Abstract

We formed composite materials with geometries approximating that of the Bruggeman model by filling the pores of a porous glass with optically nonlinear fluids spanning a range of linear refractive indices. The effective linear refractive indices of the composites were measured with a Mach–Zehnder interferometer. The effective nonlinear refractive indices were determined by the Z-scan method. In both cases good agreement between the experimental data and theoretical predictions was found.

© 1997 Optical Society of America

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  1. J. C. Maxwell Garnett, Philos. Trans. R. Soc. London 203, 385 (1904); 205, 237 (1906).
  2. D. A. G. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935).
    [CrossRef]
  3. R. Landauer, J. Appl. Phys. 23, 779 (1952).
    [CrossRef]
  4. R. K. Jain and R. C. Lind, J. Opt. Soc. Am. 73, 647 (1983).
    [CrossRef]
  5. D. Ricard, Ph. Roussignol, and C. Flytzanis, Opt. Lett. 10, 511 (1985).
    [CrossRef] [PubMed]
  6. F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, Appl. Phys. A 47, 347 (1988).
    [CrossRef]
  7. D. Ricard, P. Roussignol, F. Hache, and C. Flytzanis, Phys. Status Solidi 159, 275 (1990).
    [CrossRef]
  8. G. S. Agarwal and S. Dutta Gupta, Phys. Rev. A 38, 5678 (1988).
    [CrossRef] [PubMed]
  9. D. Stroud and P. M. Hui, Phys. Rev. B 37, 8719 (1988).
    [CrossRef]
  10. A. E. Neeves and M. H. Birnboim, J. Opt. Soc. Am. B 6, 787 (1989).
    [CrossRef]
  11. J. W. Haus, R. Inguva, and C. M. Bowden, Phys. Rev. A 40, 5729 (1989).
    [CrossRef] [PubMed]
  12. J. W. Haus, N. Kalyaniwalla, R. Inguva, M. Bloemer, and C. M. Bowden, J. Opt. Soc. Am. B 6, 797 (1989).
    [CrossRef]
  13. L. Brus, Appl. Phys. A 53, 465 (1991).
    [CrossRef]
  14. J. E. Sipe and R. W. Boyd, Phys. Rev. A 46, 1614 (1992).
    [CrossRef] [PubMed]
  15. L. Yang, K. Becker, F. M. Smith, R. H. Magruder, R. F. Haglund, L. Yang, R. Dorsinville, R. R. Alfano, and R. A. Zuhr, J. Opt. Soc. Am. B 11, 457 (1994).
    [CrossRef]
  16. K. Uchida, S. Kaneko, S. Omi, C. Hata, H. Tanji, Y. Asahara, A. J. Ikushima, T. Tokizaki, and A. Nakamura, J. Opt. Soc. Am. B 11, 1236 (1994).
    [CrossRef]
  17. X. C. Zeng, D. J. Bergman, P. M. Hui, and D. Stroud, Phys. Rev. B 38, 10970 (1988).
    [CrossRef]
  18. K. W. Yu, P. M. Hui, and D. Stroud, Phys. Rev. B 47, 14150 (1993).
    [CrossRef]
  19. Product information: VYCOR brand porous glass, PI-VPG-88, Corning Glass Works.
  20. T. H. Elmer, “Porous and reconstructed glasses,” in Ceramics and Glasses, S. J. Schneider, Jr., ed., Vol. 4 of Engineered Materials Handbook (ASM International, Cleveland, Ohio, 1992).
  21. M. E. Nordberg, J. Am. Ceram. Soc. 27, 299 (1944).
    [CrossRef]
  22. M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
    [CrossRef]
  23. R. W. Boyd and J. E. Sipe, J. Opt. Soc. Am. B 11, 297 (1994).
    [CrossRef]

1994 (3)

1993 (1)

K. W. Yu, P. M. Hui, and D. Stroud, Phys. Rev. B 47, 14150 (1993).
[CrossRef]

1992 (1)

J. E. Sipe and R. W. Boyd, Phys. Rev. A 46, 1614 (1992).
[CrossRef] [PubMed]

1991 (1)

L. Brus, Appl. Phys. A 53, 465 (1991).
[CrossRef]

1990 (2)

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

D. Ricard, P. Roussignol, F. Hache, and C. Flytzanis, Phys. Status Solidi 159, 275 (1990).
[CrossRef]

1989 (3)

1988 (4)

G. S. Agarwal and S. Dutta Gupta, Phys. Rev. A 38, 5678 (1988).
[CrossRef] [PubMed]

D. Stroud and P. M. Hui, Phys. Rev. B 37, 8719 (1988).
[CrossRef]

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, Appl. Phys. A 47, 347 (1988).
[CrossRef]

X. C. Zeng, D. J. Bergman, P. M. Hui, and D. Stroud, Phys. Rev. B 38, 10970 (1988).
[CrossRef]

1985 (1)

1983 (1)

1952 (1)

R. Landauer, J. Appl. Phys. 23, 779 (1952).
[CrossRef]

1944 (1)

M. E. Nordberg, J. Am. Ceram. Soc. 27, 299 (1944).
[CrossRef]

1935 (1)

D. A. G. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935).
[CrossRef]

Agarwal, G. S.

G. S. Agarwal and S. Dutta Gupta, Phys. Rev. A 38, 5678 (1988).
[CrossRef] [PubMed]

Alfano, R. R.

Asahara, Y.

Becker, K.

Bergman, D. J.

X. C. Zeng, D. J. Bergman, P. M. Hui, and D. Stroud, Phys. Rev. B 38, 10970 (1988).
[CrossRef]

Birnboim, M. H.

Bloemer, M.

Bowden, C. M.

Boyd, R. W.

Bruggeman, D. A. G.

D. A. G. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935).
[CrossRef]

Brus, L.

L. Brus, Appl. Phys. A 53, 465 (1991).
[CrossRef]

Dorsinville, R.

Dutta Gupta, S.

G. S. Agarwal and S. Dutta Gupta, Phys. Rev. A 38, 5678 (1988).
[CrossRef] [PubMed]

Flytzanis, C.

D. Ricard, P. Roussignol, F. Hache, and C. Flytzanis, Phys. Status Solidi 159, 275 (1990).
[CrossRef]

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, Appl. Phys. A 47, 347 (1988).
[CrossRef]

D. Ricard, Ph. Roussignol, and C. Flytzanis, Opt. Lett. 10, 511 (1985).
[CrossRef] [PubMed]

Hache, F.

D. Ricard, P. Roussignol, F. Hache, and C. Flytzanis, Phys. Status Solidi 159, 275 (1990).
[CrossRef]

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, Appl. Phys. A 47, 347 (1988).
[CrossRef]

Hagan, D. J.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Haglund, R. F.

Hata, C.

Haus, J. W.

Hui, P. M.

K. W. Yu, P. M. Hui, and D. Stroud, Phys. Rev. B 47, 14150 (1993).
[CrossRef]

X. C. Zeng, D. J. Bergman, P. M. Hui, and D. Stroud, Phys. Rev. B 38, 10970 (1988).
[CrossRef]

D. Stroud and P. M. Hui, Phys. Rev. B 37, 8719 (1988).
[CrossRef]

Ikushima, A. J.

Inguva, R.

Jain, R. K.

Kalyaniwalla, N.

Kaneko, S.

Kreibig, U.

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, Appl. Phys. A 47, 347 (1988).
[CrossRef]

Landauer, R.

R. Landauer, J. Appl. Phys. 23, 779 (1952).
[CrossRef]

Lind, R. C.

Magruder, R. H.

Nakamura, A.

Neeves, A. E.

Nordberg, M. E.

M. E. Nordberg, J. Am. Ceram. Soc. 27, 299 (1944).
[CrossRef]

Omi, S.

Ricard, D.

D. Ricard, P. Roussignol, F. Hache, and C. Flytzanis, Phys. Status Solidi 159, 275 (1990).
[CrossRef]

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, Appl. Phys. A 47, 347 (1988).
[CrossRef]

D. Ricard, Ph. Roussignol, and C. Flytzanis, Opt. Lett. 10, 511 (1985).
[CrossRef] [PubMed]

Roussignol, P.

D. Ricard, P. Roussignol, F. Hache, and C. Flytzanis, Phys. Status Solidi 159, 275 (1990).
[CrossRef]

Roussignol, Ph.

Said, A. A.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Sheik-Bahae, M.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Sipe, J. E.

Smith, F. M.

Stroud, D.

K. W. Yu, P. M. Hui, and D. Stroud, Phys. Rev. B 47, 14150 (1993).
[CrossRef]

X. C. Zeng, D. J. Bergman, P. M. Hui, and D. Stroud, Phys. Rev. B 38, 10970 (1988).
[CrossRef]

D. Stroud and P. M. Hui, Phys. Rev. B 37, 8719 (1988).
[CrossRef]

Tanji, H.

Tokizaki, T.

Uchida, K.

Van Stryland, E. W.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Wei, T.

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

Yang, L.

Yu, K. W.

K. W. Yu, P. M. Hui, and D. Stroud, Phys. Rev. B 47, 14150 (1993).
[CrossRef]

Zeng, X. C.

X. C. Zeng, D. J. Bergman, P. M. Hui, and D. Stroud, Phys. Rev. B 38, 10970 (1988).
[CrossRef]

Zuhr, R. A.

Ann. Phys. (Leipzig) (1)

D. A. G. Bruggeman, Ann. Phys. (Leipzig) 24, 636 (1935).
[CrossRef]

Appl. Phys. A (2)

F. Hache, D. Ricard, C. Flytzanis, and U. Kreibig, Appl. Phys. A 47, 347 (1988).
[CrossRef]

L. Brus, Appl. Phys. A 53, 465 (1991).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Sheik-Bahae, A. A. Said, T. Wei, D. J. Hagan, and E. W. Van Stryland, IEEE J. Quantum Electron. 26, 760 (1990).
[CrossRef]

J. Am. Ceram. Soc. (1)

M. E. Nordberg, J. Am. Ceram. Soc. 27, 299 (1944).
[CrossRef]

J. Appl. Phys. (1)

R. Landauer, J. Appl. Phys. 23, 779 (1952).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. B (5)

Opt. Lett. (1)

Phys. Rev. A (3)

G. S. Agarwal and S. Dutta Gupta, Phys. Rev. A 38, 5678 (1988).
[CrossRef] [PubMed]

J. W. Haus, R. Inguva, and C. M. Bowden, Phys. Rev. A 40, 5729 (1989).
[CrossRef] [PubMed]

J. E. Sipe and R. W. Boyd, Phys. Rev. A 46, 1614 (1992).
[CrossRef] [PubMed]

Phys. Rev. B (3)

X. C. Zeng, D. J. Bergman, P. M. Hui, and D. Stroud, Phys. Rev. B 38, 10970 (1988).
[CrossRef]

K. W. Yu, P. M. Hui, and D. Stroud, Phys. Rev. B 47, 14150 (1993).
[CrossRef]

D. Stroud and P. M. Hui, Phys. Rev. B 37, 8719 (1988).
[CrossRef]

Phys. Status Solidi (1)

D. Ricard, P. Roussignol, F. Hache, and C. Flytzanis, Phys. Status Solidi 159, 275 (1990).
[CrossRef]

Other (3)

Product information: VYCOR brand porous glass, PI-VPG-88, Corning Glass Works.

T. H. Elmer, “Porous and reconstructed glasses,” in Ceramics and Glasses, S. J. Schneider, Jr., ed., Vol. 4 of Engineered Materials Handbook (ASM International, Cleveland, Ohio, 1992).

J. C. Maxwell Garnett, Philos. Trans. R. Soc. London 203, 385 (1904); 205, 237 (1906).

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Figures (5)

Fig. 1
Fig. 1

Bruggeman composite geometry.

Fig. 2
Fig. 2

Theoretical predictions of the Bruggeman model for the effective third-order susceptibility plotted versus volume fill fraction of constituent a. It is assumed that only constituent a displays a third-order nonlinearity. The ratio of the linear dielectric constants is used as a parameter.

Fig. 3
Fig. 3

Experimental setup used to measure the linear refractive index of the composites.

Fig. 4
Fig. 4

Effective refractive index of porous Vycor glass filled with fluids of various refractive indices versus the fluid refractive index. Solid line, theoretical prediction of the Bruggeman model.

Fig. 5
Fig. 5

Typical Z-scan data. Error bars, one standard deviation to each side of the mean. Solid curves, best fits of Z-scan thin sample formula. (a) 4-mm-thick sample of pure carbon tetrachloride. (b) 4-mm-thick Vycor glass–carbon tetrachloride composite.

Tables (2)

Tables Icon

Table 1 Comparison of Experimentally Determined Effective Refractive Indices with Those Predicted by the Bruggeman Theory

Tables Icon

Table 2 Comparison of Experimentally Determined Nonlinear Susceptibilities with Those Predicted by Bruggeman and Maxwell Garnett Theories

Equations (5)

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

χeff(3)=1faeffaeffaχa(3)+1fbeffbeffbχb(3),
0=fa a-effa+2eff+fb b-effb+2eff.
T=Tn+4xΔφ(1+x2)(9+x2),
xz-zfz0.
χeff(3)=faχa(3)+fbχb(3).

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