verschieder physikalischer Konstanten von heterogenen Substanzen I. Dielektrizitätskanstanten und Leitföhigkeiten der Mischkörper aus isotropen Substanzen,” Ann. Phys. (Leipzig) 24, 636-664 (1935).
    [CrossRef]
  7. R. Landauer, “The electrical resistance of binary metallic mixtures,” J. Appl. Phys. 23, 779-784 (1952).
    [CrossRef]
  8. D. Stroud, “Generalized effective-medium approach to the conductivity of an inhomogeneous material,” Phys. Rev. B 12, 3368-3373 (1975).
    [CrossRef]
  9. P. Sheng, “Theory for the dielectric function of granular composite media,” Phys. Rev. Lett. 45, 60-63 (1980).
    [CrossRef]
  10. P. Sheng, “Pair-cluster theory for the dielectric constant of composite media,” Phys. Rev. B 22, 6364-6368 (1980).
    [CrossRef]
  11. V. M. Shalaev and A. K. Sarychev, “Nonlinear optics of random metal-dielectric films,” Phys. Rev. B 57, 13265-13288 (1998).
    [CrossRef]
  12. P. J. Reynolds, W. Klein, and H. E. Stanley, “A real-space renormalization group for site and bond percolation,” J. Phys. C 10, L167-L172 (1977).
    [CrossRef]
  13. A. K. Sarychev, “Scaling invariance and percolation in a random field,” Zh. Eksp. Teor. Fiz. 72, 1001-1004 (1977).
  14. H. B. Liao, R. F. Xiao, J. S. Fu, P. Yu, G. K. L. Wong, and P. Sheng, “Large third-order optical nonlinearity in Au:SiO2 composite films near the percolation threshold,” Appl. Phys. Lett. 70, 1-3 (1997).
    [CrossRef]
  15. H. B. Liao, R. F. Xiao, J. S. Fu, H. Wang, K. S. Wong, and G. K. L. Wong, “Origin of third-order optical nonlinearity in Au:SiO2 composite films on femtosecond and picosecond time scales,” Opt. Lett. 23, 388-390 (1998).
    [CrossRef]
  16. H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72, 1817-1819 (1998).
    [CrossRef]
  17. R. del Coso, J. Requejo-Isidro, J. Solis, J. Gonzalo, and C. N. Afonso, “Third order nonlinear optical susceptibility of Cu:Al2O3 nanocomposites: from spherical nanoparticles to the percolation threshold,” J. Appl. Phys. 95, 2755-2762 (2004).
    [CrossRef]
  18. D. D. Smith, G. Fischer, R. W. Boyd, and D. A. Gregory, “Cancellation of photoinduced absorption in metal nanoparticle composites through a counterintuitive consequence of local field effects,” J. Opt. Soc. Am. B 14, 1625-1631 (1997).
    [CrossRef]
  19. M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
    [CrossRef]
  20. M. Perner, P. Bost, U. Lemmer, G. von Plessen, J. Feldmann, U. Becker, M. Mennig, M. Schmitt, and H. Schmidt, “Optically induced damping of the surface plasmon resonance in gold colloids,” Phys. Rev. Lett. 78, 2192-2195 (1997).
    [CrossRef]
  21. U. Kreibig and M. Vollmer, “Optical properties of metal clusters,” in Springer Series in Materials Science (Springer-Verlag, 1995), Vol. 25.
  22. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Harcourt, 1976).
  23. D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, “z-scan measurement of the nonlinear absorption of a thin gold film,” J. Appl. Phys. 86, 6200-6205 (1999).
    [CrossRef]
  24. K. Seal, M. A. Nelson, Z. C. Ying, D. A. Genov, D. A. Sarychev, and V. M. Shalaev, “Growth, morphology, and optical and electrical properties of semicontinuous gold films,” Phys. Rev. B 67, 035318 (2003).
    [CrossRef]

2004 (1)

R. del Coso, J. Requejo-Isidro, J. Solis, J. Gonzalo, and C. N. Afonso, “Third order nonlinear optical susceptibility of Cu:Al2O3 nanocomposites: from spherical nanoparticles to the percolation threshold,” J. Appl. Phys. 95, 2755-2762 (2004).
[CrossRef]

2003 (1)

K. Seal, M. A. Nelson, Z. C. Ying, D. A. Genov, D. A. Sarychev, and V. M. Shalaev, “Growth, morphology, and optical and electrical properties of semicontinuous gold films,” Phys. Rev. B 67, 035318 (2003).
[CrossRef]

1999 (1)

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, “z-scan measurement of the nonlinear absorption of a thin gold film,” J. Appl. Phys. 86, 6200-6205 (1999).
[CrossRef]

1998 (3)

H. B. Liao, R. F. Xiao, J. S. Fu, H. Wang, K. S. Wong, and G. K. L. Wong, “Origin of third-order optical nonlinearity in Au:SiO2 composite films on femtosecond and picosecond time scales,” Opt. Lett. 23, 388-390 (1998).
[CrossRef]

H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72, 1817-1819 (1998).
[CrossRef]

V. M. Shalaev and A. K. Sarychev, “Nonlinear optics of random metal-dielectric films,” Phys. Rev. B 57, 13265-13288 (1998).
[CrossRef]

1997 (3)

D. D. Smith, G. Fischer, R. W. Boyd, and D. A. Gregory, “Cancellation of photoinduced absorption in metal nanoparticle composites through a counterintuitive consequence of local field effects,” J. Opt. Soc. Am. B 14, 1625-1631 (1997).
[CrossRef]

H. B. Liao, R. F. Xiao, J. S. Fu, P. Yu, G. K. L. Wong, and P. Sheng, “Large third-order optical nonlinearity in Au:SiO2 composite films near the percolation threshold,” Appl. Phys. Lett. 70, 1-3 (1997).
[CrossRef]

M. Perner, P. Bost, U. Lemmer, G. von Plessen, J. Feldmann, U. Becker, M. Mennig, M. Schmitt, and H. Schmidt, “Optically induced damping of the surface plasmon resonance in gold colloids,” Phys. Rev. Lett. 78, 2192-2195 (1997).
[CrossRef]

1992 (1)

J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46, 1614-1629 (1992).
[CrossRef] [PubMed]

1990 (1)

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

1985 (1)

1980 (2)

P. Sheng, “Theory for the dielectric function of granular composite media,” Phys. Rev. Lett. 45, 60-63 (1980).
[CrossRef]

P. Sheng, “Pair-cluster theory for the dielectric constant of composite media,” Phys. Rev. B 22, 6364-6368 (1980).
[CrossRef]

1978 (1)

C. G. Granqvist and O. Hunderi, “Optical properties of Ag-SiO2 cermet films: a comparison of effective-medium theories,” Phys. Rev. B 18, 2897-2906 (1978).
[CrossRef]

1977 (2)

P. J. Reynolds, W. Klein, and H. E. Stanley, “A real-space renormalization group for site and bond percolation,” J. Phys. C 10, L167-L172 (1977).
[CrossRef]

A. K. Sarychev, “Scaling invariance and percolation in a random field,” Zh. Eksp. Teor. Fiz. 72, 1001-1004 (1977).

1975 (1)

D. Stroud, “Generalized effective-medium approach to the conductivity of an inhomogeneous material,” Phys. Rev. B 12, 3368-3373 (1975).
[CrossRef]

1973 (1)

R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, “Optical properties of granular silver and gold films,” Phys. Rev. B 8, 3689-3701 (1973).
[CrossRef]

1952 (1)

R. Landauer, “The electrical resistance of binary metallic mixtures,” J. Appl. Phys. 23, 779-784 (1952).
[CrossRef]

1935 (1)

D. A. G. Bruggeman, “Berechung verschieder physikalischer Konstanten von heterogenen Substanzen I. Dielektrizitätskanstanten und Leitföhigkeiten der Mischkörper aus isotropen Substanzen,” Ann. Phys. (Leipzig) 24, 636-664 (1935).
[CrossRef]

1904 (1)

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London, Ser. A 203, 385-420 (1904).
[CrossRef]

Abeles, B.

R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, “Optical properties of granular silver and gold films,” Phys. Rev. B 8, 3689-3701 (1973).
[CrossRef]

Afonso, C. N.

R. del Coso, J. Requejo-Isidro, J. Solis, J. Gonzalo, and C. N. Afonso, “Third order nonlinear optical susceptibility of Cu:Al2O3 nanocomposites: from spherical nanoparticles to the percolation threshold,” J. Appl. Phys. 95, 2755-2762 (2004).
[CrossRef]

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Harcourt, 1976).

Baker, L. A.

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, “z-scan measurement of the nonlinear absorption of a thin gold film,” J. Appl. Phys. 86, 6200-6205 (1999).
[CrossRef]

Becker, U.

M. Perner, P. Bost, U. Lemmer, G. von Plessen, J. Feldmann, U. Becker, M. Mennig, M. Schmitt, and H. Schmidt, “Optically induced damping of the surface plasmon resonance in gold colloids,” Phys. Rev. Lett. 78, 2192-2195 (1997).
[CrossRef]

Bost, P.

M. Perner, P. Bost, U. Lemmer, G. von Plessen, J. Feldmann, U. Becker, M. Mennig, M. Schmitt, and H. Schmidt, “Optically induced damping of the surface plasmon resonance in gold colloids,” Phys. Rev. Lett. 78, 2192-2195 (1997).
[CrossRef]

Boyd, R. W.

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, “z-scan measurement of the nonlinear absorption of a thin gold film,” J. Appl. Phys. 86, 6200-6205 (1999).
[CrossRef]

D. D. Smith, G. Fischer, R. W. Boyd, and D. A. Gregory, “Cancellation of photoinduced absorption in metal nanoparticle composites through a counterintuitive consequence of local field effects,” J. Opt. Soc. Am. B 14, 1625-1631 (1997).
[CrossRef]

J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46, 1614-1629 (1992).
[CrossRef] [PubMed]

Bruggeman, D. A. G.

D. A. G. Bruggeman, “Berechung verschieder physikalischer Konstanten von heterogenen Substanzen I. Dielektrizitätskanstanten und Leitföhigkeiten der Mischkörper aus isotropen Substanzen,” Ann. Phys. (Leipzig) 24, 636-664 (1935).
[CrossRef]

Campbell, J. K.

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, “z-scan measurement of the nonlinear absorption of a thin gold film,” J. Appl. Phys. 86, 6200-6205 (1999).
[CrossRef]

Cody, G. D.

R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, “Optical properties of granular silver and gold films,” Phys. Rev. B 8, 3689-3701 (1973).
[CrossRef]

Cohen, R. W.

R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, “Optical properties of granular silver and gold films,” Phys. Rev. B 8, 3689-3701 (1973).
[CrossRef]

Coutts, M. D.

R. W. Cohen, G. D. Cody, M. D. Coutts, and B. Abeles, “Optical properties of granular silver and gold films,” Phys. Rev. B 8, 3689-3701 (1973).
[CrossRef]

Crooks, R. M.

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, “z-scan measurement of the nonlinear absorption of a thin gold film,” J. Appl. Phys. 86, 6200-6205 (1999).
[CrossRef]

del Coso, R.

R. del Coso, J. Requejo-Isidro, J. Solis, J. Gonzalo, and C. N. Afonso, “Third order nonlinear optical susceptibility of Cu:Al2O3 nanocomposites: from spherical nanoparticles to the percolation threshold,” J. Appl. Phys. 95, 2755-2762 (2004).
[CrossRef]

Feldmann, J.

M. Perner, P. Bost, U. Lemmer, G. von Plessen, J. Feldmann, U. Becker, M. Mennig, M. Schmitt, and H. Schmidt, “Optically induced damping of the surface plasmon resonance in gold colloids,” Phys. Rev. Lett. 78, 2192-2195 (1997).
[CrossRef]

Fischer, G.

Flytzanis, C.

Fu, J. S.

H. B. Liao, R. F. Xiao, J. S. Fu, H. Wang, K. S. Wong, and G. K. L. Wong, “Origin of third-order optical nonlinearity in Au:SiO2 composite films on femtosecond and picosecond time scales,” Opt. Lett. 23, 388-390 (1998).
[CrossRef]

H. B. Liao, R. F. Xiao, J. S. Fu, P. Yu, G. K. L. Wong, and P. Sheng, “Large third-order optical nonlinearity in Au:SiO2 composite films near the percolation threshold,” Appl. Phys. Lett. 70, 1-3 (1997).
[CrossRef]

Genov, D. A.

K. Seal, M. A. Nelson, Z. C. Ying, D. A. Genov, D. A. Sarychev, and V. M. Shalaev, “Growth, morphology, and optical and electrical properties of semicontinuous gold films,” Phys. Rev. B 67, 035318 (2003).
[CrossRef]

George, M.

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, “z-scan measurement of the nonlinear absorption of a thin gold film,” J. Appl. Phys. 86, 6200-6205 (1999).
[CrossRef]

Gonzalo, J.

R. del Coso, J. Requejo-Isidro, J. Solis, J. Gonzalo, and C. N. Afonso, “Third order nonlinear optical susceptibility of Cu:Al2O3 nanocomposites: from spherical nanoparticles to the percolation threshold,” J. Appl. Phys. 95, 2755-2762 (2004).
[CrossRef]

Granqvist, C. G.

C. G. Granqvist and O. Hunderi, “Optical properties of Ag-SiO2 cermet films: a comparison of effective-medium theories,” Phys. Rev. B 18, 2897-2906 (1978).
[CrossRef]

Gregory, D. A.

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Hunderi, O.

C. G. Granqvist and O. Hunderi, “Optical properties of Ag-SiO2 cermet films: a comparison of effective-medium theories,” Phys. Rev. B 18, 2897-2906 (1978).
[CrossRef]

Klein, W.

P. J. Reynolds, W. Klein, and H. E. Stanley, “A real-space renormalization group for site and bond percolation,” J. Phys. C 10, L167-L172 (1977).
[CrossRef]

Kreibig, U.

U. Kreibig and M. Vollmer, “Optical properties of metal clusters,” in Springer Series in Materials Science (Springer-Verlag, 1995), Vol. 25.

Landauer, R.

R. Landauer, “The electrical resistance of binary metallic mixtures,” J. Appl. Phys. 23, 779-784 (1952).
[CrossRef]

Lemmer, U.

M. Perner, P. Bost, U. Lemmer, G. von Plessen, J. Feldmann, U. Becker, M. Mennig, M. Schmitt, and H. Schmidt, “Optically induced damping of the surface plasmon resonance in gold colloids,” Phys. Rev. Lett. 78, 2192-2195 (1997).
[CrossRef]

Liao, H. B.

H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72, 1817-1819 (1998).
[CrossRef]

H. B. Liao, R. F. Xiao, J. S. Fu, H. Wang, K. S. Wong, and G. K. L. Wong, “Origin of third-order optical nonlinearity in Au:SiO2 composite films on femtosecond and picosecond time scales,” Opt. Lett. 23, 388-390 (1998).
[CrossRef]

H. B. Liao, R. F. Xiao, J. S. Fu, P. Yu, G. K. L. Wong, and P. Sheng, “Large third-order optical nonlinearity in Au:SiO2 composite films near the percolation threshold,” Appl. Phys. Lett. 70, 1-3 (1997).
[CrossRef]

Maxwell Garnett, J. C.

J. C. Maxwell Garnett, “Colours in metal glasses and in metallic films,” Philos. Trans. R. Soc. London, Ser. A 203, 385-420 (1904).
[CrossRef]

Mennig, M.

M. Perner, P. Bost, U. Lemmer, G. von Plessen, J. Feldmann, U. Becker, M. Mennig, M. Schmitt, and H. Schmidt, “Optically induced damping of the surface plasmon resonance in gold colloids,” Phys. Rev. Lett. 78, 2192-2195 (1997).
[CrossRef]

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Harcourt, 1976).

Nelson, M. A.

K. Seal, M. A. Nelson, Z. C. Ying, D. A. Genov, D. A. Sarychev, and V. M. Shalaev, “Growth, morphology, and optical and electrical properties of semicontinuous gold films,” Phys. Rev. B 67, 035318 (2003).
[CrossRef]

Perner, M.

M. Perner, P. Bost, U. Lemmer, G. von Plessen, J. Feldmann, U. Becker, M. Mennig, M. Schmitt, and H. Schmidt, “Optically induced damping of the surface plasmon resonance in gold colloids,” Phys. Rev. Lett. 78, 2192-2195 (1997).
[CrossRef]

Requejo-Isidro, J.

R. del Coso, J. Requejo-Isidro, J. Solis, J. Gonzalo, and C. N. Afonso, “Third order nonlinear optical susceptibility of Cu:Al2O3 nanocomposites: from spherical nanoparticles to the percolation threshold,” J. Appl. Phys. 95, 2755-2762 (2004).
[CrossRef]

Reynolds, P. J.

P. J. Reynolds, W. Klein, and H. E. Stanley, “A real-space renormalization group for site and bond percolation,” J. Phys. C 10, L167-L172 (1977).
[CrossRef]

Ricard, D.

Roussignol, P.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Sarychev, A. K.

V. M. Shalaev and A. K. Sarychev, “Nonlinear optics of random metal-dielectric films,” Phys. Rev. B 57, 13265-13288 (1998).
[CrossRef]

A. K. Sarychev, “Scaling invariance and percolation in a random field,” Zh. Eksp. Teor. Fiz. 72, 1001-1004 (1977).

Sarychev, D. A.

K. Seal, M. A. Nelson, Z. C. Ying, D. A. Genov, D. A. Sarychev, and V. M. Shalaev, “Growth, morphology, and optical and electrical properties of semicontinuous gold films,” Phys. Rev. B 67, 035318 (2003).
[CrossRef]

Schmidt, H.

M. Perner, P. Bost, U. Lemmer, G. von Plessen, J. Feldmann, U. Becker, M. Mennig, M. Schmitt, and H. Schmidt, “Optically induced damping of the surface plasmon resonance in gold colloids,” Phys. Rev. Lett. 78, 2192-2195 (1997).
[CrossRef]

Schmitt, M.

M. Perner, P. Bost, U. Lemmer, G. von Plessen, J. Feldmann, U. Becker, M. Mennig, M. Schmitt, and H. Schmidt, “Optically induced damping of the surface plasmon resonance in gold colloids,” Phys. Rev. Lett. 78, 2192-2195 (1997).
[CrossRef]

Seal, K.

K. Seal, M. A. Nelson, Z. C. Ying, D. A. Genov, D. A. Sarychev, and V. M. Shalaev, “Growth, morphology, and optical and electrical properties of semicontinuous gold films,” Phys. Rev. B 67, 035318 (2003).
[CrossRef]

Shalaev, V. M.

K. Seal, M. A. Nelson, Z. C. Ying, D. A. Genov, D. A. Sarychev, and V. M. Shalaev, “Growth, morphology, and optical and electrical properties of semicontinuous gold films,” Phys. Rev. B 67, 035318 (2003).
[CrossRef]

V. M. Shalaev and A. K. Sarychev, “Nonlinear optics of random metal-dielectric films,” Phys. Rev. B 57, 13265-13288 (1998).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Sheng, P.

H. B. Liao, R. F. Xiao, J. S. Fu, P. Yu, G. K. L. Wong, and P. Sheng, “Large third-order optical nonlinearity in Au:SiO2 composite films near the percolation threshold,” Appl. Phys. Lett. 70, 1-3 (1997).
[CrossRef]

P. Sheng, “Theory for the dielectric function of granular composite media,” Phys. Rev. Lett. 45, 60-63 (1980).
[CrossRef]

P. Sheng, “Pair-cluster theory for the dielectric constant of composite media,” Phys. Rev. B 22, 6364-6368 (1980).
[CrossRef]

Sipe, J. E.

J. E. Sipe and R. W. Boyd, “Nonlinear susceptibility of composite optical materials in the Maxwell Garnett model,” Phys. Rev. A 46, 1614-1629 (1992).
[CrossRef] [PubMed]

Smith, D. D.

D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks, and M. George, “z-scan measurement of the nonlinear absorption of a thin gold film,” J. Appl. Phys. 86, 6200-6205 (1999).
[CrossRef]

D. D. Smith, G. Fischer, R. W. Boyd, and D. A. Gregory, “Cancellation of photoinduced absorption in metal nanoparticle composites through a counterintuitive consequence of local field effects,” J. Opt. Soc. Am. B 14, 1625-1631 (1997).
[CrossRef]

Solis, J.

R. del Coso, J. Requejo-Isidro, J. Solis, J. Gonzalo, and C. N. Afonso, “Third order nonlinear optical susceptibility of Cu:Al2O3 nanocomposites: from spherical nanoparticles to the percolation threshold,” J. Appl. Phys. 95, 2755-2762 (2004).
[CrossRef]

Stanley, H. E.

P. J. Reynolds, W. Klein, and H. E. Stanley, “A real-space renormalization group for site and bond percolation,” J. Phys. C 10, L167-L172 (1977).
[CrossRef]

Stroud, D.

D. Stroud, “Generalized effective-medium approach to the conductivity of an inhomogeneous material,” Phys. Rev. B 12, 3368-3373 (1975).
[CrossRef]

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Vollmer, M.

U. Kreibig and M. Vollmer, “Optical properties of metal clusters,” in Springer Series in Materials Science (Springer-Verlag, 1995), Vol. 25.

von Plessen, G.

M. Perner, P. Bost, U. Lemmer, G. von Plessen, J. Feldmann, U. Becker, M. Mennig, M. Schmitt, and H. Schmidt, “Optically induced damping of the surface plasmon resonance in gold colloids,” Phys. Rev. Lett. 78, 2192-2195 (1997).
[CrossRef]

Wang, H.

H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72, 1817-1819 (1998).
[CrossRef]

H. B. Liao, R. F. Xiao, J. S. Fu, H. Wang, K. S. Wong, and G. K. L. Wong, “Origin of third-order optical nonlinearity in Au:SiO2 composite films on femtosecond and picosecond time scales,” Opt. Lett. 23, 388-390 (1998).
[CrossRef]

Wei, T.-H.

M. Sheik-Bahae, A. A. Said, T.-H. Wei, D. J. Hagan, and E. W. Van Stryland, “Sensitive measurement of optical nonlinearities using a single beam,” IEEE J. Quantum Electron. 26, 760-769 (1990).
[CrossRef]

Wong, G. K. L.

H. B. Liao, R. F. Xiao, J. S. Fu, H. Wang, K. S. Wong, and G. K. L. Wong, “Origin of third-order optical nonlinearity in Au:SiO2 composite films on femtosecond and picosecond time scales,” Opt. Lett. 23, 388-390 (1998).
[CrossRef]

H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72, 1817-1819 (1998).
[CrossRef]

H. B. Liao, R. F. Xiao, J. S. Fu, P. Yu, G. K. L. Wong, and P. Sheng, “Large third-order optical nonlinearity in Au:SiO2 composite films near the percolation threshold,” Appl. Phys. Lett. 70, 1-3 (1997).
[CrossRef]

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H. B. Liao, R. F. Xiao, J. S. Fu, H. Wang, K. S. Wong, and G. K. L. Wong, “Origin of third-order optical nonlinearity in Au:SiO2 composite films on femtosecond and picosecond time scales,” Opt. Lett. 23, 388-390 (1998).
[CrossRef]

H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72, 1817-1819 (1998).
[CrossRef]

Xiao, R. F.

H. B. Liao, R. F. Xiao, H. Wang, K. S. Wong, and G. K. L. Wong, “Large third-order optical nonlinearity in Au:TiO2 composite films measured on a femtosecond time scale,” Appl. Phys. Lett. 72, 1817-1819 (1998).
[CrossRef]

H. B. Liao, R. F. Xiao, J. S. Fu, H. Wang, K. S. Wong, and G. K. L. Wong, “Origin of third-order optical nonlinearity in Au:SiO2 composite films on femtosecond and picosecond time scales,” Opt. Lett. 23, 388-390 (1998).
[CrossRef]

H. B. Liao, R. F. Xiao, J. S. Fu, P. Yu, G. K. L. Wong, and P. Sheng, “Large third-order optical nonlinearity in Au:SiO2 composite films near the percolation threshold,” Appl. Phys. Lett. 70, 1-3 (1997).
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H. B. Liao, R. F. Xiao, J. S. Fu, P. Yu, G. K. L. Wong, and P. Sheng, “Large third-order optical nonlinearity in Au:SiO2 composite films near the percolation threshold,” Appl. Phys. Lett. 70, 1-3 (1997).
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Figures (5)

Fig. 1
Fig. 1

SEM micrographs of the gold-silica composite. The clear areas of the micrograph represent gold. (a) Sample at f = 0.05 ; the diameter of most nanoparticles can be estimated as 10 nm . (b) Sample at f = 0.55 ; even at this high fill fraction the sample consists of isolated gold nanoparticles.

Fig. 2
Fig. 2

Linear attenuation spectra of the gold-silica composite samples for various fill fractions.

Fig. 3
Fig. 3

Nonlinear absorption coefficient of the gold-silica composite film at fill fraction (a) f = 0.05 , (b) f = 0.23 , and (c) f = 0.41 , respectively. A fit to the Maxwell Garnett theory with D = 2.40 is shown for the data for f = 0.05 . The Maxwell Garnett theory is not valid at the higher fill fractions.

Fig. 4
Fig. 4

Nonlinear absorption coefficient of a gold-silica composite film plotted as a function of fill fraction at a wavelength of 532 nm . An error bar is shown for one data point; the estimated error is 35% for all data points.

Fig. 5
Fig. 5

Section of the model for a Maxwell Garnett two-dimensional composite, a host with infinitely long cylindrical inclusions.

Equations (20)

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T ( z ) = 1 q 0 ( z , 0 ) 2 3 2 ,
ϵ ϵ h ϵ + ( D 1 ) ϵ h = f ϵ i ϵ h ϵ i + ( D 1 ) ϵ h ,
ϵ ϵ h [ 1 + D f ϵ i ϵ h ϵ i + ϵ h ( D 1 ) ] .
α = ω c Im ϵ 2 ω c D f ϵ h Im { ϵ i ϵ h ϵ i + ϵ h ( D 1 ) } ,
α ω c D 2 f ϵ h 3 2 ϵ i [ ϵ i + ( D 1 ) ϵ h ] 2 + ϵ i 2 .
χ ( 3 ) = f q i 2 ( q i ) 2 χ i ( 3 ) ,
q i = ϵ + ( D 1 ) ϵ h ϵ i + ( D 1 ) ϵ h .
ϵ i = ϵ i ( bulk ) + 3 ω p 2 v F 4 ω p 3 R .
Π cyl = ε h R 2 2 ε i ε h ε i + ε h E = α cyl E .
P = P h + N Π cyl = χ h E + N α cyl E loc ,
E loc = E + 2 π Π ϵ h ,
χ = χ h + N α cyl 1 2 π N α cyl ϵ h .
ϵ ϵ h ϵ + ϵ h = f ϵ i ϵ h ϵ i + ϵ h .
E i = q i E ,
q i = ϵ + ϵ h ϵ i + ϵ h
ϵ ϵ h ϵ + ( D 1 ) ϵ h = f ϵ i ϵ h ϵ i + ( D 1 ) ϵ h ,
q i = ϵ + ( D 1 ) ϵ h ϵ i + ( D 1 ) ϵ h .
ϵ ( ϵ ϵ h ϵ + ( D 1 ) ϵ h ) Δ ϵ = f ϵ i ( ϵ i ϵ h ϵ i + ( D 1 ) ϵ h ) Δ ϵ i ,
Δ ϵ = f q i 2 Δ ϵ i .
χ ( 3 ) = f χ i ( 3 ) q i 2 q i 2 .

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