Abstract

We report on the observation of the forward degenerate four-wave mixing in four composite samples with Cu nanoclusters embedded in fused silica. The mean diameters of the copper particles in the four samples were 5, 7, 10, and 13 nm. The independent tensor elements of optical Kerr susceptibility were measured with different wave-mixing polarizations by use of 35-ps laser pulses from a mode-locked, frequency-doubled Nd:YAG laser. The measured third-order susceptibilities were on the order of 10−9–10−8 esu; the response time of the nonlinearity is faster than the laser pulse duration. The experimental results are consistent with a d−3 size dependence predicted for quantum-confined conduction band electrons in Cu nanoclusters.

© 1994 Optical Society of America

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References

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  1. C. Flytzanis and J. Hutter, in Contemporary Nonlinear Optics, G. P. A. Agrawal and R. W. Boyd, eds. (Academic, San Diego, 1992).
  2. D. Ricard, P. Roussignol, and C. Flytzanis, “Surface-mediated enhancement of optical phase conjugation in metal colloids,” Opt. Lett. 10, 511 (1985).
    [CrossRef] [PubMed]
  3. F. Hache, D. Ricard, and C. Flytzanis, “Optical nonlinearities of small metal particles: surface-mediated resonance and quantum size effects,” J. Opt. Soc. Am. B 3, 1647 (1986).
    [CrossRef]
  4. 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]
  5. 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]
  6. R. H. Magruder, R. F. Haglund, L. Yang, J. E. Wittig, and R. A. Zuhr, “Optical properties of Cu-nanocluster composites formed by ion implantation in fused silica: dose-rate dependence,” submitted to J. Appl. Phys.
  7. R. H. Magruder, R. F. Haglund, L. Yang, K. Becker, J. E. Wittig, and R. A. Zuhr, “Picosecond nonlinear optical response of Cu nanocluster created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 244, 369 (1992).
    [CrossRef]
  8. R. H. Doremus, “Optical properties of small gold particles,” J. Chem. Phys. 40, 2389 (1964).
    [CrossRef]
  9. R. F. Haglund, H. C. Mogul, R. A. Weeks, and R. A. Zuhr, “Effects of implanted transition metal ions on the refractive index of fused silica,” J. Non-Cryst. Solids 130, 326 (1991).
    [CrossRef]
  10. L. Yang, R. Dorsinville, Q. Z. Wang, W. K. Zou, P. P. Ho, N. L. Yang, and R. R. Alfano, “Third-order optical nonlinearity in polycondensed thiophene-based polymers and polysilane polymers,” J. Opt. Soc. Am. B 6, 753 (1989).
    [CrossRef]
  11. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  12. C. M. Carter, “Excited-state dynamics and temporally resolved nonresonant nonlinear-optical processes in polydiacetylenes,” J. Opt. Soc. Am. B 4, 1018 (1987).
    [CrossRef]
  13. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).
  14. P. B. Johnson and R. W. Christy, “Optical constants of the noble metals,” Phys. Rev. B 6, 6 (1972).
    [CrossRef]
  15. O. Cheshnovsky, K. J. Taylor, J. Conceicao, and R. E. Smalley, “Ultraviolet photoelectron spectra of mass-selected copper clusters: evolution of the 3d band,” Phys. Rev. Lett. 64, 1785 (1990).
    [CrossRef] [PubMed]
  16. W. P. Halperin, “Quantum size effects in metal particles,” Rev. Mod. Phys. 58, 533 (1986).
    [CrossRef]
  17. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt-Saunders, Philadelphia, 1976).
  18. B. S. Wherrett, A. L. Smirl, and T. F. Boggess, “Theory of degenerate four-wave mixing in picosecond excitation-probe experiments,” IEEE J. Quantum Electron. QE-19, 680 (1983).
    [CrossRef]
  19. U. Kreibig, “The transition clusters–solid state in small gold particles,” Solid State Commun. 28, 767 (1978).
    [CrossRef]
  20. G. L. Eesley, “Generation of nonequilibrium electron and lattice temperatures in copper by picosecond laser pulses,” Phys. Rev. B 33, 2144 (1986).
    [CrossRef]
  21. R. W. Schoenlein, W. Z. Lin, J. G. Fujimoto, and G. L. Eesley, “Femtosecond studies of nonequilibrium electronic processes in metals,” Phys. Rev. B 58, 1680 (1987).

1992 (1)

R. H. Magruder, R. F. Haglund, L. Yang, K. Becker, J. E. Wittig, and R. A. Zuhr, “Picosecond nonlinear optical response of Cu nanocluster created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 244, 369 (1992).
[CrossRef]

1991 (1)

R. F. Haglund, H. C. Mogul, R. A. Weeks, and R. A. Zuhr, “Effects of implanted transition metal ions on the refractive index of fused silica,” J. Non-Cryst. Solids 130, 326 (1991).
[CrossRef]

1990 (2)

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]

O. Cheshnovsky, K. J. Taylor, J. Conceicao, and R. E. Smalley, “Ultraviolet photoelectron spectra of mass-selected copper clusters: evolution of the 3d band,” Phys. Rev. Lett. 64, 1785 (1990).
[CrossRef] [PubMed]

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]

1987 (2)

C. M. Carter, “Excited-state dynamics and temporally resolved nonresonant nonlinear-optical processes in polydiacetylenes,” J. Opt. Soc. Am. B 4, 1018 (1987).
[CrossRef]

R. W. Schoenlein, W. Z. Lin, J. G. Fujimoto, and G. L. Eesley, “Femtosecond studies of nonequilibrium electronic processes in metals,” Phys. Rev. B 58, 1680 (1987).

1986 (3)

G. L. Eesley, “Generation of nonequilibrium electron and lattice temperatures in copper by picosecond laser pulses,” Phys. Rev. B 33, 2144 (1986).
[CrossRef]

W. P. Halperin, “Quantum size effects in metal particles,” Rev. Mod. Phys. 58, 533 (1986).
[CrossRef]

F. Hache, D. Ricard, and C. Flytzanis, “Optical nonlinearities of small metal particles: surface-mediated resonance and quantum size effects,” J. Opt. Soc. Am. B 3, 1647 (1986).
[CrossRef]

1985 (1)

1983 (1)

B. S. Wherrett, A. L. Smirl, and T. F. Boggess, “Theory of degenerate four-wave mixing in picosecond excitation-probe experiments,” IEEE J. Quantum Electron. QE-19, 680 (1983).
[CrossRef]

1978 (1)

U. Kreibig, “The transition clusters–solid state in small gold particles,” Solid State Commun. 28, 767 (1978).
[CrossRef]

1972 (1)

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

1964 (1)

R. H. Doremus, “Optical properties of small gold particles,” J. Chem. Phys. 40, 2389 (1964).
[CrossRef]

Alfano, R. R.

Ashcroft, N. W.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt-Saunders, Philadelphia, 1976).

Ashley, P. R.

Becker, K.

R. H. Magruder, R. F. Haglund, L. Yang, K. Becker, J. E. Wittig, and R. A. Zuhr, “Picosecond nonlinear optical response of Cu nanocluster created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 244, 369 (1992).
[CrossRef]

Bloemer, M. J.

Boggess, T. F.

B. S. Wherrett, A. L. Smirl, and T. F. Boggess, “Theory of degenerate four-wave mixing in picosecond excitation-probe experiments,” IEEE J. Quantum Electron. QE-19, 680 (1983).
[CrossRef]

Carter, C. M.

Cheshnovsky, O.

O. Cheshnovsky, K. J. Taylor, J. Conceicao, and R. E. Smalley, “Ultraviolet photoelectron spectra of mass-selected copper clusters: evolution of the 3d band,” Phys. Rev. Lett. 64, 1785 (1990).
[CrossRef] [PubMed]

Christy, R. W.

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

Conceicao, J.

O. Cheshnovsky, K. J. Taylor, J. Conceicao, and R. E. Smalley, “Ultraviolet photoelectron spectra of mass-selected copper clusters: evolution of the 3d band,” Phys. Rev. Lett. 64, 1785 (1990).
[CrossRef] [PubMed]

Doremus, R. H.

R. H. Doremus, “Optical properties of small gold particles,” J. Chem. Phys. 40, 2389 (1964).
[CrossRef]

Dorsinville, R.

Eesley, G. L.

R. W. Schoenlein, W. Z. Lin, J. G. Fujimoto, and G. L. Eesley, “Femtosecond studies of nonequilibrium electronic processes in metals,” Phys. Rev. B 58, 1680 (1987).

G. L. Eesley, “Generation of nonequilibrium electron and lattice temperatures in copper by picosecond laser pulses,” Phys. Rev. B 33, 2144 (1986).
[CrossRef]

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]

F. Hache, D. Ricard, and C. Flytzanis, “Optical nonlinearities of small metal particles: surface-mediated resonance and quantum size effects,” J. Opt. Soc. Am. B 3, 1647 (1986).
[CrossRef]

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

C. Flytzanis and J. Hutter, in Contemporary Nonlinear Optics, G. P. A. Agrawal and R. W. Boyd, eds. (Academic, San Diego, 1992).

Fujimoto, J. G.

R. W. Schoenlein, W. Z. Lin, J. G. Fujimoto, and G. L. Eesley, “Femtosecond studies of nonequilibrium electronic processes in metals,” Phys. Rev. B 58, 1680 (1987).

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]

F. Hache, D. Ricard, and C. Flytzanis, “Optical nonlinearities of small metal particles: surface-mediated resonance and quantum size effects,” J. Opt. Soc. Am. B 3, 1647 (1986).
[CrossRef]

Haglund, R. F.

R. H. Magruder, R. F. Haglund, L. Yang, K. Becker, J. E. Wittig, and R. A. Zuhr, “Picosecond nonlinear optical response of Cu nanocluster created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 244, 369 (1992).
[CrossRef]

R. F. Haglund, H. C. Mogul, R. A. Weeks, and R. A. Zuhr, “Effects of implanted transition metal ions on the refractive index of fused silica,” J. Non-Cryst. Solids 130, 326 (1991).
[CrossRef]

R. H. Magruder, R. F. Haglund, L. Yang, J. E. Wittig, and R. A. Zuhr, “Optical properties of Cu-nanocluster composites formed by ion implantation in fused silica: dose-rate dependence,” submitted to J. Appl. Phys.

Halperin, W. P.

W. P. Halperin, “Quantum size effects in metal particles,” Rev. Mod. Phys. 58, 533 (1986).
[CrossRef]

Haus, J. W.

Ho, P. P.

Hutter, J.

C. Flytzanis and J. Hutter, in Contemporary Nonlinear Optics, G. P. A. Agrawal and R. W. Boyd, eds. (Academic, San Diego, 1992).

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

Johnson, P. B.

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

U. Kreibig, “The transition clusters–solid state in small gold particles,” Solid State Commun. 28, 767 (1978).
[CrossRef]

Lin, W. Z.

R. W. Schoenlein, W. Z. Lin, J. G. Fujimoto, and G. L. Eesley, “Femtosecond studies of nonequilibrium electronic processes in metals,” Phys. Rev. B 58, 1680 (1987).

Magruder, R. H.

R. H. Magruder, R. F. Haglund, L. Yang, K. Becker, J. E. Wittig, and R. A. Zuhr, “Picosecond nonlinear optical response of Cu nanocluster created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 244, 369 (1992).
[CrossRef]

R. H. Magruder, R. F. Haglund, L. Yang, J. E. Wittig, and R. A. Zuhr, “Optical properties of Cu-nanocluster composites formed by ion implantation in fused silica: dose-rate dependence,” submitted to J. Appl. Phys.

Mermin, N. D.

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt-Saunders, Philadelphia, 1976).

Mogul, H. C.

R. F. Haglund, H. C. Mogul, R. A. Weeks, and R. A. Zuhr, “Effects of implanted transition metal ions on the refractive index of fused silica,” J. Non-Cryst. Solids 130, 326 (1991).
[CrossRef]

Ricard, D.

Roussignol, P.

Schoenlein, R. W.

R. W. Schoenlein, W. Z. Lin, J. G. Fujimoto, and G. L. Eesley, “Femtosecond studies of nonequilibrium electronic processes in metals,” Phys. Rev. B 58, 1680 (1987).

Shen, Y. R.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

Smalley, R. E.

O. Cheshnovsky, K. J. Taylor, J. Conceicao, and R. E. Smalley, “Ultraviolet photoelectron spectra of mass-selected copper clusters: evolution of the 3d band,” Phys. Rev. Lett. 64, 1785 (1990).
[CrossRef] [PubMed]

Smirl, A. L.

B. S. Wherrett, A. L. Smirl, and T. F. Boggess, “Theory of degenerate four-wave mixing in picosecond excitation-probe experiments,” IEEE J. Quantum Electron. QE-19, 680 (1983).
[CrossRef]

Taylor, K. J.

O. Cheshnovsky, K. J. Taylor, J. Conceicao, and R. E. Smalley, “Ultraviolet photoelectron spectra of mass-selected copper clusters: evolution of the 3d band,” Phys. Rev. Lett. 64, 1785 (1990).
[CrossRef] [PubMed]

Wang, Q. Z.

Weeks, R. A.

R. F. Haglund, H. C. Mogul, R. A. Weeks, and R. A. Zuhr, “Effects of implanted transition metal ions on the refractive index of fused silica,” J. Non-Cryst. Solids 130, 326 (1991).
[CrossRef]

Wherrett, B. S.

B. S. Wherrett, A. L. Smirl, and T. F. Boggess, “Theory of degenerate four-wave mixing in picosecond excitation-probe experiments,” IEEE J. Quantum Electron. QE-19, 680 (1983).
[CrossRef]

Wittig, J. E.

R. H. Magruder, R. F. Haglund, L. Yang, K. Becker, J. E. Wittig, and R. A. Zuhr, “Picosecond nonlinear optical response of Cu nanocluster created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 244, 369 (1992).
[CrossRef]

R. H. Magruder, R. F. Haglund, L. Yang, J. E. Wittig, and R. A. Zuhr, “Optical properties of Cu-nanocluster composites formed by ion implantation in fused silica: dose-rate dependence,” submitted to J. Appl. Phys.

Yang, L.

R. H. Magruder, R. F. Haglund, L. Yang, K. Becker, J. E. Wittig, and R. A. Zuhr, “Picosecond nonlinear optical response of Cu nanocluster created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 244, 369 (1992).
[CrossRef]

L. Yang, R. Dorsinville, Q. Z. Wang, W. K. Zou, P. P. Ho, N. L. Yang, and R. R. Alfano, “Third-order optical nonlinearity in polycondensed thiophene-based polymers and polysilane polymers,” J. Opt. Soc. Am. B 6, 753 (1989).
[CrossRef]

R. H. Magruder, R. F. Haglund, L. Yang, J. E. Wittig, and R. A. Zuhr, “Optical properties of Cu-nanocluster composites formed by ion implantation in fused silica: dose-rate dependence,” submitted to J. Appl. Phys.

Yang, N. L.

Zou, W. K.

Zuhr, R. A.

R. H. Magruder, R. F. Haglund, L. Yang, K. Becker, J. E. Wittig, and R. A. Zuhr, “Picosecond nonlinear optical response of Cu nanocluster created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 244, 369 (1992).
[CrossRef]

R. F. Haglund, H. C. Mogul, R. A. Weeks, and R. A. Zuhr, “Effects of implanted transition metal ions on the refractive index of fused silica,” J. Non-Cryst. Solids 130, 326 (1991).
[CrossRef]

R. H. Magruder, R. F. Haglund, L. Yang, J. E. Wittig, and R. A. Zuhr, “Optical properties of Cu-nanocluster composites formed by ion implantation in fused silica: dose-rate dependence,” submitted to J. Appl. Phys.

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]

IEEE J. Quantum Electron. (1)

B. S. Wherrett, A. L. Smirl, and T. F. Boggess, “Theory of degenerate four-wave mixing in picosecond excitation-probe experiments,” IEEE J. Quantum Electron. QE-19, 680 (1983).
[CrossRef]

J. Chem. Phys. (1)

R. H. Doremus, “Optical properties of small gold particles,” J. Chem. Phys. 40, 2389 (1964).
[CrossRef]

J. Non-Cryst. Solids (1)

R. F. Haglund, H. C. Mogul, R. A. Weeks, and R. A. Zuhr, “Effects of implanted transition metal ions on the refractive index of fused silica,” J. Non-Cryst. Solids 130, 326 (1991).
[CrossRef]

J. Opt. Soc. Am. B (4)

Mat. Res. Soc. Symp. Proc. (1)

R. H. Magruder, R. F. Haglund, L. Yang, K. Becker, J. E. Wittig, and R. A. Zuhr, “Picosecond nonlinear optical response of Cu nanocluster created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 244, 369 (1992).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. B (3)

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

G. L. Eesley, “Generation of nonequilibrium electron and lattice temperatures in copper by picosecond laser pulses,” Phys. Rev. B 33, 2144 (1986).
[CrossRef]

R. W. Schoenlein, W. Z. Lin, J. G. Fujimoto, and G. L. Eesley, “Femtosecond studies of nonequilibrium electronic processes in metals,” Phys. Rev. B 58, 1680 (1987).

Phys. Rev. Lett. (1)

O. Cheshnovsky, K. J. Taylor, J. Conceicao, and R. E. Smalley, “Ultraviolet photoelectron spectra of mass-selected copper clusters: evolution of the 3d band,” Phys. Rev. Lett. 64, 1785 (1990).
[CrossRef] [PubMed]

Rev. Mod. Phys. (1)

W. P. Halperin, “Quantum size effects in metal particles,” Rev. Mod. Phys. 58, 533 (1986).
[CrossRef]

Solid State Commun. (1)

U. Kreibig, “The transition clusters–solid state in small gold particles,” Solid State Commun. 28, 767 (1978).
[CrossRef]

Other (5)

N. W. Ashcroft and N. D. Mermin, Solid State Physics (Holt-Saunders, Philadelphia, 1976).

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975).

C. Flytzanis and J. Hutter, in Contemporary Nonlinear Optics, G. P. A. Agrawal and R. W. Boyd, eds. (Academic, San Diego, 1992).

R. H. Magruder, R. F. Haglund, L. Yang, J. E. Wittig, and R. A. Zuhr, “Optical properties of Cu-nanocluster composites formed by ion implantation in fused silica: dose-rate dependence,” submitted to J. Appl. Phys.

Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).

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Figures (3)

Fig. 1
Fig. 1

Beam geometry of three-dimensional DFWM. Beam 4 is generated in the sample by DFWM.

Fig. 2
Fig. 2

Normalized DFWM signal from Cu clusters (sample 4) as a function of time delay of the probe beam: (a) Result for the xxxx combination of polarizations. (b) Results for the xyxy combination. The laser wavelength for both sets of data was 532 nm.

Fig. 3
Fig. 3

Third-order susceptibility of the Cu clusters as a function of mean particle diameter for the four Cu-implanted samples. The solid line is the fit of 1/d3.

Tables (1)

Tables Icon

Table 1 Characteristics of the Four Cu Ion Implanted Fused Silica Samplesa

Equations (9)

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

P 4 ( 3 ) ( k 1 - k 2 + k 3 , ω ) = χ ( 3 ) ( ω ) : E 1 ( k 1 ) E 2 * ( k 2 ) E 3 ( k 3 ) ,
P 4 x ( x ) = χ x x x x ( 3 ) E 1 x E 2 x * E 3 x + χ x x y y ( 3 ) E 1 x E 2 y * E 3 y + χ x y y x ( 3 ) E 1 y E 2 y * E 3 x + χ x y x y ( 3 ) E 1 y E 2 x * E 3 y .
E T ( ω , t , r ) = i e ^ i E i ( ω , t , r ) exp ( i k i · r ) = i e ^ i A i ( ω , r ) f ( t ) exp ( i k i · r ) ,
E i n = 3 d m + 2 d E = f 1 E ,
χ ( 3 ) = p f 1 2 f 1 2 χ m ( 3 ) ,
χ m ( 3 ) ( ω ; ω , ω , - ω ) int r a ~ 1 d 3 e 4 E f 4 m 2 5 ω 7 g ( υ ) ( 1 - d d 0 ) ,
g ( υ ) = 1 υ 3 1 - υ 1 d x x 3 / 2 ( x + υ ) 1 / 2
υ = ω / E f ,
χ m ( 3 ) int e r ~ 2 3 T 1 T 2 μ c d 4 ,

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