Abstract

Experimental measurements of the frequency dependence of the isotropically averaged, molecular dc-induced second-harmonic susceptibility 〈γ(−2ω; ω, ω, 0)〉 and third-harmonic susceptibility 〈γ(−3ω; ω, ω, ω)〉 of conjugated linear-chain structures are in excellent agreement with the results of many-electron, multiple-excited-configuration-interaction calculations. For hexatriene, the N = 6 carbon site linear polyene chain, we demonstrate the first successful comparison, to our knowledge, between experiment and theory for the magnitude, sign, and dispersion of 〈γ(−2ω; ω, ω, 0)〉 and 〈γ(−3ω; ω, ω, ω)〉. These results provide experimental verification of the importance of electron-correlation effects in the third-order nonlinear-optical properties of conjugated structures. Measurements of 〈γ(−2ω; ω, ω, 0)〉 and 〈γ(−3ω; ω, ω, ω)〉 for β-carotene, the intermediate length, N = 22, conjugated chain, are also reported, and the frequency dependence is well described by a three-level model that is developed based on the results of the electron-correlation description of γijkl(−ω4; ω1, ω2, ω3) for shorter chains. Finally, through the detailed comparisons of 〈γ(−2ω; ω, ω, 0)〉 with 〈γ(−3ω; ω, ω, ω)〉 and of experiment with theory, as well as through examination of previously reported values of the macroscopic third-order susceptibility χ(3)(−ω4; ω1, ω2, ω3) of glasses by other nonlinear-optical techniques, it is demonstrated that the common reference standard for χ(3)(−ω4; ω1, ω2, ω3) of glass is inaccurate, and an improved value is recommended.

© 1991 Optical Society of America

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  1. J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, Phys. Rev. B 38, 1573 (1988); Mol. Cryst. Liq. Cryst. 160, 37 (1988); in Nonlinear Optical Properties of Polymers, A. J. Heeger, D. Ulrich, and J. Orenstein, eds., Mater. Res. Soc. Proc.109, 90–102 (1988).
    [CrossRef]
  2. J. W. Wu, J. R. Heflin, R. A. Norwood, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, P. Kalyanaraman, and J. Sounik, J. Opt. Soc. Am. B 6, 707 (1989).
    [CrossRef]
  3. A. F. Garito, J. R. Heflin, K. Y. Wong, and O. Zamani-Khamiri, in Organic Materials for Nonlinear Optics, R. A. Hann and D. Bloor, eds. (Royal Society of Chemistry, London, 1989); in Nonlinear Optical Properties of Organic Materials, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.971, 9 (1989); in Photoresponsive Materials, S. Tazuke, ed., Mater. Res. Soc. Proc.IMAM-12, 3–20 (1989).
  4. Z. G. Soos and S. Ramasesha, Chem. Phys. Lett. 153, 171 (1988); J. Chem. Phys. 90, 1067 (1989).
    [CrossRef]
  5. B. M. Pierce, J. Chem. Phys. 91, 791 (1989).
    [CrossRef]
  6. M. Choy and R. L. Byer, Phys. Rev. B 14, 1693 (1976).
    [CrossRef]
  7. K. D. Singer and A. F. Garito, J. Chem. Phys. 75, 3572 (1981).
    [CrossRef]
  8. C. C. Teng and A. F. Garito, Phys. Rev. Lett. 50, 350 (1983); Phys. Rev. B 28, 6766 (1983).
    [CrossRef]
  9. J. P. Herrmann and J. Ducuing, J. Appl. Phys. 45, 5100 (1974).
    [CrossRef]
  10. S. H. Stevenson, D. S. Donald, and G. R. Meredith, in Nonlinear Optical Properties of Polymers, A. J. Heeger, D. Ulrich, and J. Orenstein, eds., Mater. Res. Soc. Proc.109, 103–108 (1988).
  11. J. F. Ward and D. S. Elliot, J. Chem. Phys. 69, 5438 (1978).
    [CrossRef]
  12. B. J. Orr and J. F. Ward, Mol. Phys. 20, 513 (1971). This paper uses an alternative convention in which γijkl(−ω4; ω1, ω2, ω3) is made equal for all processes in the absence of dispersion by including an additional factor K(−ω4; ω1, ω2, ω3) in the constitutive equation that is analogous to Eq. (1).
    [CrossRef]
  13. R. M. Gavin, S. Risemberg, and S. M. Rice, J. Chem. Phys. 58, 3160 (1973).
    [CrossRef]
  14. F. Kajzar and J. Messier, J. Opt. Soc. Am. B 4, 1040 (1987).
    [CrossRef]
  15. J. L. Oudar, J. Chem. Phys. 67, 446 (1977).
    [CrossRef]
  16. R. C. Miller, Appl. Phys. Lett. 5, 17 (1964).
    [CrossRef]
  17. D. E. Gray, ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).
  18. Optical Glass [Schott Glass Technologies Inc. catalog] (Schott Glass, Duryea, Pa., 1990).
  19. E. W. Washburn, C. J. West, N. E. Dorsey, and M. D. Ring, International Critical Tables of Numerical Data (McGraw-Hill, New York, 1930), Vol. VII.
  20. Aldrich Chemical Company Catalog (Aldrich Chemical, Milwaukee, Wisc., 1990).
  21. N. Gee, K. Shinsaka, J. Dodelet, and G. R. Freeman, J. Chem. Thermodyn. 18, 221 (1986).
    [CrossRef]
  22. G. R. Meredith, B. Buchalter, and C. Hanzlik, J. Chem. Phys. 78, 1533 (1983).
    [CrossRef]
  23. F. Kajzar and J. Messier, Phys. Rev. A 32, 2352 (1985).
    [CrossRef] [PubMed]
  24. F. Kajzar and J. Messier, Rev. Sci. Instrum. 58, 2081 (1987).
    [CrossRef]
  25. B. Buchalter and G. R. Meredith, Appl. Opt. 21, 3221 (1982).
    [CrossRef] [PubMed]
  26. G. R. Meredith, Phys. Rev. B 24, 5522 (1981).
    [CrossRef]
  27. J. L. Oudar, J. Chem. Phys. 67, 446 (1977).
    [CrossRef]
  28. B. F. Levine and C. G. Bethea, J. Chem. Phys. 63, 2666 (1975). The reported value has been multiplied by an additional factor of 3/2 to account for the more reliable value of d11= 1.2 × 10−9 for quartz that is now taken as the standard.
    [CrossRef]
  29. C. C. Teng, “Molecular optics: dispersion of the nonlinear second order susceptibility,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1983).
  30. R. Adair, L. L. Chase, and S. Payne, J. Opt. Soc. Am. B 4, 875 (1987).
    [CrossRef]
  31. D. Milam and M. J. Weber, J. Appl. Phys. 47, 2497 (1976).
    [CrossRef]
  32. R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
    [CrossRef]
  33. J. R. Heflin, “Electron correlation theory and experimental measurements of the third order nonlinear optical properties of conjugated linear chains,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1990).

1989 (2)

1988 (2)

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, Phys. Rev. B 38, 1573 (1988); Mol. Cryst. Liq. Cryst. 160, 37 (1988); in Nonlinear Optical Properties of Polymers, A. J. Heeger, D. Ulrich, and J. Orenstein, eds., Mater. Res. Soc. Proc.109, 90–102 (1988).
[CrossRef]

Z. G. Soos and S. Ramasesha, Chem. Phys. Lett. 153, 171 (1988); J. Chem. Phys. 90, 1067 (1989).
[CrossRef]

1987 (3)

1986 (1)

N. Gee, K. Shinsaka, J. Dodelet, and G. R. Freeman, J. Chem. Thermodyn. 18, 221 (1986).
[CrossRef]

1985 (1)

F. Kajzar and J. Messier, Phys. Rev. A 32, 2352 (1985).
[CrossRef] [PubMed]

1983 (2)

G. R. Meredith, B. Buchalter, and C. Hanzlik, J. Chem. Phys. 78, 1533 (1983).
[CrossRef]

C. C. Teng and A. F. Garito, Phys. Rev. Lett. 50, 350 (1983); Phys. Rev. B 28, 6766 (1983).
[CrossRef]

1982 (1)

1981 (2)

K. D. Singer and A. F. Garito, J. Chem. Phys. 75, 3572 (1981).
[CrossRef]

G. R. Meredith, Phys. Rev. B 24, 5522 (1981).
[CrossRef]

1978 (1)

J. F. Ward and D. S. Elliot, J. Chem. Phys. 69, 5438 (1978).
[CrossRef]

1977 (3)

J. L. Oudar, J. Chem. Phys. 67, 446 (1977).
[CrossRef]

J. L. Oudar, J. Chem. Phys. 67, 446 (1977).
[CrossRef]

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

1976 (2)

D. Milam and M. J. Weber, J. Appl. Phys. 47, 2497 (1976).
[CrossRef]

M. Choy and R. L. Byer, Phys. Rev. B 14, 1693 (1976).
[CrossRef]

1975 (1)

B. F. Levine and C. G. Bethea, J. Chem. Phys. 63, 2666 (1975). The reported value has been multiplied by an additional factor of 3/2 to account for the more reliable value of d11= 1.2 × 10−9 for quartz that is now taken as the standard.
[CrossRef]

1974 (1)

J. P. Herrmann and J. Ducuing, J. Appl. Phys. 45, 5100 (1974).
[CrossRef]

1973 (1)

R. M. Gavin, S. Risemberg, and S. M. Rice, J. Chem. Phys. 58, 3160 (1973).
[CrossRef]

1971 (1)

B. J. Orr and J. F. Ward, Mol. Phys. 20, 513 (1971). This paper uses an alternative convention in which γijkl(−ω4; ω1, ω2, ω3) is made equal for all processes in the absence of dispersion by including an additional factor K(−ω4; ω1, ω2, ω3) in the constitutive equation that is analogous to Eq. (1).
[CrossRef]

1964 (1)

R. C. Miller, Appl. Phys. Lett. 5, 17 (1964).
[CrossRef]

Adair, R.

Bethea, C. G.

B. F. Levine and C. G. Bethea, J. Chem. Phys. 63, 2666 (1975). The reported value has been multiplied by an additional factor of 3/2 to account for the more reliable value of d11= 1.2 × 10−9 for quartz that is now taken as the standard.
[CrossRef]

Buchalter, B.

G. R. Meredith, B. Buchalter, and C. Hanzlik, J. Chem. Phys. 78, 1533 (1983).
[CrossRef]

B. Buchalter and G. R. Meredith, Appl. Opt. 21, 3221 (1982).
[CrossRef] [PubMed]

Byer, R. L.

M. Choy and R. L. Byer, Phys. Rev. B 14, 1693 (1976).
[CrossRef]

Chase, L. L.

Choy, M.

M. Choy and R. L. Byer, Phys. Rev. B 14, 1693 (1976).
[CrossRef]

Dodelet, J.

N. Gee, K. Shinsaka, J. Dodelet, and G. R. Freeman, J. Chem. Thermodyn. 18, 221 (1986).
[CrossRef]

Donald, D. S.

S. H. Stevenson, D. S. Donald, and G. R. Meredith, in Nonlinear Optical Properties of Polymers, A. J. Heeger, D. Ulrich, and J. Orenstein, eds., Mater. Res. Soc. Proc.109, 103–108 (1988).

Dorsey, N. E.

E. W. Washburn, C. J. West, N. E. Dorsey, and M. D. Ring, International Critical Tables of Numerical Data (McGraw-Hill, New York, 1930), Vol. VII.

Ducuing, J.

J. P. Herrmann and J. Ducuing, J. Appl. Phys. 45, 5100 (1974).
[CrossRef]

Elliot, D. S.

J. F. Ward and D. S. Elliot, J. Chem. Phys. 69, 5438 (1978).
[CrossRef]

Freeman, G. R.

N. Gee, K. Shinsaka, J. Dodelet, and G. R. Freeman, J. Chem. Thermodyn. 18, 221 (1986).
[CrossRef]

Garito, A. F.

J. W. Wu, J. R. Heflin, R. A. Norwood, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, P. Kalyanaraman, and J. Sounik, J. Opt. Soc. Am. B 6, 707 (1989).
[CrossRef]

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, Phys. Rev. B 38, 1573 (1988); Mol. Cryst. Liq. Cryst. 160, 37 (1988); in Nonlinear Optical Properties of Polymers, A. J. Heeger, D. Ulrich, and J. Orenstein, eds., Mater. Res. Soc. Proc.109, 90–102 (1988).
[CrossRef]

C. C. Teng and A. F. Garito, Phys. Rev. Lett. 50, 350 (1983); Phys. Rev. B 28, 6766 (1983).
[CrossRef]

K. D. Singer and A. F. Garito, J. Chem. Phys. 75, 3572 (1981).
[CrossRef]

A. F. Garito, J. R. Heflin, K. Y. Wong, and O. Zamani-Khamiri, in Organic Materials for Nonlinear Optics, R. A. Hann and D. Bloor, eds. (Royal Society of Chemistry, London, 1989); in Nonlinear Optical Properties of Organic Materials, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.971, 9 (1989); in Photoresponsive Materials, S. Tazuke, ed., Mater. Res. Soc. Proc.IMAM-12, 3–20 (1989).

Gavin, R. M.

R. M. Gavin, S. Risemberg, and S. M. Rice, J. Chem. Phys. 58, 3160 (1973).
[CrossRef]

Gee, N.

N. Gee, K. Shinsaka, J. Dodelet, and G. R. Freeman, J. Chem. Thermodyn. 18, 221 (1986).
[CrossRef]

Hanzlik, C.

G. R. Meredith, B. Buchalter, and C. Hanzlik, J. Chem. Phys. 78, 1533 (1983).
[CrossRef]

Heflin, J. R.

J. W. Wu, J. R. Heflin, R. A. Norwood, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, P. Kalyanaraman, and J. Sounik, J. Opt. Soc. Am. B 6, 707 (1989).
[CrossRef]

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, Phys. Rev. B 38, 1573 (1988); Mol. Cryst. Liq. Cryst. 160, 37 (1988); in Nonlinear Optical Properties of Polymers, A. J. Heeger, D. Ulrich, and J. Orenstein, eds., Mater. Res. Soc. Proc.109, 90–102 (1988).
[CrossRef]

J. R. Heflin, “Electron correlation theory and experimental measurements of the third order nonlinear optical properties of conjugated linear chains,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1990).

A. F. Garito, J. R. Heflin, K. Y. Wong, and O. Zamani-Khamiri, in Organic Materials for Nonlinear Optics, R. A. Hann and D. Bloor, eds. (Royal Society of Chemistry, London, 1989); in Nonlinear Optical Properties of Organic Materials, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.971, 9 (1989); in Photoresponsive Materials, S. Tazuke, ed., Mater. Res. Soc. Proc.IMAM-12, 3–20 (1989).

Hellwarth, R. W.

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Herrmann, J. P.

J. P. Herrmann and J. Ducuing, J. Appl. Phys. 45, 5100 (1974).
[CrossRef]

Kajzar, F.

F. Kajzar and J. Messier, Rev. Sci. Instrum. 58, 2081 (1987).
[CrossRef]

F. Kajzar and J. Messier, J. Opt. Soc. Am. B 4, 1040 (1987).
[CrossRef]

F. Kajzar and J. Messier, Phys. Rev. A 32, 2352 (1985).
[CrossRef] [PubMed]

Kalyanaraman, P.

Levine, B. F.

B. F. Levine and C. G. Bethea, J. Chem. Phys. 63, 2666 (1975). The reported value has been multiplied by an additional factor of 3/2 to account for the more reliable value of d11= 1.2 × 10−9 for quartz that is now taken as the standard.
[CrossRef]

Meredith, G. R.

G. R. Meredith, B. Buchalter, and C. Hanzlik, J. Chem. Phys. 78, 1533 (1983).
[CrossRef]

B. Buchalter and G. R. Meredith, Appl. Opt. 21, 3221 (1982).
[CrossRef] [PubMed]

G. R. Meredith, Phys. Rev. B 24, 5522 (1981).
[CrossRef]

S. H. Stevenson, D. S. Donald, and G. R. Meredith, in Nonlinear Optical Properties of Polymers, A. J. Heeger, D. Ulrich, and J. Orenstein, eds., Mater. Res. Soc. Proc.109, 103–108 (1988).

Messier, J.

F. Kajzar and J. Messier, Rev. Sci. Instrum. 58, 2081 (1987).
[CrossRef]

F. Kajzar and J. Messier, J. Opt. Soc. Am. B 4, 1040 (1987).
[CrossRef]

F. Kajzar and J. Messier, Phys. Rev. A 32, 2352 (1985).
[CrossRef] [PubMed]

Milam, D.

D. Milam and M. J. Weber, J. Appl. Phys. 47, 2497 (1976).
[CrossRef]

Miller, R. C.

R. C. Miller, Appl. Phys. Lett. 5, 17 (1964).
[CrossRef]

Norwood, R. A.

Orr, B. J.

B. J. Orr and J. F. Ward, Mol. Phys. 20, 513 (1971). This paper uses an alternative convention in which γijkl(−ω4; ω1, ω2, ω3) is made equal for all processes in the absence of dispersion by including an additional factor K(−ω4; ω1, ω2, ω3) in the constitutive equation that is analogous to Eq. (1).
[CrossRef]

Oudar, J. L.

J. L. Oudar, J. Chem. Phys. 67, 446 (1977).
[CrossRef]

J. L. Oudar, J. Chem. Phys. 67, 446 (1977).
[CrossRef]

Payne, S.

Pierce, B. M.

B. M. Pierce, J. Chem. Phys. 91, 791 (1989).
[CrossRef]

Ramasesha, S.

Z. G. Soos and S. Ramasesha, Chem. Phys. Lett. 153, 171 (1988); J. Chem. Phys. 90, 1067 (1989).
[CrossRef]

Rice, S. M.

R. M. Gavin, S. Risemberg, and S. M. Rice, J. Chem. Phys. 58, 3160 (1973).
[CrossRef]

Ring, M. D.

E. W. Washburn, C. J. West, N. E. Dorsey, and M. D. Ring, International Critical Tables of Numerical Data (McGraw-Hill, New York, 1930), Vol. VII.

Risemberg, S.

R. M. Gavin, S. Risemberg, and S. M. Rice, J. Chem. Phys. 58, 3160 (1973).
[CrossRef]

Shinsaka, K.

N. Gee, K. Shinsaka, J. Dodelet, and G. R. Freeman, J. Chem. Thermodyn. 18, 221 (1986).
[CrossRef]

Singer, K. D.

K. D. Singer and A. F. Garito, J. Chem. Phys. 75, 3572 (1981).
[CrossRef]

Soos, Z. G.

Z. G. Soos and S. Ramasesha, Chem. Phys. Lett. 153, 171 (1988); J. Chem. Phys. 90, 1067 (1989).
[CrossRef]

Sounik, J.

Stevenson, S. H.

S. H. Stevenson, D. S. Donald, and G. R. Meredith, in Nonlinear Optical Properties of Polymers, A. J. Heeger, D. Ulrich, and J. Orenstein, eds., Mater. Res. Soc. Proc.109, 103–108 (1988).

Teng, C. C.

C. C. Teng and A. F. Garito, Phys. Rev. Lett. 50, 350 (1983); Phys. Rev. B 28, 6766 (1983).
[CrossRef]

C. C. Teng, “Molecular optics: dispersion of the nonlinear second order susceptibility,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1983).

Ward, J. F.

J. F. Ward and D. S. Elliot, J. Chem. Phys. 69, 5438 (1978).
[CrossRef]

B. J. Orr and J. F. Ward, Mol. Phys. 20, 513 (1971). This paper uses an alternative convention in which γijkl(−ω4; ω1, ω2, ω3) is made equal for all processes in the absence of dispersion by including an additional factor K(−ω4; ω1, ω2, ω3) in the constitutive equation that is analogous to Eq. (1).
[CrossRef]

Washburn, E. W.

E. W. Washburn, C. J. West, N. E. Dorsey, and M. D. Ring, International Critical Tables of Numerical Data (McGraw-Hill, New York, 1930), Vol. VII.

Weber, M. J.

D. Milam and M. J. Weber, J. Appl. Phys. 47, 2497 (1976).
[CrossRef]

West, C. J.

E. W. Washburn, C. J. West, N. E. Dorsey, and M. D. Ring, International Critical Tables of Numerical Data (McGraw-Hill, New York, 1930), Vol. VII.

Wong, K. Y.

J. W. Wu, J. R. Heflin, R. A. Norwood, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, P. Kalyanaraman, and J. Sounik, J. Opt. Soc. Am. B 6, 707 (1989).
[CrossRef]

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, Phys. Rev. B 38, 1573 (1988); Mol. Cryst. Liq. Cryst. 160, 37 (1988); in Nonlinear Optical Properties of Polymers, A. J. Heeger, D. Ulrich, and J. Orenstein, eds., Mater. Res. Soc. Proc.109, 90–102 (1988).
[CrossRef]

A. F. Garito, J. R. Heflin, K. Y. Wong, and O. Zamani-Khamiri, in Organic Materials for Nonlinear Optics, R. A. Hann and D. Bloor, eds. (Royal Society of Chemistry, London, 1989); in Nonlinear Optical Properties of Organic Materials, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.971, 9 (1989); in Photoresponsive Materials, S. Tazuke, ed., Mater. Res. Soc. Proc.IMAM-12, 3–20 (1989).

Wu, J. W.

Zamani-Khamiri, O.

J. W. Wu, J. R. Heflin, R. A. Norwood, K. Y. Wong, O. Zamani-Khamiri, A. F. Garito, P. Kalyanaraman, and J. Sounik, J. Opt. Soc. Am. B 6, 707 (1989).
[CrossRef]

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, Phys. Rev. B 38, 1573 (1988); Mol. Cryst. Liq. Cryst. 160, 37 (1988); in Nonlinear Optical Properties of Polymers, A. J. Heeger, D. Ulrich, and J. Orenstein, eds., Mater. Res. Soc. Proc.109, 90–102 (1988).
[CrossRef]

A. F. Garito, J. R. Heflin, K. Y. Wong, and O. Zamani-Khamiri, in Organic Materials for Nonlinear Optics, R. A. Hann and D. Bloor, eds. (Royal Society of Chemistry, London, 1989); in Nonlinear Optical Properties of Organic Materials, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.971, 9 (1989); in Photoresponsive Materials, S. Tazuke, ed., Mater. Res. Soc. Proc.IMAM-12, 3–20 (1989).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. C. Miller, Appl. Phys. Lett. 5, 17 (1964).
[CrossRef]

Chem. Phys. Lett. (1)

Z. G. Soos and S. Ramasesha, Chem. Phys. Lett. 153, 171 (1988); J. Chem. Phys. 90, 1067 (1989).
[CrossRef]

J. Appl. Phys. (2)

J. P. Herrmann and J. Ducuing, J. Appl. Phys. 45, 5100 (1974).
[CrossRef]

D. Milam and M. J. Weber, J. Appl. Phys. 47, 2497 (1976).
[CrossRef]

J. Chem. Phys. (8)

J. L. Oudar, J. Chem. Phys. 67, 446 (1977).
[CrossRef]

B. F. Levine and C. G. Bethea, J. Chem. Phys. 63, 2666 (1975). The reported value has been multiplied by an additional factor of 3/2 to account for the more reliable value of d11= 1.2 × 10−9 for quartz that is now taken as the standard.
[CrossRef]

J. L. Oudar, J. Chem. Phys. 67, 446 (1977).
[CrossRef]

G. R. Meredith, B. Buchalter, and C. Hanzlik, J. Chem. Phys. 78, 1533 (1983).
[CrossRef]

K. D. Singer and A. F. Garito, J. Chem. Phys. 75, 3572 (1981).
[CrossRef]

B. M. Pierce, J. Chem. Phys. 91, 791 (1989).
[CrossRef]

J. F. Ward and D. S. Elliot, J. Chem. Phys. 69, 5438 (1978).
[CrossRef]

R. M. Gavin, S. Risemberg, and S. M. Rice, J. Chem. Phys. 58, 3160 (1973).
[CrossRef]

J. Chem. Thermodyn. (1)

N. Gee, K. Shinsaka, J. Dodelet, and G. R. Freeman, J. Chem. Thermodyn. 18, 221 (1986).
[CrossRef]

J. Opt. Soc. Am. B (3)

Mol. Phys. (1)

B. J. Orr and J. F. Ward, Mol. Phys. 20, 513 (1971). This paper uses an alternative convention in which γijkl(−ω4; ω1, ω2, ω3) is made equal for all processes in the absence of dispersion by including an additional factor K(−ω4; ω1, ω2, ω3) in the constitutive equation that is analogous to Eq. (1).
[CrossRef]

Phys. Rev. A (1)

F. Kajzar and J. Messier, Phys. Rev. A 32, 2352 (1985).
[CrossRef] [PubMed]

Phys. Rev. B (3)

J. R. Heflin, K. Y. Wong, O. Zamani-Khamiri, and A. F. Garito, Phys. Rev. B 38, 1573 (1988); Mol. Cryst. Liq. Cryst. 160, 37 (1988); in Nonlinear Optical Properties of Polymers, A. J. Heeger, D. Ulrich, and J. Orenstein, eds., Mater. Res. Soc. Proc.109, 90–102 (1988).
[CrossRef]

G. R. Meredith, Phys. Rev. B 24, 5522 (1981).
[CrossRef]

M. Choy and R. L. Byer, Phys. Rev. B 14, 1693 (1976).
[CrossRef]

Phys. Rev. Lett. (1)

C. C. Teng and A. F. Garito, Phys. Rev. Lett. 50, 350 (1983); Phys. Rev. B 28, 6766 (1983).
[CrossRef]

Prog. Quantum Electron. (1)

R. W. Hellwarth, Prog. Quantum Electron. 5, 1 (1977).
[CrossRef]

Rev. Sci. Instrum. (1)

F. Kajzar and J. Messier, Rev. Sci. Instrum. 58, 2081 (1987).
[CrossRef]

Other (8)

C. C. Teng, “Molecular optics: dispersion of the nonlinear second order susceptibility,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1983).

J. R. Heflin, “Electron correlation theory and experimental measurements of the third order nonlinear optical properties of conjugated linear chains,” Ph.D. dissertation (University of Pennsylvania, Philadelphia, Pa., 1990).

S. H. Stevenson, D. S. Donald, and G. R. Meredith, in Nonlinear Optical Properties of Polymers, A. J. Heeger, D. Ulrich, and J. Orenstein, eds., Mater. Res. Soc. Proc.109, 103–108 (1988).

A. F. Garito, J. R. Heflin, K. Y. Wong, and O. Zamani-Khamiri, in Organic Materials for Nonlinear Optics, R. A. Hann and D. Bloor, eds. (Royal Society of Chemistry, London, 1989); in Nonlinear Optical Properties of Organic Materials, G. Khanarian, ed., Proc. Soc. Photo-Opt. Instrum. Eng.971, 9 (1989); in Photoresponsive Materials, S. Tazuke, ed., Mater. Res. Soc. Proc.IMAM-12, 3–20 (1989).

D. E. Gray, ed., American Institute of Physics Handbook (McGraw-Hill, New York, 1972).

Optical Glass [Schott Glass Technologies Inc. catalog] (Schott Glass, Duryea, Pa., 1990).

E. W. Washburn, C. J. West, N. E. Dorsey, and M. D. Ring, International Critical Tables of Numerical Data (McGraw-Hill, New York, 1930), Vol. VII.

Aldrich Chemical Company Catalog (Aldrich Chemical, Milwaukee, Wisc., 1990).

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Figures (12)

Fig. 1
Fig. 1

Schematic diagrams of the molecular structures for (a) all-trans and (b) cistransoid hexatriene (HT).

Fig. 2
Fig. 2

Calculated dispersions of 〈γ(−2ω; ω, ω, 0)〉 (solid curve) and 〈γ(−3ω; ω, ω, ω)〉 (dashed curve) for HT. The values of 〈γ(−3ω; ω, ω, ω)〉 have been multiplied by 6.

Fig. 3
Fig. 3

Experimental layout of the DCSHG experiment. P’s, prisms; L’s, lenses; PD, photodiode; PH, pinhole; F’s, filters; M, monochromator; PMT’s, photomultiplier tubes; R, reference crystal; S, liquid sample cell. The wedged sample cell is mounted on a configuration of translation stages and connected to a pulsed HV source.

Fig. 4
Fig. 4

Linear absorption spectrum of HT neat liquid in the region of the 1 1Bu ← 1 1Agπ-electron transition.

Fig. 5
Fig. 5

Experimentally determined values of 〈γ(−2ω; ω, ω, 0)〉 for HT at λ’s of 1907, 1543, and 1064 nm and the theoretical dispersion curve.

Fig. 6
Fig. 6

Linear absorption spectrum of β-carotene in solution with 1, 4-dioxane in the region of the 1 1Bu ← 11Agπ-electron transition. The molecular structure of β-carotene is also shown.

Fig. 7
Fig. 7

Concentration dependence of χ(3)(−2ω; ω, ω, 0) for β-carotene in solution with dioxane at λ = 1543 nm.

Fig. 8
Fig. 8

Experimentally determined values of 〈γ(−2ω; ω, ω, 0)〉 for β-carotene at λ’s of 1907, 1543, and 1064 nm, compared with a three-level model for the dispersion of 〈γ(−2ω; ω, ω, 0)〉 of β-carotene (dashed curve).

Fig. 9
Fig. 9

Experimentally determined values of 〈γ(−3ω; ω, ω, ω)〉 for HT at λ’s of 1907, 1543, and 1064 nm and the theoretical dispersion curve.

Fig. 10
Fig. 10

Sample THG Maker fringes for (a) HT and (b) acetone at λ = 1064 nm. The nonzero minimum in the case of the fringes for HT is due to the effect of the finite beam size. For HT the coherence length lc = 1.18 μm, while for acetone lc = 6.6 μm. The horizontal scale of (a) is expanded by a factor of three compared to (b) for clarity.

Fig. 11
Fig. 11

Concentration dependence of χ(3)(−3ω; ω, ω, ω) for β-carotene in solution with dioxane at λ = 2148 nm.

Fig. 12
Fig. 12

Experimentally determined values of 〈γ(−3ω; ω, ω, ω)〉 for β-carotene at λ’s of 2148, 1907, and 1543 nm compared with a three-level model for the dispersion of 〈γ(−3ω; ω, ω, ω)〉 for β-carotene (dashed curve).

Tables (13)

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Table 1 Fundamental and Second-Harmonic Refractive Indices, Calculated and Experimental Coherence Lengths, and Derived d11 Values for Quartz

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Table 2 Fundamental and Second-Harmonic Refractive Indices, Coherence Lengths, and χ(3)(−2ω; ω, ω, 0) for BK-7 Glass

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Table 3 Fundamental and Second-Harmonic Indices, Coherence Length, χ(3)(−2ω; ω, ω, 0), and 〈γ(−2ω; ω, ω, 0)〉 for Dioxane

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Table 4 Fundamental and Second-Harmonic Refractive Indices, Coherence Length, and χ(3)(−2ω; ω, ω, 0) for HT

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Table 5 Experimental and Theoretical Values of 〈γ(−2ω; ω, ω, 0)〉 for HT

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Table 6χ(3)(−2ω; ω, ω, 0)/∂C and 〈γ(−2ω; ω, ω, 0)〉 for β-Carotene

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Table 7 Fundamental and Third-Harmonic Refractice Indices, Coherence Length, and χ(3)(−3ω; ω, ω, ω) for BK-7 Glass

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Table 8 Fundamental and Third-Harmonic Refractive Indices, Coherence Length, χ(3)(−3ω; ω, ω, ω), and 〈γ(−3ω; ω, ω, ω)〉 for Dioxane

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Table 9 Fundamental and Third-Harmonic Refractive Indices, Coherence Length, and χ(3)(−3ω; ω, ω, ω) for HT

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Table 10 Experimental and Theoretical Values for 〈γ(−3ω; ω, ω, ω)〉 for HT

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Table 11 Effect of Finite Beam Diameter on Ratio of Minimum to Maximum Maker-Fringe Intensities

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Table 12χ(3)(−3ω; ω, ω, ω)/∂C and 〈γ(−3ω; ω, ω, ω)〉 for β-Carotene

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Table 13 Measured Values of χ(3)(−ω4; ω1, ω2, ω3) for BK-7 Glass through Several Nonlinear-Optical Processes

Equations (34)

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p i ω 4 = γ i j k l ( - ω 4 ; ω 1 , ω 2 , ω 3 ) E j ω 1 E k ω 2 E l ω 3 ,
χ ( 3 ) ( - ω 4 ; ω 1 , ω 2 , ω 3 ) = N f ω 4 f ω 1 f ω 2 f ω 3 γ ( - ω 4 ; ω 1 , ω 2 , ω 3 ) ,
γ ( - ω 4 ; ω 1 , ω 2 , ω 3 ) = 1 5 { i γ i i i i ( - ω 4 ; ω 1 , ω 2 , ω 3 ) + 1 3 i j [ γ i i j j ( - ω 4 ; ω 1 , ω 2 , ω 3 ) + γ i j i j ( - ω 4 ; ω 1 , ω 2 , ω 3 ) + γ i j j i ( - ω 4 ; ω 1 , ω 2 , ω 3 ) ] } .
( E ω cos ω t + E 0 ) 3 = ¼ ( E ω ) 3 cos 3 ω t + ³ / ( E ω ) 2 E 0 cos 2 ω t + [ ¾ ( E ω ) 3 + 3 E ω ( E 0 ) 2 ] cos ω t + [ ³ / ( E ω ) 2 E 0 + ( E 0 ) 3 ] .
γ ( - 2 ω ; ω , ω , 0 ) = 0.6 γ t r a n s ( - 2 ω ; ω , ω , 0 ) + 0.4 γ c i s ( - 2 ω ; ω , ω , 0 ) + 1.64 × 10 - 36 esu ,
γ ( - 3 ω ; ω , ω , ω ) = 0.6 γ t r a n s ( - 3 ω ; ω , ω , ω ) + 0.4 γ c i s ( - 3 ω ; ω , ω , ω ) + 0.27 × 10 - 36 esu .
I L 2 ω ( l ) = 2 c 8 π [ T 2 ω G ( T G E b G - T L E b L ) ] 2 exp [ - ( α ω + α 2 ω 2 ) l ] × { cosh [ ( α ω - α 2 ω 2 ) l ] - cos [ ( k f - k b ) l } ,
E b G = - 4 π ( n 2 ω G ) 2 - ( n ω G ) 2 χ G ( 3 ) ( - 2 ω ; ω , ω , 0 ) E 0 ( E ω t ω ( 1 ) ) 2 , E b L = - 4 π ( n 2 ω L ) 2 - ( n ω L ) 2 χ L ( 3 ) ( - 2 ω ; ω , ω , 0 ) E 0 ( E ω t ω ( 1 ) t ω ( 2 ) ) 2 ,
t ω ( 1 ) = 2 / ( 1 + n ω G ) ,             t ω ( 2 ) = 2 n ω G / ( n ω G + n ω L ) , T L = n ω L + n 2 ω L n 2 ω G + n 2 ω L ,             T G = n ω G + n 2 ω L n 2 ω G + n 2 ω L ,
I L 2 ω ( l ) = c 2 π [ T 2 ω G ( T G E b G - T L E b L ) ] 2 sin 2 [ ( k f - k b ) l 2 ] ,
I Q 2 ω ( l ) = c 2 π ( T Q E b Q ) 2 sin 2 [ ( k f Q - k b Q ) l / 2 ] ,
T Q = n ω Q + n 2 ω Q 1 + n 2 ω Q ,
E b Q = - 4 π d 11 Q ( n 2 ω Q ) 2 - ( n ω Q ) 2 ( 2 n ω Q 1 + n ω Q ) 2 E ω 2 .
χ L ( 3 ) ( - 2 ω ; ω , ω , 0 ) = n ω L + n 2 ω L l c L T L [ t ω ( 1 ) t ω ( 2 ) ] 2 × { T G l c G χ G ( 3 ) ( - 2 ω ; ω , ω , 0 ) [ t ω ( 1 ) ] 2 n ω G + n 2 ω G ± T Q E 0 ( 1 + n 2 ω G 2 n 2 ω G ) l c Q d 11 Q ( n ω Q + n 2 ω Q ) × ( 2 n ω Q 1 + n ω Q ) 2 ( A ¯ L 2 ω A ¯ Q 2 ω ) 1 / 2 } ,
I 2 ω ( l ) = A 1 sin 2 ( π l 2 A 3 + A 4 ) + A 2 ,
l c = λ 4 ( n 2 ω - n ω )
χ ( 3 ) ( - 2 ω ; ω , ω , 0 ) = N ( n ω 2 + 2 3 ) 2 ( n 2 ω 2 + 2 3 ) × [ ( n ω 2 + 2 ) ) n ω 2 + 2 ] γ ( - 2 ω ; ω , ω , 0 ) ,
χ ( 3 ) ( - 2 ω ; ω , ω , 0 ) = ( n ω 2 + 2 3 ) 2 ( n 2 ω 2 + 2 3 ) [ ( n ω 2 + 2 ) n ω 2 + 2 ] × [ N 1 γ 1 ( - 2 ω ; ω , ω , 0 ) + N 2 ( γ 2 ( - 2 ω ; ω , ω , 0 ) ] ,
γ 2 ( - 2 ω ; ω , ω , 0 ) = ( 3 n ω 2 + 2 ) 2 ( 3 n 2 2 ω + 2 ) [ n ω 2 + 2 ( n ω 2 + 2 ) ] × ( 1 6.02 × 10 20 ) χ ( 3 ) ( - 2 ω ; ω , ω , 0 ) C .
γ x x x x ( - 2 ω ; ω , ω , 0 ) = ( e 4 / 2 3 ) ( x 01 2 x 12 2 { [ ( Ω 10 - 2 ω ) ( Ω 20 - 2 ω ) ( Ω 10 - ω ) ] - 1 + [ Ω 10 * + 0 ) ( Ω 20 - 2 ω ) ( Ω 10 - ω ) ] - 1 + [ ( Ω 10 * + ω ) ( Ω 20 * + 2 ω ) ( Ω 10 - 0 ) ] - 1 + [ Ω 10 * + ω ) ( Ω 20 * + 2 ω ) ( Ω 10 * + 2 ω ) ] - 1 + [ ( Ω 10 - 2 ω ) ( Ω 20 - ω ) ( Ω 10 - ω ) ] - 1 + [ Ω 10 * + ω ) ( Ω 20 - ω ) ( Ω 10 - ω ) ] - 1 + [ ( Ω 10 * + ω ) ( Ω 20 * + ω ) ( Ω 10 - ω ) ] - 1 + [ Ω 10 * + ω ) ( Ω 20 * + ω ) ( Ω 10 * + 2 ω ) ] - 1 + [ ( Ω 10 - 2 ω ) [ Ω 20 - ω ) ( Ω 10 - 0 ) ] - 1 + [ Ω 10 * + ω ) ( Ω 20 - ω ) ( Ω 10 - 0 ) ] - 1 + [ ( Ω 10 * + 0 ) ( Ω 20 * + ω ) ( Ω 10 - ω ) ] - 1 + [ Ω 10 * + 0 ) ( Ω 20 * + ω ) ( Ω 10 * + 2 ω ) ] - 1 } - x 01 4 { [ ( Ω 10 - 2 ω ) ( Ω 10 - 0 ) ( Ω 10 - ω ) ] - 1 + [ Ω 10 - 0 ) ( Ω 10 * + ω ) ( Ω 10 - ω ) ] - 1 + [ ( Ω 10 * + 2 ω ) ( Ω 10 * + 0 ) ( Ω 10 * + ω ) ] - 1 + [ Ω 10 * + 0 ) ( Ω 10 - ω ) ( Ω 10 * + ω ) ] - 1 + [ ( Ω 10 - 2 ω ) ( Ω 10 - ω ) ( Ω 10 - ω ) ] - 1 + [ Ω 10 - ω ) ( Ω 10 * + 0 ) ( Ω 10 - ω ) ] - 1 + [ ( Ω 10 * + 2 ω ) ( Ω 10 * + ω ) ( Ω 10 * + ω ) ] - 1 + [ Ω 10 * + ω ) ( Ω 10 - 0 ) ( Ω 10 * + ω ) ] - 1 + [ ( Ω 10 - 2 ω ) ( Ω 10 - ω ) ( Ω 10 - 0 ) ] - 1 + [ Ω 10 - ω ) ( Ω 10 * + ω ) ( Ω 10 - 0 ) ] - 1 + [ ( Ω 10 * + 2 ω ) ( Ω 10 * + ω ) ( Ω 10 * + 0 ) ] - 1 + [ Ω 10 * + ω ) ( Ω 10 - ω ) ( Ω 10 * + 0 ) ] - 1 } ) ,
γ i j k l ( - 2 ω ; ω , ω , 0 ) = 6 γ i j k l ( - 3 ω ; ω , ω , ω ) .
I 3 ω ( l ) = 2 c 8 π [ T 3 ω G ( T G E b G - T L E b L ) ] 2 exp { - [ ( 3 α ω / 2 ) + ( α 3 ω / 2 ) ] l } { cosh [ ( 3 α ω 2 - α 3 ω 2 ) l ] - cos [ ( k f - k b ) l ] } ,
E b G = - 4 π ( n 3 ω G ) 2 - ( n ω G ) 2 χ G ( 3 ) ( - 3 ω ; ω , ω , ω ) ( E ω t ω ( 1 ) ) 3 , E b L = - 4 π ( n 3 ω L ) 2 - ( n ω L ) 2 χ L ( 3 ) ( - 3 ω ; ω , ω , ω ) ( E ω t ω ( 1 ) t ω ( 2 ) ) 3 ,
T L = n ω L + n 3 ω L n 3 ω G + n 3 ω L ,             T G = n ω G + n 3 ω L n 3 ω G + n 3 ω L .
I 3 ω ( l ) = c 2 π [ T 3 ω G ( T G E b G - T L E b L ) ] 2 sin 2 ( π l 2 l c L ) ,
χ L ( 3 ) = n 3 ω L + n ω L l c L T L ( t L ( 2 ) ) 3 [ T G L l c G χ G ( 3 ) n 3 ω G + n ω G ± ( A ¯ L A ¯ R ) 1 / 2 | T G R l c G χ G ( 3 ) n 3 ω G + n ω G - T R l c R χ R ( 3 ) n 3 ω R + n ω R ( t R ( 2 ) ) 3 | ] ,
l c = λ 6 ( n 3 ω - n ω ) .
χ ( 3 ) ( - 3 ω ; ω , ω , ω ) = N ( N ω 2 + 2 3 ) 3 ( n 3 ω 2 + 2 3 ) × γ ( - 3 ω ; ω , ω , ω ) ,
f ( l ) = sin 2 ( π l 2 l c ) .
I ( c ) = 1 d c - d / 2 c + d / 2 sin 2 x d x .
I min = 1 d - d / 2 d / 2 sin 2 x d x = 1 2 - sin d 2 d
I max = 1 d π / 2 - d / 2 π / 2 + d / 2 sin 2 x d x = 1 2 + sin d 2 d ,
γ ( - 3 ω ; ω , ω , ω ) = ( 3 n ω 2 + 2 ) 3 ( 3 n 3 ω 2 + 2 ) ( 1 6.02 × 10 20 ) × χ ( 3 ) ( - 3 ω ; ω , ω , ω ) C ,
γ x x x x ( - 3 ω ; ω , ω , ω ) = e 4 4 3 ( x 01 2 x 12 2 { [ ( Ω 10 - 3 ω ) ( Ω 20 - 2 ω ) ( Ω 10 - ω ) ] - 1 + [ ( Ω 10 * + ω ) ( Ω 20 - 2 ω ) ( Ω 10 - ω ) ] - 1 + [ ( Ω 10 * + ω ) ( Ω 20 * + 2 ω ) ( Ω 10 - ω ) ] - 1 + [ ( Ω 10 * + ω ) ( Ω 20 * + 2 ω ) ( Ω 10 * + 3 ω ) ] - 1 } - x 01 4 { [ ( Ω 10 - 3 ω ) ( Ω 10 - ω ) ( Ω 10 - ω ) ] - 1 + [ ( Ω 10 - ω ) ( Ω 10 * + ω ) ( Ω 10 - ω ) ] - 1 + [ ( Ω 10 * + 3 ω ) ( Ω 10 * + ω ) ( Ω 10 * + ω ) ] - 1 + [ ( Ω 10 * + ω ) ( Ω 10 - ω ) ( Ω 10 * + ω ) ] - 1 } ) .

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