Abstract

The higher-order nonlinear optical response of a composite medium having metal nanoparticles is usually attributed to that originating from the third-order nonlinearity of the metal. In this article, the time dependence of hot-electron contribution to the third-, fifth-, and seventh-order nonlinear absorption coefficients of the composite medium has been studied. By comparing the results of the calculation with that of the experiments, it has been shown that the higher-order nonlinearities originating from the hot electrons of metal do contribute to the measured higher-order nonlinear absorption coefficients of the composite material.

© 2011 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91, 223901 (2003).
    [CrossRef] [PubMed]
  2. M. Hawton and M. Dignam, “Infinite-order excitonic Bloch equations for asymmetric nanostructures,” Phys. Rev. Lett. 91, 267402 (2003).
    [CrossRef]
  3. Y. Yosia and S. Ping, “Double optical bistability and its application in nonlinear chalcogenide-fiber Bragg gratings,” Physica B 394, 293–296 (2007).
    [CrossRef]
  4. Yosia and P. Shum, “Optical bistability in periodic media with third-, fifth-, and seventh-order nonlinearities,” J. Lightwave Technol. 25, 875–882 (2007).
    [CrossRef]
  5. K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103, 113902 (2009).
    [CrossRef] [PubMed]
  6. Y. Akiyama, K. Midorikawa, Y. Matsunawa, Y. Nagata, M. Obara, H. Tashiro, and K. Toyoda, “Generation of high-order harmonics using laser-produced rare-gas-like ions,” Phys. Rev. Lett. 69, 2176–2179 (1992).
    [CrossRef] [PubMed]
  7. 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]
  8. N. D. Fatti and F. Vallee, “Ultrafast optical nonlinear properties of metal nanoparticles,” Appl. Phys. B. 73, 383–390 (2001).
    [CrossRef]
  9. G. S. Agarwal and S. D. Gupta, “T-matrix approach to the nonlinear susceptibilities of heterogeneous media,” Phys. Rev. A 38, 5678–5687 (1988).
    [CrossRef] [PubMed]
  10. N. C. Kothari, “Effective-medium theory of a nonlinear composite medium using the T-matrix approach: exact results for spherical grains,” Phys. Rev. A 41, 4486–4492 (1990).
    [CrossRef] [PubMed]
  11. X. Y. Liu and Z. Y. Li, “High order nonlinear susceptibilities of composite medium,” Solid State Commun. 96, 981–985 (1995).
    [CrossRef]
  12. E. L. Falcao-Filho, C. B. de Araujo, and J. J. Rodrigues, Jr., “High-order nonlinearities of aqueous colloids containing silver nanoparticles,” J. Opt. Soc. Am. B 24, 2948–2956 (2007).
    [CrossRef]
  13. D. Rativa, R. E. de Araujo, and A. S. L. Gomes, “One photon nonresonant high-order nonlinear optical properties of silver nanoparticles in aqueous solution,” Opt. Express 16, 19244–19252 (2008).
    [CrossRef]
  14. C. Voisin, N. D. Fatti, D. Christofilos, and F. Vallée, “Ultrafast electron dynamics and optical nonlinearities in metal nanoparticles,” J. Phys. Chem. B 105, 2264–2280 (2001).
    [CrossRef]
  15. Y. Tang and M. Ouyang, “Tailoring properties and functionalities of metal nanoparticles through crystallinity engineering,” Nat. Mater. 6, 754–759 (2007).
    [CrossRef] [PubMed]
  16. J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94, 181902 (2009).
    [CrossRef]
  17. F. Vallee, Non-Equilibrium Dynamics of Semiconductors and Nanostructures (CRC Press, 2005), Chap. 5, pp. 101–142.
    [CrossRef]
  18. Y. Hamanaka, A. Nakamura, S. Omi, N. D. Fatti, F. Vallee, and C. Flytzanis, “Ultrafast response of nonlinear refractive index of silver nanocrystals embedded in glass,” Appl. Phys. Lett. 75, 1712–1714 (1999).
    [CrossRef]
  19. N. D. Fatti, C. Voisin, M. Achermann, S. Tzortzakis, D. Christofilos, and F. Vallee, “Non-equilibrium electron dynamics in noble metals,” Phys. Rev. B 61, 16956–16966 (2000).
    [CrossRef]
  20. M. Perner, S. Gresillon, J. Mrz, G. von Plessen, J. Feldmann, J. Porstendorfer, K.-J. Berg, and G. Berg, “Observation of hot-electron pressure in the vibration dynamics of metal nanoparticles,” Phys. Rev. Lett. 85, 792–795 (2000).
    [CrossRef] [PubMed]
  21. J. Y. Bigot, V. Halte, J. C. Merle, and A. Daunois, “Electron dynamics in metallic nanoparticles,” Chem. Phys. 251, 181–203(2000).
    [CrossRef]
  22. S. Giordano and W. Rocchia, “Shape-dependent effects of dielectrically nonlinear inclusions in heterogeneous media,” J. Appl. Phys. 98, 104101 (2005).
    [CrossRef]
  23. N. Okada, Y. Hamanaka, A. Nakamura, I. Pastoriza-Santos, and L. M. Liz-Marzan, “Linear and nonlinear optical response of silver nanoprisms: local electric fields of dipole and quadrupole plasmon resonances,” J. Phys. Chem. B 108, 8751–8755(2004).
    [CrossRef]
  24. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
    [CrossRef]
  25. Y. Hamanaka, A. Nakamura, N. Hayashi, and S. Omi, “Dispersion curves of complex third-order optical susceptibilities around the surface plasmon resonance in Ag nanocrystal-glass composites,” J. Opt. Soc. Am. B 20, 1227–1232 (2003).
    [CrossRef]
  26. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley & Sons, 1983).
  27. L. Bonacina, A. Gallegari, C. Bonati, F. V. Mourik, and M. Chergui, “Time resolved photodynamics of triangular-shaped silver nanoplates,” Nano Lett. 6, 7–10 (2006).
    [CrossRef] [PubMed]

2009 (2)

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103, 113902 (2009).
[CrossRef] [PubMed]

J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94, 181902 (2009).
[CrossRef]

2008 (1)

2007 (4)

E. L. Falcao-Filho, C. B. de Araujo, and J. J. Rodrigues, Jr., “High-order nonlinearities of aqueous colloids containing silver nanoparticles,” J. Opt. Soc. Am. B 24, 2948–2956 (2007).
[CrossRef]

Y. Tang and M. Ouyang, “Tailoring properties and functionalities of metal nanoparticles through crystallinity engineering,” Nat. Mater. 6, 754–759 (2007).
[CrossRef] [PubMed]

Y. Yosia and S. Ping, “Double optical bistability and its application in nonlinear chalcogenide-fiber Bragg gratings,” Physica B 394, 293–296 (2007).
[CrossRef]

Yosia and P. Shum, “Optical bistability in periodic media with third-, fifth-, and seventh-order nonlinearities,” J. Lightwave Technol. 25, 875–882 (2007).
[CrossRef]

2006 (1)

L. Bonacina, A. Gallegari, C. Bonati, F. V. Mourik, and M. Chergui, “Time resolved photodynamics of triangular-shaped silver nanoplates,” Nano Lett. 6, 7–10 (2006).
[CrossRef] [PubMed]

2005 (1)

S. Giordano and W. Rocchia, “Shape-dependent effects of dielectrically nonlinear inclusions in heterogeneous media,” J. Appl. Phys. 98, 104101 (2005).
[CrossRef]

2004 (1)

N. Okada, Y. Hamanaka, A. Nakamura, I. Pastoriza-Santos, and L. M. Liz-Marzan, “Linear and nonlinear optical response of silver nanoprisms: local electric fields of dipole and quadrupole plasmon resonances,” J. Phys. Chem. B 108, 8751–8755(2004).
[CrossRef]

2003 (3)

Y. Hamanaka, A. Nakamura, N. Hayashi, and S. Omi, “Dispersion curves of complex third-order optical susceptibilities around the surface plasmon resonance in Ag nanocrystal-glass composites,” J. Opt. Soc. Am. B 20, 1227–1232 (2003).
[CrossRef]

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef] [PubMed]

M. Hawton and M. Dignam, “Infinite-order excitonic Bloch equations for asymmetric nanostructures,” Phys. Rev. Lett. 91, 267402 (2003).
[CrossRef]

2001 (2)

N. D. Fatti and F. Vallee, “Ultrafast optical nonlinear properties of metal nanoparticles,” Appl. Phys. B. 73, 383–390 (2001).
[CrossRef]

C. Voisin, N. D. Fatti, D. Christofilos, and F. Vallée, “Ultrafast electron dynamics and optical nonlinearities in metal nanoparticles,” J. Phys. Chem. B 105, 2264–2280 (2001).
[CrossRef]

2000 (3)

N. D. Fatti, C. Voisin, M. Achermann, S. Tzortzakis, D. Christofilos, and F. Vallee, “Non-equilibrium electron dynamics in noble metals,” Phys. Rev. B 61, 16956–16966 (2000).
[CrossRef]

M. Perner, S. Gresillon, J. Mrz, G. von Plessen, J. Feldmann, J. Porstendorfer, K.-J. Berg, and G. Berg, “Observation of hot-electron pressure in the vibration dynamics of metal nanoparticles,” Phys. Rev. Lett. 85, 792–795 (2000).
[CrossRef] [PubMed]

J. Y. Bigot, V. Halte, J. C. Merle, and A. Daunois, “Electron dynamics in metallic nanoparticles,” Chem. Phys. 251, 181–203(2000).
[CrossRef]

1999 (1)

Y. Hamanaka, A. Nakamura, S. Omi, N. D. Fatti, F. Vallee, and C. Flytzanis, “Ultrafast response of nonlinear refractive index of silver nanocrystals embedded in glass,” Appl. Phys. Lett. 75, 1712–1714 (1999).
[CrossRef]

1995 (1)

X. Y. Liu and Z. Y. Li, “High order nonlinear susceptibilities of composite medium,” Solid State Commun. 96, 981–985 (1995).
[CrossRef]

1992 (1)

Y. Akiyama, K. Midorikawa, Y. Matsunawa, Y. Nagata, M. Obara, H. Tashiro, and K. Toyoda, “Generation of high-order harmonics using laser-produced rare-gas-like ions,” Phys. Rev. Lett. 69, 2176–2179 (1992).
[CrossRef] [PubMed]

1990 (1)

N. C. Kothari, “Effective-medium theory of a nonlinear composite medium using the T-matrix approach: exact results for spherical grains,” Phys. Rev. A 41, 4486–4492 (1990).
[CrossRef] [PubMed]

1988 (1)

G. S. Agarwal and S. D. Gupta, “T-matrix approach to the nonlinear susceptibilities of heterogeneous media,” Phys. Rev. A 38, 5678–5687 (1988).
[CrossRef] [PubMed]

1985 (1)

1972 (1)

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Achermann, M.

N. D. Fatti, C. Voisin, M. Achermann, S. Tzortzakis, D. Christofilos, and F. Vallee, “Non-equilibrium electron dynamics in noble metals,” Phys. Rev. B 61, 16956–16966 (2000).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and S. D. Gupta, “T-matrix approach to the nonlinear susceptibilities of heterogeneous media,” Phys. Rev. A 38, 5678–5687 (1988).
[CrossRef] [PubMed]

Aitchison, J. S.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef] [PubMed]

Akiyama, Y.

Y. Akiyama, K. Midorikawa, Y. Matsunawa, Y. Nagata, M. Obara, H. Tashiro, and K. Toyoda, “Generation of high-order harmonics using laser-produced rare-gas-like ions,” Phys. Rev. Lett. 69, 2176–2179 (1992).
[CrossRef] [PubMed]

Bar-Ad, S.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef] [PubMed]

Berg, G.

M. Perner, S. Gresillon, J. Mrz, G. von Plessen, J. Feldmann, J. Porstendorfer, K.-J. Berg, and G. Berg, “Observation of hot-electron pressure in the vibration dynamics of metal nanoparticles,” Phys. Rev. Lett. 85, 792–795 (2000).
[CrossRef] [PubMed]

Berg, K.-J.

M. Perner, S. Gresillon, J. Mrz, G. von Plessen, J. Feldmann, J. Porstendorfer, K.-J. Berg, and G. Berg, “Observation of hot-electron pressure in the vibration dynamics of metal nanoparticles,” Phys. Rev. Lett. 85, 792–795 (2000).
[CrossRef] [PubMed]

Bigot, J. Y.

J. Y. Bigot, V. Halte, J. C. Merle, and A. Daunois, “Electron dynamics in metallic nanoparticles,” Chem. Phys. 251, 181–203(2000).
[CrossRef]

Bohren, C. F.

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

Bonacina, L.

L. Bonacina, A. Gallegari, C. Bonati, F. V. Mourik, and M. Chergui, “Time resolved photodynamics of triangular-shaped silver nanoplates,” Nano Lett. 6, 7–10 (2006).
[CrossRef] [PubMed]

Bonati, C.

L. Bonacina, A. Gallegari, C. Bonati, F. V. Mourik, and M. Chergui, “Time resolved photodynamics of triangular-shaped silver nanoplates,” Nano Lett. 6, 7–10 (2006).
[CrossRef] [PubMed]

Boyd, R. W.

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103, 113902 (2009).
[CrossRef] [PubMed]

Chari, R.

J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94, 181902 (2009).
[CrossRef]

Chergui, M.

L. Bonacina, A. Gallegari, C. Bonati, F. V. Mourik, and M. Chergui, “Time resolved photodynamics of triangular-shaped silver nanoplates,” Nano Lett. 6, 7–10 (2006).
[CrossRef] [PubMed]

Cheskis, D.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef] [PubMed]

Christofilos, D.

C. Voisin, N. D. Fatti, D. Christofilos, and F. Vallée, “Ultrafast electron dynamics and optical nonlinearities in metal nanoparticles,” J. Phys. Chem. B 105, 2264–2280 (2001).
[CrossRef]

N. D. Fatti, C. Voisin, M. Achermann, S. Tzortzakis, D. Christofilos, and F. Vallee, “Non-equilibrium electron dynamics in noble metals,” Phys. Rev. B 61, 16956–16966 (2000).
[CrossRef]

Christy, R. W.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Daunois, A.

J. Y. Bigot, V. Halte, J. C. Merle, and A. Daunois, “Electron dynamics in metallic nanoparticles,” Chem. Phys. 251, 181–203(2000).
[CrossRef]

de Araujo, C. B.

de Araujo, R. E.

Dignam, M.

M. Hawton and M. Dignam, “Infinite-order excitonic Bloch equations for asymmetric nanostructures,” Phys. Rev. Lett. 91, 267402 (2003).
[CrossRef]

Dolgaleva, K.

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103, 113902 (2009).
[CrossRef] [PubMed]

Eisenberg, H. S.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef] [PubMed]

Falcao-Filho, E. L.

Fatti, N. D.

N. D. Fatti and F. Vallee, “Ultrafast optical nonlinear properties of metal nanoparticles,” Appl. Phys. B. 73, 383–390 (2001).
[CrossRef]

C. Voisin, N. D. Fatti, D. Christofilos, and F. Vallée, “Ultrafast electron dynamics and optical nonlinearities in metal nanoparticles,” J. Phys. Chem. B 105, 2264–2280 (2001).
[CrossRef]

N. D. Fatti, C. Voisin, M. Achermann, S. Tzortzakis, D. Christofilos, and F. Vallee, “Non-equilibrium electron dynamics in noble metals,” Phys. Rev. B 61, 16956–16966 (2000).
[CrossRef]

Y. Hamanaka, A. Nakamura, S. Omi, N. D. Fatti, F. Vallee, and C. Flytzanis, “Ultrafast response of nonlinear refractive index of silver nanocrystals embedded in glass,” Appl. Phys. Lett. 75, 1712–1714 (1999).
[CrossRef]

Feldmann, J.

M. Perner, S. Gresillon, J. Mrz, G. von Plessen, J. Feldmann, J. Porstendorfer, K.-J. Berg, and G. Berg, “Observation of hot-electron pressure in the vibration dynamics of metal nanoparticles,” Phys. Rev. Lett. 85, 792–795 (2000).
[CrossRef] [PubMed]

Flytzanis, C.

Y. Hamanaka, A. Nakamura, S. Omi, N. D. Fatti, F. Vallee, and C. Flytzanis, “Ultrafast response of nonlinear refractive index of silver nanocrystals embedded in glass,” Appl. Phys. Lett. 75, 1712–1714 (1999).
[CrossRef]

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]

Gallegari, A.

L. Bonacina, A. Gallegari, C. Bonati, F. V. Mourik, and M. Chergui, “Time resolved photodynamics of triangular-shaped silver nanoplates,” Nano Lett. 6, 7–10 (2006).
[CrossRef] [PubMed]

Giordano, S.

S. Giordano and W. Rocchia, “Shape-dependent effects of dielectrically nonlinear inclusions in heterogeneous media,” J. Appl. Phys. 98, 104101 (2005).
[CrossRef]

Gomes, A. S. L.

Gresillon, S.

M. Perner, S. Gresillon, J. Mrz, G. von Plessen, J. Feldmann, J. Porstendorfer, K.-J. Berg, and G. Berg, “Observation of hot-electron pressure in the vibration dynamics of metal nanoparticles,” Phys. Rev. Lett. 85, 792–795 (2000).
[CrossRef] [PubMed]

Gupta, S. D.

G. S. Agarwal and S. D. Gupta, “T-matrix approach to the nonlinear susceptibilities of heterogeneous media,” Phys. Rev. A 38, 5678–5687 (1988).
[CrossRef] [PubMed]

Halte, V.

J. Y. Bigot, V. Halte, J. C. Merle, and A. Daunois, “Electron dynamics in metallic nanoparticles,” Chem. Phys. 251, 181–203(2000).
[CrossRef]

Hamanaka, Y.

N. Okada, Y. Hamanaka, A. Nakamura, I. Pastoriza-Santos, and L. M. Liz-Marzan, “Linear and nonlinear optical response of silver nanoprisms: local electric fields of dipole and quadrupole plasmon resonances,” J. Phys. Chem. B 108, 8751–8755(2004).
[CrossRef]

Y. Hamanaka, A. Nakamura, N. Hayashi, and S. Omi, “Dispersion curves of complex third-order optical susceptibilities around the surface plasmon resonance in Ag nanocrystal-glass composites,” J. Opt. Soc. Am. B 20, 1227–1232 (2003).
[CrossRef]

Y. Hamanaka, A. Nakamura, S. Omi, N. D. Fatti, F. Vallee, and C. Flytzanis, “Ultrafast response of nonlinear refractive index of silver nanocrystals embedded in glass,” Appl. Phys. Lett. 75, 1712–1714 (1999).
[CrossRef]

Hawton, M.

M. Hawton and M. Dignam, “Infinite-order excitonic Bloch equations for asymmetric nanostructures,” Phys. Rev. Lett. 91, 267402 (2003).
[CrossRef]

Hayashi, N.

Huffman, D. R.

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

Jayabalan, J.

J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94, 181902 (2009).
[CrossRef]

Johnson, P. B.

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Khan, S.

J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94, 181902 (2009).
[CrossRef]

Kothari, N. C.

N. C. Kothari, “Effective-medium theory of a nonlinear composite medium using the T-matrix approach: exact results for spherical grains,” Phys. Rev. A 41, 4486–4492 (1990).
[CrossRef] [PubMed]

Li, Z. Y.

X. Y. Liu and Z. Y. Li, “High order nonlinear susceptibilities of composite medium,” Solid State Commun. 96, 981–985 (1995).
[CrossRef]

Liu, X. Y.

X. Y. Liu and Z. Y. Li, “High order nonlinear susceptibilities of composite medium,” Solid State Commun. 96, 981–985 (1995).
[CrossRef]

Liz-Marzan, L. M.

N. Okada, Y. Hamanaka, A. Nakamura, I. Pastoriza-Santos, and L. M. Liz-Marzan, “Linear and nonlinear optical response of silver nanoprisms: local electric fields of dipole and quadrupole plasmon resonances,” J. Phys. Chem. B 108, 8751–8755(2004).
[CrossRef]

Matsunawa, Y.

Y. Akiyama, K. Midorikawa, Y. Matsunawa, Y. Nagata, M. Obara, H. Tashiro, and K. Toyoda, “Generation of high-order harmonics using laser-produced rare-gas-like ions,” Phys. Rev. Lett. 69, 2176–2179 (1992).
[CrossRef] [PubMed]

Merle, J. C.

J. Y. Bigot, V. Halte, J. C. Merle, and A. Daunois, “Electron dynamics in metallic nanoparticles,” Chem. Phys. 251, 181–203(2000).
[CrossRef]

Midorikawa, K.

Y. Akiyama, K. Midorikawa, Y. Matsunawa, Y. Nagata, M. Obara, H. Tashiro, and K. Toyoda, “Generation of high-order harmonics using laser-produced rare-gas-like ions,” Phys. Rev. Lett. 69, 2176–2179 (1992).
[CrossRef] [PubMed]

Morandotti, R.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef] [PubMed]

Mourik, F. V.

L. Bonacina, A. Gallegari, C. Bonati, F. V. Mourik, and M. Chergui, “Time resolved photodynamics of triangular-shaped silver nanoplates,” Nano Lett. 6, 7–10 (2006).
[CrossRef] [PubMed]

Mrz, J.

M. Perner, S. Gresillon, J. Mrz, G. von Plessen, J. Feldmann, J. Porstendorfer, K.-J. Berg, and G. Berg, “Observation of hot-electron pressure in the vibration dynamics of metal nanoparticles,” Phys. Rev. Lett. 85, 792–795 (2000).
[CrossRef] [PubMed]

Nagata, Y.

Y. Akiyama, K. Midorikawa, Y. Matsunawa, Y. Nagata, M. Obara, H. Tashiro, and K. Toyoda, “Generation of high-order harmonics using laser-produced rare-gas-like ions,” Phys. Rev. Lett. 69, 2176–2179 (1992).
[CrossRef] [PubMed]

Nakamura, A.

N. Okada, Y. Hamanaka, A. Nakamura, I. Pastoriza-Santos, and L. M. Liz-Marzan, “Linear and nonlinear optical response of silver nanoprisms: local electric fields of dipole and quadrupole plasmon resonances,” J. Phys. Chem. B 108, 8751–8755(2004).
[CrossRef]

Y. Hamanaka, A. Nakamura, N. Hayashi, and S. Omi, “Dispersion curves of complex third-order optical susceptibilities around the surface plasmon resonance in Ag nanocrystal-glass composites,” J. Opt. Soc. Am. B 20, 1227–1232 (2003).
[CrossRef]

Y. Hamanaka, A. Nakamura, S. Omi, N. D. Fatti, F. Vallee, and C. Flytzanis, “Ultrafast response of nonlinear refractive index of silver nanocrystals embedded in glass,” Appl. Phys. Lett. 75, 1712–1714 (1999).
[CrossRef]

Oak, S. M.

J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94, 181902 (2009).
[CrossRef]

Obara, M.

Y. Akiyama, K. Midorikawa, Y. Matsunawa, Y. Nagata, M. Obara, H. Tashiro, and K. Toyoda, “Generation of high-order harmonics using laser-produced rare-gas-like ions,” Phys. Rev. Lett. 69, 2176–2179 (1992).
[CrossRef] [PubMed]

Okada, N.

N. Okada, Y. Hamanaka, A. Nakamura, I. Pastoriza-Santos, and L. M. Liz-Marzan, “Linear and nonlinear optical response of silver nanoprisms: local electric fields of dipole and quadrupole plasmon resonances,” J. Phys. Chem. B 108, 8751–8755(2004).
[CrossRef]

Omi, S.

Y. Hamanaka, A. Nakamura, N. Hayashi, and S. Omi, “Dispersion curves of complex third-order optical susceptibilities around the surface plasmon resonance in Ag nanocrystal-glass composites,” J. Opt. Soc. Am. B 20, 1227–1232 (2003).
[CrossRef]

Y. Hamanaka, A. Nakamura, S. Omi, N. D. Fatti, F. Vallee, and C. Flytzanis, “Ultrafast response of nonlinear refractive index of silver nanocrystals embedded in glass,” Appl. Phys. Lett. 75, 1712–1714 (1999).
[CrossRef]

Ouyang, M.

Y. Tang and M. Ouyang, “Tailoring properties and functionalities of metal nanoparticles through crystallinity engineering,” Nat. Mater. 6, 754–759 (2007).
[CrossRef] [PubMed]

Pastoriza-Santos, I.

N. Okada, Y. Hamanaka, A. Nakamura, I. Pastoriza-Santos, and L. M. Liz-Marzan, “Linear and nonlinear optical response of silver nanoprisms: local electric fields of dipole and quadrupole plasmon resonances,” J. Phys. Chem. B 108, 8751–8755(2004).
[CrossRef]

Perner, M.

M. Perner, S. Gresillon, J. Mrz, G. von Plessen, J. Feldmann, J. Porstendorfer, K.-J. Berg, and G. Berg, “Observation of hot-electron pressure in the vibration dynamics of metal nanoparticles,” Phys. Rev. Lett. 85, 792–795 (2000).
[CrossRef] [PubMed]

Ping, S.

Y. Yosia and S. Ping, “Double optical bistability and its application in nonlinear chalcogenide-fiber Bragg gratings,” Physica B 394, 293–296 (2007).
[CrossRef]

Porstendorfer, J.

M. Perner, S. Gresillon, J. Mrz, G. von Plessen, J. Feldmann, J. Porstendorfer, K.-J. Berg, and G. Berg, “Observation of hot-electron pressure in the vibration dynamics of metal nanoparticles,” Phys. Rev. Lett. 85, 792–795 (2000).
[CrossRef] [PubMed]

Rativa, D.

Ricard, D.

Rocchia, W.

S. Giordano and W. Rocchia, “Shape-dependent effects of dielectrically nonlinear inclusions in heterogeneous media,” J. Appl. Phys. 98, 104101 (2005).
[CrossRef]

Rodrigues, J. J.

Ross, D.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef] [PubMed]

Roussignol, P.

Shin, H.

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103, 113902 (2009).
[CrossRef] [PubMed]

Shum, P.

Silberberg, Y.

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef] [PubMed]

Singh, A.

J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94, 181902 (2009).
[CrossRef]

Srivastava, H.

J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94, 181902 (2009).
[CrossRef]

Tang, Y.

Y. Tang and M. Ouyang, “Tailoring properties and functionalities of metal nanoparticles through crystallinity engineering,” Nat. Mater. 6, 754–759 (2007).
[CrossRef] [PubMed]

Tashiro, H.

Y. Akiyama, K. Midorikawa, Y. Matsunawa, Y. Nagata, M. Obara, H. Tashiro, and K. Toyoda, “Generation of high-order harmonics using laser-produced rare-gas-like ions,” Phys. Rev. Lett. 69, 2176–2179 (1992).
[CrossRef] [PubMed]

Toyoda, K.

Y. Akiyama, K. Midorikawa, Y. Matsunawa, Y. Nagata, M. Obara, H. Tashiro, and K. Toyoda, “Generation of high-order harmonics using laser-produced rare-gas-like ions,” Phys. Rev. Lett. 69, 2176–2179 (1992).
[CrossRef] [PubMed]

Tzortzakis, S.

N. D. Fatti, C. Voisin, M. Achermann, S. Tzortzakis, D. Christofilos, and F. Vallee, “Non-equilibrium electron dynamics in noble metals,” Phys. Rev. B 61, 16956–16966 (2000).
[CrossRef]

Vallee, F.

N. D. Fatti and F. Vallee, “Ultrafast optical nonlinear properties of metal nanoparticles,” Appl. Phys. B. 73, 383–390 (2001).
[CrossRef]

N. D. Fatti, C. Voisin, M. Achermann, S. Tzortzakis, D. Christofilos, and F. Vallee, “Non-equilibrium electron dynamics in noble metals,” Phys. Rev. B 61, 16956–16966 (2000).
[CrossRef]

Y. Hamanaka, A. Nakamura, S. Omi, N. D. Fatti, F. Vallee, and C. Flytzanis, “Ultrafast response of nonlinear refractive index of silver nanocrystals embedded in glass,” Appl. Phys. Lett. 75, 1712–1714 (1999).
[CrossRef]

F. Vallee, Non-Equilibrium Dynamics of Semiconductors and Nanostructures (CRC Press, 2005), Chap. 5, pp. 101–142.
[CrossRef]

Vallée, F.

C. Voisin, N. D. Fatti, D. Christofilos, and F. Vallée, “Ultrafast electron dynamics and optical nonlinearities in metal nanoparticles,” J. Phys. Chem. B 105, 2264–2280 (2001).
[CrossRef]

Voisin, C.

C. Voisin, N. D. Fatti, D. Christofilos, and F. Vallée, “Ultrafast electron dynamics and optical nonlinearities in metal nanoparticles,” J. Phys. Chem. B 105, 2264–2280 (2001).
[CrossRef]

N. D. Fatti, C. Voisin, M. Achermann, S. Tzortzakis, D. Christofilos, and F. Vallee, “Non-equilibrium electron dynamics in noble metals,” Phys. Rev. B 61, 16956–16966 (2000).
[CrossRef]

von Plessen, G.

M. Perner, S. Gresillon, J. Mrz, G. von Plessen, J. Feldmann, J. Porstendorfer, K.-J. Berg, and G. Berg, “Observation of hot-electron pressure in the vibration dynamics of metal nanoparticles,” Phys. Rev. Lett. 85, 792–795 (2000).
[CrossRef] [PubMed]

Yosia,

Yosia, Y.

Y. Yosia and S. Ping, “Double optical bistability and its application in nonlinear chalcogenide-fiber Bragg gratings,” Physica B 394, 293–296 (2007).
[CrossRef]

Appl. Phys. B. (1)

N. D. Fatti and F. Vallee, “Ultrafast optical nonlinear properties of metal nanoparticles,” Appl. Phys. B. 73, 383–390 (2001).
[CrossRef]

Appl. Phys. Lett. (2)

J. Jayabalan, A. Singh, R. Chari, S. Khan, H. Srivastava, and S. M. Oak, “Transient absorption and higher-order nonlinearities in silver nanoplatelets,” Appl. Phys. Lett. 94, 181902 (2009).
[CrossRef]

Y. Hamanaka, A. Nakamura, S. Omi, N. D. Fatti, F. Vallee, and C. Flytzanis, “Ultrafast response of nonlinear refractive index of silver nanocrystals embedded in glass,” Appl. Phys. Lett. 75, 1712–1714 (1999).
[CrossRef]

Chem. Phys. (1)

J. Y. Bigot, V. Halte, J. C. Merle, and A. Daunois, “Electron dynamics in metallic nanoparticles,” Chem. Phys. 251, 181–203(2000).
[CrossRef]

J. Appl. Phys. (1)

S. Giordano and W. Rocchia, “Shape-dependent effects of dielectrically nonlinear inclusions in heterogeneous media,” J. Appl. Phys. 98, 104101 (2005).
[CrossRef]

J. Lightwave Technol. (1)

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

J. Phys. Chem. B (2)

N. Okada, Y. Hamanaka, A. Nakamura, I. Pastoriza-Santos, and L. M. Liz-Marzan, “Linear and nonlinear optical response of silver nanoprisms: local electric fields of dipole and quadrupole plasmon resonances,” J. Phys. Chem. B 108, 8751–8755(2004).
[CrossRef]

C. Voisin, N. D. Fatti, D. Christofilos, and F. Vallée, “Ultrafast electron dynamics and optical nonlinearities in metal nanoparticles,” J. Phys. Chem. B 105, 2264–2280 (2001).
[CrossRef]

Nano Lett. (1)

L. Bonacina, A. Gallegari, C. Bonati, F. V. Mourik, and M. Chergui, “Time resolved photodynamics of triangular-shaped silver nanoplates,” Nano Lett. 6, 7–10 (2006).
[CrossRef] [PubMed]

Nat. Mater. (1)

Y. Tang and M. Ouyang, “Tailoring properties and functionalities of metal nanoparticles through crystallinity engineering,” Nat. Mater. 6, 754–759 (2007).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. A (2)

G. S. Agarwal and S. D. Gupta, “T-matrix approach to the nonlinear susceptibilities of heterogeneous media,” Phys. Rev. A 38, 5678–5687 (1988).
[CrossRef] [PubMed]

N. C. Kothari, “Effective-medium theory of a nonlinear composite medium using the T-matrix approach: exact results for spherical grains,” Phys. Rev. A 41, 4486–4492 (1990).
[CrossRef] [PubMed]

Phys. Rev. B (2)

N. D. Fatti, C. Voisin, M. Achermann, S. Tzortzakis, D. Christofilos, and F. Vallee, “Non-equilibrium electron dynamics in noble metals,” Phys. Rev. B 61, 16956–16966 (2000).
[CrossRef]

P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 4370–4379 (1972).
[CrossRef]

Phys. Rev. Lett. (5)

M. Perner, S. Gresillon, J. Mrz, G. von Plessen, J. Feldmann, J. Porstendorfer, K.-J. Berg, and G. Berg, “Observation of hot-electron pressure in the vibration dynamics of metal nanoparticles,” Phys. Rev. Lett. 85, 792–795 (2000).
[CrossRef] [PubMed]

K. Dolgaleva, H. Shin, and R. W. Boyd, “Observation of a microscopic cascaded contribution to the fifth-order nonlinear susceptibility,” Phys. Rev. Lett. 103, 113902 (2009).
[CrossRef] [PubMed]

Y. Akiyama, K. Midorikawa, Y. Matsunawa, Y. Nagata, M. Obara, H. Tashiro, and K. Toyoda, “Generation of high-order harmonics using laser-produced rare-gas-like ions,” Phys. Rev. Lett. 69, 2176–2179 (1992).
[CrossRef] [PubMed]

D. Cheskis, S. Bar-Ad, R. Morandotti, J. S. Aitchison, H. S. Eisenberg, Y. Silberberg, and D. Ross, “Strong spatiotemporal localization in a silica nonlinear waveguide array,” Phys. Rev. Lett. 91, 223901 (2003).
[CrossRef] [PubMed]

M. Hawton and M. Dignam, “Infinite-order excitonic Bloch equations for asymmetric nanostructures,” Phys. Rev. Lett. 91, 267402 (2003).
[CrossRef]

Physica B (1)

Y. Yosia and S. Ping, “Double optical bistability and its application in nonlinear chalcogenide-fiber Bragg gratings,” Physica B 394, 293–296 (2007).
[CrossRef]

Solid State Commun. (1)

X. Y. Liu and Z. Y. Li, “High order nonlinear susceptibilities of composite medium,” Solid State Commun. 96, 981–985 (1995).
[CrossRef]

Other (2)

F. Vallee, Non-Equilibrium Dynamics of Semiconductors and Nanostructures (CRC Press, 2005), Chap. 5, pp. 101–142.
[CrossRef]

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

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1

Time dependence of Δ T e / T 0 : thick curve, full numerical solution to Eq. (11); thin curve, plot of Eq. (18); dotted curve, difference between the above two; and dashed curve, only the first term of Eq. (18). T 0 = 300 K .

Fig. 2
Fig. 2

Dispersion of third-, fifth-, and seventh-order nonlinear absorption coefficients of a composite material around its LSPR. α 0 is the linear absorption coefficient.

Fig. 3
Fig. 3

Measured extinction coefficient of the silver nanoplatelets in water.

Fig. 4
Fig. 4

Measured change in absorption of silver nanoplatelets at different peak pump intensities. Note that at higher powers of pump intensity, the recovery of Δ α is slower.

Fig. 5
Fig. 5

Experimental pump–probe delay dependent (a)  α 2 , (b)  α 4 , and (c)  α 6 of silver nanoplatelets in water. The solid line is a guide for the eye.

Fig. 6
Fig. 6

Calculated time dependence of (a)  α 2 , (b)  α 4 , and (c)  α 6 in a silver nanocomposite material, after the thermalization of electrons.

Equations (35)

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

f ( ω ) = 3 ε h ε m + 2 ε h ,
χ e ( 3 ) = p f ( ω ) 2 | f ( ω ) | 2 χ m ( 3 ) ,
T e t = g C e ( T e ) ( T e T l ) ,
T l t = g C l ( T e T l ) ,
T e , T l C l γ 0 100 T 0
T exc T e T e q ln [ T e T e q T exc T e q ] = G t γ 0 T e q ,
Δ T e m e = T exc T 0 ,
Δ T e m e = [ T 0 2 + 2 Δ Q γ 0 ] ( 1 / 2 ) T 0 ,
Δ T e m e T 0 = [ 1 + 2 ξ ( ω ) | E L | 2 ] ( 1 / 2 ) 1 ,
ξ ( ω ) = ε 0 c n m ( ω ) k m ( ω ) γ 0 T 0 2 ,
m ( 1 z ) l n z = n t ,
m = Δ T e m e T 0 ,
z = Δ T e ( t ) Δ T e m e ,
n = G γ 0 T 0 ,
Δ T e ( t ) = T e ( t ) T 0 .
m z = W ( m e m n t ) .
m z = m e ( m n t ) m 2 e 2 ( m n t ) + 3 2 m 3 e 3 ( m n t ) .
Δ T e T 0 ( Δ T e m e T 0 ) e n t ( Δ T e m e T 0 ) 2 ( e 2 n t e n t ) + ( Δ T e m e T 0 ) 3 ( 3 2 e 3 n t 2 e 2 n t + 1 2 e n t ) .
Δ T e T 0 ξ e n t | E L | 2 ξ 2 ( e 2 n t 1 2 e n t ) | E L | 4 + ξ 3 ( 3 2 e 3 n t e 2 n t ) | E L | 6 .
Δ ε m ( ω p ) = η ( ω p ) Δ T e T 0 ,
Δ ε m ( ω p ) = η ξ e n t | E L | 2 η ξ 2 ( e 2 n t 1 2 e n t ) | E L | 4 + η ξ 3 ( 3 2 e 3 n t e 2 n t ) | E L | 6 .
Δ ε m ( ω p ) = η ξ e n t | f ( ω ) | 2 | E 0 | 2 η ξ 2 | f ( ω ) | 4 ( e 2 n t 1 2 e n t ) | E 0 | 4 + η ξ 3 | f ( ω ) | 6 ( 3 2 e 3 n t e 2 n t ) | E 0 | 6 .
ε e ( ω p ) = ε h + 3 p ε h ε m ( ω p ) ε h ( ε m ( ω p ) + 2 ε h ) ,
α ( ω p ) = ω p c ε h Im [ ε e ( ω p ) ] ,
| 2 ( ε m l + 2 ε h ) Δ ε m ( ε m l + 2 ε h ) 2 + ( ε m l ) 2 | 1 ,
Δ α = ω p p c ε h Im [ f 2 ( ω p ) ] Δ ε m ( ω p ) ,
Δ α ( t , I ) = α 2 ( t ) I + α 4 ( t ) I 2 + α 6 ( t ) I 3 ,
α 2 ( t ) = ω p p η ζ c ε h Im [ f 2 ( ω p ) ] | f ( ω ) | 2 e n t ,
α 4 ( t ) = ω p p η ζ 2 c ε h Im [ f 2 ( ω p ) ] | f ( ω ) | 4 ( e 2 n t 1 2 e n t ) ,
α 6 ( t ) = ω p p η ζ 3 c ε h Im [ f 2 ( ω p ) ] | f ( ω ) | 6 ( 3 2 e 3 n t e 2 n t ) ,
ζ = 2 n m ( ω ) k m ( ω ) γ 0 T 0 2 ε h .
f i ( ω ) = E L i E 0 i = a i ε h ( ε m + b i ε h ) ,
a i = 1 L i , and b i = ( 1 L i ) L i .
ε e i = ε h + a i p ε h ε m ε h ( ε m + b i ε h ) .
Δ α ( t p p , I ) = α 2 ( t p p ) I + α 4 ( t p p ) I 2 + α 6 ( t p p ) I 3 ,

Metrics