Abstract

Third-order nonlinearities of glasses doped with a large number of copper or silver particles are studied by degenerate four-wave mixing with an emphasis on particle-size dependence. The nonlinear susceptibility χ(3) exhibits a peak at the wavelength of the absorption peak, with a maximum value of the order of 10−7 esu. The value of χ(3)/α is roughly independent of the absorption coefficient α and increases as the particle radius increases. This result is well explained by the size dependence of the imaginary part of the dielectric constant of metal particles and the local-field factor. The time response of the nonlinearity exhibits two-component behavior: the fast decay time is shorter than the pulse width of the laser (~12 ps), whereas the slow one is 120–200 ps, being weakly dependent on the radius.

© 1994 Optical Society of America

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References

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1992 (3)

A. Nakamura, T. Tokizaki, H. Akiyama, and T. Kataoka, J. Lumin. 53, 105 (1992).
[CrossRef]

C. C. Yang, A. Villeneuve, and G. I. Stegeman, “Effects of three-photon absorption on nonlinear directional coupling,” Opt. Lett. 17, 710–712 (1992).
[CrossRef] [PubMed]

R. H. Magruder, R. F. Haglund, L. Yang, J. E. Wittig, K. Becker, and R. A. Zuhr, “Picosecond nonlinear optical response of copper clusters created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 224, 369 (1992).

1990 (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, 347–357 (1988).
[CrossRef]

1987 (2)

B. K. Russell, J. G. Mantovani, V. E. Anderson, R. J. Warmack, and T. L. Ferrell, “Experimental test of the Mie theory for microlithographically produced silver spheres,” Phys. Rev. B 35, 2151 (1987).
[CrossRef]

N. F. Borrelli, D. W. Hall, H. J. Holland, and D. W. Smith, “Quantum confinement effects of semiconducting microcrystallites in glass,” J. Appl. Phys. 61, 5399 (1987).
[CrossRef]

1986 (1)

1985 (1)

1981 (1)

J. A. A. J. Perenboom, P. Wyder, and F. Meier, “Electronic properties of small metallic particles,” Phys. Rep. 78, 173–292 (1981).
[CrossRef]

1969 (1)

U. Kreibig and C. V. Fragstein, “The limitation of electron mean free path in small silver particles,” Z. Phys. 224, 307–323 (1969).
[CrossRef]

Akiyama, H.

A. Nakamura, T. Tokizaki, H. Akiyama, and T. Kataoka, J. Lumin. 53, 105 (1992).
[CrossRef]

Anderson, V. E.

B. K. Russell, J. G. Mantovani, V. E. Anderson, R. J. Warmack, and T. L. Ferrell, “Experimental test of the Mie theory for microlithographically produced silver spheres,” Phys. Rev. B 35, 2151 (1987).
[CrossRef]

Ashley, P. R.

Becker, K.

R. H. Magruder, R. F. Haglund, L. Yang, J. E. Wittig, K. Becker, and R. A. Zuhr, “Picosecond nonlinear optical response of copper clusters created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 224, 369 (1992).

Bloemer, M. J.

Borrelli, N. F.

N. F. Borrelli, D. W. Hall, H. J. Holland, and D. W. Smith, “Quantum confinement effects of semiconducting microcrystallites in glass,” J. Appl. Phys. 61, 5399 (1987).
[CrossRef]

Ferrell, T. L.

B. K. Russell, J. G. Mantovani, V. E. Anderson, R. J. Warmack, and T. L. Ferrell, “Experimental test of the Mie theory for microlithographically produced silver spheres,” Phys. Rev. B 35, 2151 (1987).
[CrossRef]

Flytzanis, C.

Fragstein, C. V.

U. Kreibig and C. V. Fragstein, “The limitation of electron mean free path in small silver particles,” Z. Phys. 224, 307–323 (1969).
[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, 347–357 (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, 1647–1655 (1986).
[CrossRef]

Haglund, R. F.

R. H. Magruder, R. F. Haglund, L. Yang, J. E. Wittig, K. Becker, and R. A. Zuhr, “Picosecond nonlinear optical response of copper clusters created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 224, 369 (1992).

Hall, D. W.

N. F. Borrelli, D. W. Hall, H. J. Holland, and D. W. Smith, “Quantum confinement effects of semiconducting microcrystallites in glass,” J. Appl. Phys. 61, 5399 (1987).
[CrossRef]

Haus, J. W.

Holland, H. J.

N. F. Borrelli, D. W. Hall, H. J. Holland, and D. W. Smith, “Quantum confinement effects of semiconducting microcrystallites in glass,” J. Appl. Phys. 61, 5399 (1987).
[CrossRef]

Kataoka, T.

A. Nakamura, T. Tokizaki, H. Akiyama, and T. Kataoka, J. Lumin. 53, 105 (1992).
[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, 347–357 (1988).
[CrossRef]

U. Kreibig and C. V. Fragstein, “The limitation of electron mean free path in small silver particles,” Z. Phys. 224, 307–323 (1969).
[CrossRef]

Magruder, R. H.

R. H. Magruder, R. F. Haglund, L. Yang, J. E. Wittig, K. Becker, and R. A. Zuhr, “Picosecond nonlinear optical response of copper clusters created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 224, 369 (1992).

Mantovani, J. G.

B. K. Russell, J. G. Mantovani, V. E. Anderson, R. J. Warmack, and T. L. Ferrell, “Experimental test of the Mie theory for microlithographically produced silver spheres,” Phys. Rev. B 35, 2151 (1987).
[CrossRef]

Meier, F.

J. A. A. J. Perenboom, P. Wyder, and F. Meier, “Electronic properties of small metallic particles,” Phys. Rep. 78, 173–292 (1981).
[CrossRef]

Nakamura, A.

A. Nakamura, T. Tokizaki, H. Akiyama, and T. Kataoka, J. Lumin. 53, 105 (1992).
[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, 173–292 (1981).
[CrossRef]

Ricard, D.

Roussignol, Ph.

Russell, B. K.

B. K. Russell, J. G. Mantovani, V. E. Anderson, R. J. Warmack, and T. L. Ferrell, “Experimental test of the Mie theory for microlithographically produced silver spheres,” Phys. Rev. B 35, 2151 (1987).
[CrossRef]

Smith, D. W.

N. F. Borrelli, D. W. Hall, H. J. Holland, and D. W. Smith, “Quantum confinement effects of semiconducting microcrystallites in glass,” J. Appl. Phys. 61, 5399 (1987).
[CrossRef]

Stegeman, G. I.

Tokizaki, T.

A. Nakamura, T. Tokizaki, H. Akiyama, and T. Kataoka, J. Lumin. 53, 105 (1992).
[CrossRef]

Villeneuve, A.

Warmack, R. J.

B. K. Russell, J. G. Mantovani, V. E. Anderson, R. J. Warmack, and T. L. Ferrell, “Experimental test of the Mie theory for microlithographically produced silver spheres,” Phys. Rev. B 35, 2151 (1987).
[CrossRef]

Wittig, J. E.

R. H. Magruder, R. F. Haglund, L. Yang, J. E. Wittig, K. Becker, and R. A. Zuhr, “Picosecond nonlinear optical response of copper clusters created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 224, 369 (1992).

Wyder, P.

J. A. A. J. Perenboom, P. Wyder, and F. Meier, “Electronic properties of small metallic particles,” Phys. Rep. 78, 173–292 (1981).
[CrossRef]

Yang, C. C.

Yang, L.

R. H. Magruder, R. F. Haglund, L. Yang, J. E. Wittig, K. Becker, and R. A. Zuhr, “Picosecond nonlinear optical response of copper clusters created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 224, 369 (1992).

Zuhr, R. A.

R. H. Magruder, R. F. Haglund, L. Yang, J. E. Wittig, K. Becker, and R. A. Zuhr, “Picosecond nonlinear optical response of copper clusters created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 224, 369 (1992).

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, 347–357 (1988).
[CrossRef]

J. Appl. Phys. (1)

N. F. Borrelli, D. W. Hall, H. J. Holland, and D. W. Smith, “Quantum confinement effects of semiconducting microcrystallites in glass,” J. Appl. Phys. 61, 5399 (1987).
[CrossRef]

J. Lumin. (1)

A. Nakamura, T. Tokizaki, H. Akiyama, and T. Kataoka, J. Lumin. 53, 105 (1992).
[CrossRef]

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

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

R. H. Magruder, R. F. Haglund, L. Yang, J. E. Wittig, K. Becker, and R. A. Zuhr, “Picosecond nonlinear optical response of copper clusters created by ion implantation in fused silica,” Mat. Res. Soc. Symp. Proc. 224, 369 (1992).

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, 173–292 (1981).
[CrossRef]

Phys. Rev. B (1)

B. K. Russell, J. G. Mantovani, V. E. Anderson, R. J. Warmack, and T. L. Ferrell, “Experimental test of the Mie theory for microlithographically produced silver spheres,” Phys. Rev. B 35, 2151 (1987).
[CrossRef]

Z. Phys. (1)

U. Kreibig and C. V. Fragstein, “The limitation of electron mean free path in small silver particles,” Z. Phys. 224, 307–323 (1969).
[CrossRef]

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Figures (10)

Fig. 1
Fig. 1

Preparation process of glass doped with small metal particles.

Fig. 2
Fig. 2

X-ray diffraction patterns of (a) 50P2O5–50BaO–6SnO–6Cu2O glass, heat treated at 490°C for 1h and (b) 50P2O5–50BaO–10SnO–10Ag2O glass, heat treated at 500°C for 65 h. R is the average radius of the metal particles.

Fig. 3
Fig. 3

Transmission electron micrographs of (a) 50P2O5–50BaO–6SnO–6Cu2O glass, heat treated at 460°C for 120 h and (b) 50P2O5–50BaO–4SnO–4Ag2O glass, heat treated at 480°C for 16 h. Average radii are (a) 12.5 nm and (b) 6.4 nm.

Fig. 4
Fig. 4

Size distributions of copper and silver particles, obtained from analysis of TEM measurements. R is the average radius of the metal particles, and S is the standard deviation.

Fig. 5
Fig. 5

Absorption spectra of glasses doped with copper and silver particles for various particle sizes: (a) 50P2O5–50BaO–6SnO–6Cu2O glass, heat treated at 420 °C (b) 50P2O5–50BaO–4SnO–4Ag2O glass, heat treated at 520 °C;(c) 50P2O5–50CaO–8SnO–8Cu2O glass, heat treated for 16 h. R is the average radius of the metal particles.

Fig. 6
Fig. 6

Diffraction-signal intensity versus pump intensity for (a) 50P2O5–50BaO–6SnO–6Cu2O glass, heat treated at 480 °C for 1.5 h, and (b) 50P2O5–50BaO–6SnO–4Ag2O glass, heat treated at 520 °C for 16 h. λ is the wavelength used for measurement.

Fig. 7
Fig. 7

Dependence of χ(3) on the pumping wavelength: (a) 50P2O5–50BaO–6SnO–6Cu2O glass, heat treated at 440 °C for 65 h, and (b) 50P2O5–50BaO–6SnO–4Ag2O glass, heat treated at 520 °C for 16 h. R is the average radius of the metal particles.

Fig. 8
Fig. 8

χ(3) and χ(3)/α as a function of absorption coefficient. R is the average radius of the metal particles.

Fig. 9
Fig. 9

χ(3)/α and fi2/m″ as a function of particle size. Solid curves represent the calculation of fi2/m″ based on the mean-free-path theory. λ is the wavelength used for measurement.

Fig. 10
Fig. 10

Time response of copper-doped glasses as a function of the delay time of the probe beam for various particle sizes. R is the average radius of the metal particles, and τ is the decay time.

Tables (2)

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Table 1 Characteristics of Copper-Doped Glasses

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Table 2 Characteristics of Silver-Doped Glasses

Equations (7)

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E i = 3 d ( ω ) E 0 / [ m ( ω ) + 2 d ( ω ) ] = f i ( ω ) E 0 ,
χ ( 3 ) = p f i ( ω ) 2 f i ( ω ) χ m ( 3 ) ,
m ( ω s ) + 2 d ( ω s ) = 0.
2 Cu + + Sn 2 + 2 Cu 0 + Sn 4 + ,
χ ( 3 ) = ( n 2 c λ / 2 8 π 3 ) [ α / ( 1 - T ) T ] ( η / I 0 ) ,
α = p ( ω / n c ) f i 2 m ;
χ ( 3 ) / α ~ p f i 2 f i 2 χ m ( 3 ) / p f i 2 m ~ ( f i 2 / m ) χ m ( 3 ) .

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