Abstract

We report on the nonlinear optical characterization experiments of squaraine dyes in solid poly(methyl methacrylate) solutions. We find that a quantum three-level model of a squaraine best agrees with the quadratic electroabsorption measurements when the isomer composition is taken into account. We compare the nonlinear response of several dyes with the three- and four-level models to help determine which models are most suitable for predicting nonlinear behavior. Four-level models that include either two one-photon states or two two-photon states are inconsistent with quadratic electroabsorption spectroscopy. Furthermore, we find that the effect of isomers is more significant than molecular reorientation at room temperature and that the isomer model best agrees with the experimental results.

© 1998 Optical Society of America

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References

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  1. J. Zyss, “Nonlinear organic materials for integrated optics: a review,” J. Molec. Electron. 1, 25 (1985).
  2. M. G. Kuzyk, J. E. Sohn, and C. W. Dirk, “Mechanisms of quadratic electro-optic modulation of dye-doped polymer systems,” J. Opt. Soc. Am. B 7, 842 (1990).
    [CrossRef]
  3. C. W. Dirk and M. G. Kuzyk, “Squarylium dye-doped polymer systems as quadratic electrooptic materials,” Chem. Mater. 2, 4 (1990).
    [CrossRef]
  4. Q. L. Zhou, R. F. Shi, O. Zamani-Khamari, and A. F. Garito, “Negative third-order optical responses in squaraines,” Nonlinear Opt. 6, 145 (1993).
  5. C. W. Dirk, W. C. Herndon, F. Cervantes-Lee, H. Selnau, S. Martinez, P. Kalamegham, A. Tan, G. Campos, M. Velez, J. Zyss, I. Ledoux, and L. Cheng, “Squarylium dyes: structural factors pertaining to the negative third-order nonlinear optical response,” J. Am. Chem. Soc. 117, 2214 (1995).
    [CrossRef]
  6. S. Marder, J. W. Perry, G. Bourhill, C. B. Gorman, B. G. Tiemann, and K. Mansour, “Relation between bond-length alternation and second electronic hyperpolarizability of conjugated organic molecules,” Science 261, 186 (1993).
    [CrossRef] [PubMed]
  7. J. C. Luong, N. F. Borrelli, and A. R. Olszewski, “Quadratic electro-optical characterization of molecular nonlinear optical materials,” Mater. Res. Soc. Symp. Proc. 109, 251 (1988).
    [CrossRef]
  8. C. W. Dirk and M. G. Kuzyk, “Damping corrections and the calculation of optical nonlinearities in organic molecules,” Phys. Rev. B 41, 1636 (1990).
    [CrossRef]
  9. M. G. Kuzyk and C. W. Dirk, “Effects of centrosymmetry on the nonresonant electronic third-order nonlinear optical susceptibility,” Phys. Rev. A 41, 5098 (1990).
    [CrossRef] [PubMed]
  10. C. W. Dirk, L.-T. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27 (1992).
    [CrossRef]
  11. Y. Z. Yu, R. F. Shi, A. F. Garito, and C. H. Grossman, “Origin of negative χ(3) in squaraines: experimental observation of two-photon states,” Opt. Lett. 19, 786 (1994).
    [CrossRef] [PubMed]
  12. J. H. Andrews, J. D. V. Khaydarov, K. D. Singer, D. L. Hull, and K. C. Chuang, “Characterization of excited states of centrosymmetric and noncentrosymmetric squaraines by third harmonic spectral dispersion,” J. Opt. Soc. Am. B 12, 2360 (1995).
    [CrossRef]
  13. C. Poga, T. M. Brown, M. G. Kuzyk, and C. W. Dirk, “Characterization of the excited states of a squaraine molecule with quadratic electroabsorption spectroscopy,” J. Opt. Soc. Am. B 12, 531 (1995).
    [CrossRef]
  14. R. W. Bigelow and H. Freund, “An MNDO and CNDO/S(S+DES CI) study on the structural and electronic properties of a model squaraine dye and related cyanine,” Chem. Phys. 107, 159 (1986).
    [CrossRef]
  15. Y. R. Shen, Principles of Nonlinear Optics (Wiley-Interscience, New York, 1984).
  16. C. Poga, M. G. Kuzyk, and C. W. Dirk, “Quadratic electroabsorption studies of third-order susceptibility mechanisms in dye-doped polymers,” J. Opt. Soc. Am. B 11, 80 (1994).
    [CrossRef]
  17. B. J. Orr and J. F. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513 (1971).
    [CrossRef]
  18. C. Poga, “Mechanisms of the third-order nonlinear optical response in dye-doped polymers,” Ph.D. dissertation (Washington State University, Pullman, Wash., 1994).
  19. R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).
  20. K. D. Singer, M. G. Kuzyk, and J. E. Sohn, “Second-order nonlinear-optical processes in orientationally ordered materials: relationship between molecular and macroscopic properties,” J. Opt. Soc. Am. B 4, 968 (1987).
    [CrossRef]
  21. K. Zimmerman, F. Ghebremichael, and M. G. Kuzyk, “Electric-field-induced polarization current studies in guest–host polymers,” J. Appl. Phys. 75, 1270 (1994).
    [CrossRef]
  22. M. G. Kuzyk and C. Poga, “Quadratic electro-optics of guest–host polymers,” in Molecular Nonlinear Optics: Materials, Physics, and Devices, J. Zyss, ed. (Academic, San Diego, Calif., 1993), pp. 299–337.

1995

1994

1993

S. Marder, J. W. Perry, G. Bourhill, C. B. Gorman, B. G. Tiemann, and K. Mansour, “Relation between bond-length alternation and second electronic hyperpolarizability of conjugated organic molecules,” Science 261, 186 (1993).
[CrossRef] [PubMed]

Q. L. Zhou, R. F. Shi, O. Zamani-Khamari, and A. F. Garito, “Negative third-order optical responses in squaraines,” Nonlinear Opt. 6, 145 (1993).

1992

C. W. Dirk, L.-T. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27 (1992).
[CrossRef]

1990

C. W. Dirk and M. G. Kuzyk, “Damping corrections and the calculation of optical nonlinearities in organic molecules,” Phys. Rev. B 41, 1636 (1990).
[CrossRef]

M. G. Kuzyk and C. W. Dirk, “Effects of centrosymmetry on the nonresonant electronic third-order nonlinear optical susceptibility,” Phys. Rev. A 41, 5098 (1990).
[CrossRef] [PubMed]

C. W. Dirk and M. G. Kuzyk, “Squarylium dye-doped polymer systems as quadratic electrooptic materials,” Chem. Mater. 2, 4 (1990).
[CrossRef]

M. G. Kuzyk, J. E. Sohn, and C. W. Dirk, “Mechanisms of quadratic electro-optic modulation of dye-doped polymer systems,” J. Opt. Soc. Am. B 7, 842 (1990).
[CrossRef]

1988

J. C. Luong, N. F. Borrelli, and A. R. Olszewski, “Quadratic electro-optical characterization of molecular nonlinear optical materials,” Mater. Res. Soc. Symp. Proc. 109, 251 (1988).
[CrossRef]

1987

1986

R. W. Bigelow and H. Freund, “An MNDO and CNDO/S(S+DES CI) study on the structural and electronic properties of a model squaraine dye and related cyanine,” Chem. Phys. 107, 159 (1986).
[CrossRef]

1971

B. J. Orr and J. F. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513 (1971).
[CrossRef]

Andrews, J. H.

Bigelow, R. W.

R. W. Bigelow and H. Freund, “An MNDO and CNDO/S(S+DES CI) study on the structural and electronic properties of a model squaraine dye and related cyanine,” Chem. Phys. 107, 159 (1986).
[CrossRef]

Borrelli, N. F.

J. C. Luong, N. F. Borrelli, and A. R. Olszewski, “Quadratic electro-optical characterization of molecular nonlinear optical materials,” Mater. Res. Soc. Symp. Proc. 109, 251 (1988).
[CrossRef]

Bourhill, G.

S. Marder, J. W. Perry, G. Bourhill, C. B. Gorman, B. G. Tiemann, and K. Mansour, “Relation between bond-length alternation and second electronic hyperpolarizability of conjugated organic molecules,” Science 261, 186 (1993).
[CrossRef] [PubMed]

Brown, T. M.

Campos, G.

C. W. Dirk, W. C. Herndon, F. Cervantes-Lee, H. Selnau, S. Martinez, P. Kalamegham, A. Tan, G. Campos, M. Velez, J. Zyss, I. Ledoux, and L. Cheng, “Squarylium dyes: structural factors pertaining to the negative third-order nonlinear optical response,” J. Am. Chem. Soc. 117, 2214 (1995).
[CrossRef]

Cervantes-Lee, F.

C. W. Dirk, W. C. Herndon, F. Cervantes-Lee, H. Selnau, S. Martinez, P. Kalamegham, A. Tan, G. Campos, M. Velez, J. Zyss, I. Ledoux, and L. Cheng, “Squarylium dyes: structural factors pertaining to the negative third-order nonlinear optical response,” J. Am. Chem. Soc. 117, 2214 (1995).
[CrossRef]

Cheng, L.

C. W. Dirk, W. C. Herndon, F. Cervantes-Lee, H. Selnau, S. Martinez, P. Kalamegham, A. Tan, G. Campos, M. Velez, J. Zyss, I. Ledoux, and L. Cheng, “Squarylium dyes: structural factors pertaining to the negative third-order nonlinear optical response,” J. Am. Chem. Soc. 117, 2214 (1995).
[CrossRef]

Cheng, L.-T.

C. W. Dirk, L.-T. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27 (1992).
[CrossRef]

Chuang, K. C.

Dirk, C. W.

C. W. Dirk, W. C. Herndon, F. Cervantes-Lee, H. Selnau, S. Martinez, P. Kalamegham, A. Tan, G. Campos, M. Velez, J. Zyss, I. Ledoux, and L. Cheng, “Squarylium dyes: structural factors pertaining to the negative third-order nonlinear optical response,” J. Am. Chem. Soc. 117, 2214 (1995).
[CrossRef]

C. Poga, T. M. Brown, M. G. Kuzyk, and C. W. Dirk, “Characterization of the excited states of a squaraine molecule with quadratic electroabsorption spectroscopy,” J. Opt. Soc. Am. B 12, 531 (1995).
[CrossRef]

C. Poga, M. G. Kuzyk, and C. W. Dirk, “Quadratic electroabsorption studies of third-order susceptibility mechanisms in dye-doped polymers,” J. Opt. Soc. Am. B 11, 80 (1994).
[CrossRef]

C. W. Dirk, L.-T. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27 (1992).
[CrossRef]

C. W. Dirk and M. G. Kuzyk, “Damping corrections and the calculation of optical nonlinearities in organic molecules,” Phys. Rev. B 41, 1636 (1990).
[CrossRef]

M. G. Kuzyk, J. E. Sohn, and C. W. Dirk, “Mechanisms of quadratic electro-optic modulation of dye-doped polymer systems,” J. Opt. Soc. Am. B 7, 842 (1990).
[CrossRef]

C. W. Dirk and M. G. Kuzyk, “Squarylium dye-doped polymer systems as quadratic electrooptic materials,” Chem. Mater. 2, 4 (1990).
[CrossRef]

M. G. Kuzyk and C. W. Dirk, “Effects of centrosymmetry on the nonresonant electronic third-order nonlinear optical susceptibility,” Phys. Rev. A 41, 5098 (1990).
[CrossRef] [PubMed]

Freund, H.

R. W. Bigelow and H. Freund, “An MNDO and CNDO/S(S+DES CI) study on the structural and electronic properties of a model squaraine dye and related cyanine,” Chem. Phys. 107, 159 (1986).
[CrossRef]

Garito, A. F.

Y. Z. Yu, R. F. Shi, A. F. Garito, and C. H. Grossman, “Origin of negative χ(3) in squaraines: experimental observation of two-photon states,” Opt. Lett. 19, 786 (1994).
[CrossRef] [PubMed]

Q. L. Zhou, R. F. Shi, O. Zamani-Khamari, and A. F. Garito, “Negative third-order optical responses in squaraines,” Nonlinear Opt. 6, 145 (1993).

Ghebremichael, F.

K. Zimmerman, F. Ghebremichael, and M. G. Kuzyk, “Electric-field-induced polarization current studies in guest–host polymers,” J. Appl. Phys. 75, 1270 (1994).
[CrossRef]

Gorman, C. B.

S. Marder, J. W. Perry, G. Bourhill, C. B. Gorman, B. G. Tiemann, and K. Mansour, “Relation between bond-length alternation and second electronic hyperpolarizability of conjugated organic molecules,” Science 261, 186 (1993).
[CrossRef] [PubMed]

Grossman, C. H.

Herndon, W. C.

C. W. Dirk, W. C. Herndon, F. Cervantes-Lee, H. Selnau, S. Martinez, P. Kalamegham, A. Tan, G. Campos, M. Velez, J. Zyss, I. Ledoux, and L. Cheng, “Squarylium dyes: structural factors pertaining to the negative third-order nonlinear optical response,” J. Am. Chem. Soc. 117, 2214 (1995).
[CrossRef]

Hull, D. L.

Kalamegham, P.

C. W. Dirk, W. C. Herndon, F. Cervantes-Lee, H. Selnau, S. Martinez, P. Kalamegham, A. Tan, G. Campos, M. Velez, J. Zyss, I. Ledoux, and L. Cheng, “Squarylium dyes: structural factors pertaining to the negative third-order nonlinear optical response,” J. Am. Chem. Soc. 117, 2214 (1995).
[CrossRef]

Khaydarov, J. D. V.

Kuzyk, M. G.

C. Poga, T. M. Brown, M. G. Kuzyk, and C. W. Dirk, “Characterization of the excited states of a squaraine molecule with quadratic electroabsorption spectroscopy,” J. Opt. Soc. Am. B 12, 531 (1995).
[CrossRef]

K. Zimmerman, F. Ghebremichael, and M. G. Kuzyk, “Electric-field-induced polarization current studies in guest–host polymers,” J. Appl. Phys. 75, 1270 (1994).
[CrossRef]

C. Poga, M. G. Kuzyk, and C. W. Dirk, “Quadratic electroabsorption studies of third-order susceptibility mechanisms in dye-doped polymers,” J. Opt. Soc. Am. B 11, 80 (1994).
[CrossRef]

C. W. Dirk, L.-T. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27 (1992).
[CrossRef]

C. W. Dirk and M. G. Kuzyk, “Damping corrections and the calculation of optical nonlinearities in organic molecules,” Phys. Rev. B 41, 1636 (1990).
[CrossRef]

C. W. Dirk and M. G. Kuzyk, “Squarylium dye-doped polymer systems as quadratic electrooptic materials,” Chem. Mater. 2, 4 (1990).
[CrossRef]

M. G. Kuzyk, J. E. Sohn, and C. W. Dirk, “Mechanisms of quadratic electro-optic modulation of dye-doped polymer systems,” J. Opt. Soc. Am. B 7, 842 (1990).
[CrossRef]

M. G. Kuzyk and C. W. Dirk, “Effects of centrosymmetry on the nonresonant electronic third-order nonlinear optical susceptibility,” Phys. Rev. A 41, 5098 (1990).
[CrossRef] [PubMed]

K. D. Singer, M. G. Kuzyk, and J. E. Sohn, “Second-order nonlinear-optical processes in orientationally ordered materials: relationship between molecular and macroscopic properties,” J. Opt. Soc. Am. B 4, 968 (1987).
[CrossRef]

Ledoux, I.

C. W. Dirk, W. C. Herndon, F. Cervantes-Lee, H. Selnau, S. Martinez, P. Kalamegham, A. Tan, G. Campos, M. Velez, J. Zyss, I. Ledoux, and L. Cheng, “Squarylium dyes: structural factors pertaining to the negative third-order nonlinear optical response,” J. Am. Chem. Soc. 117, 2214 (1995).
[CrossRef]

Luong, J. C.

J. C. Luong, N. F. Borrelli, and A. R. Olszewski, “Quadratic electro-optical characterization of molecular nonlinear optical materials,” Mater. Res. Soc. Symp. Proc. 109, 251 (1988).
[CrossRef]

Mansour, K.

S. Marder, J. W. Perry, G. Bourhill, C. B. Gorman, B. G. Tiemann, and K. Mansour, “Relation between bond-length alternation and second electronic hyperpolarizability of conjugated organic molecules,” Science 261, 186 (1993).
[CrossRef] [PubMed]

Marder, S.

S. Marder, J. W. Perry, G. Bourhill, C. B. Gorman, B. G. Tiemann, and K. Mansour, “Relation between bond-length alternation and second electronic hyperpolarizability of conjugated organic molecules,” Science 261, 186 (1993).
[CrossRef] [PubMed]

Martinez, S.

C. W. Dirk, W. C. Herndon, F. Cervantes-Lee, H. Selnau, S. Martinez, P. Kalamegham, A. Tan, G. Campos, M. Velez, J. Zyss, I. Ledoux, and L. Cheng, “Squarylium dyes: structural factors pertaining to the negative third-order nonlinear optical response,” J. Am. Chem. Soc. 117, 2214 (1995).
[CrossRef]

Olszewski, A. R.

J. C. Luong, N. F. Borrelli, and A. R. Olszewski, “Quadratic electro-optical characterization of molecular nonlinear optical materials,” Mater. Res. Soc. Symp. Proc. 109, 251 (1988).
[CrossRef]

Orr, B. J.

B. J. Orr and J. F. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513 (1971).
[CrossRef]

Perry, J. W.

S. Marder, J. W. Perry, G. Bourhill, C. B. Gorman, B. G. Tiemann, and K. Mansour, “Relation between bond-length alternation and second electronic hyperpolarizability of conjugated organic molecules,” Science 261, 186 (1993).
[CrossRef] [PubMed]

Poga, C.

Selnau, H.

C. W. Dirk, W. C. Herndon, F. Cervantes-Lee, H. Selnau, S. Martinez, P. Kalamegham, A. Tan, G. Campos, M. Velez, J. Zyss, I. Ledoux, and L. Cheng, “Squarylium dyes: structural factors pertaining to the negative third-order nonlinear optical response,” J. Am. Chem. Soc. 117, 2214 (1995).
[CrossRef]

Shi, R. F.

Y. Z. Yu, R. F. Shi, A. F. Garito, and C. H. Grossman, “Origin of negative χ(3) in squaraines: experimental observation of two-photon states,” Opt. Lett. 19, 786 (1994).
[CrossRef] [PubMed]

Q. L. Zhou, R. F. Shi, O. Zamani-Khamari, and A. F. Garito, “Negative third-order optical responses in squaraines,” Nonlinear Opt. 6, 145 (1993).

Singer, K. D.

Sohn, J. E.

Tan, A.

C. W. Dirk, W. C. Herndon, F. Cervantes-Lee, H. Selnau, S. Martinez, P. Kalamegham, A. Tan, G. Campos, M. Velez, J. Zyss, I. Ledoux, and L. Cheng, “Squarylium dyes: structural factors pertaining to the negative third-order nonlinear optical response,” J. Am. Chem. Soc. 117, 2214 (1995).
[CrossRef]

Tiemann, B. G.

S. Marder, J. W. Perry, G. Bourhill, C. B. Gorman, B. G. Tiemann, and K. Mansour, “Relation between bond-length alternation and second electronic hyperpolarizability of conjugated organic molecules,” Science 261, 186 (1993).
[CrossRef] [PubMed]

Velez, M.

C. W. Dirk, W. C. Herndon, F. Cervantes-Lee, H. Selnau, S. Martinez, P. Kalamegham, A. Tan, G. Campos, M. Velez, J. Zyss, I. Ledoux, and L. Cheng, “Squarylium dyes: structural factors pertaining to the negative third-order nonlinear optical response,” J. Am. Chem. Soc. 117, 2214 (1995).
[CrossRef]

Ward, J. F.

B. J. Orr and J. F. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513 (1971).
[CrossRef]

Yu, Y. Z.

Zamani-Khamari, O.

Q. L. Zhou, R. F. Shi, O. Zamani-Khamari, and A. F. Garito, “Negative third-order optical responses in squaraines,” Nonlinear Opt. 6, 145 (1993).

Zhou, Q. L.

Q. L. Zhou, R. F. Shi, O. Zamani-Khamari, and A. F. Garito, “Negative third-order optical responses in squaraines,” Nonlinear Opt. 6, 145 (1993).

Zimmerman, K.

K. Zimmerman, F. Ghebremichael, and M. G. Kuzyk, “Electric-field-induced polarization current studies in guest–host polymers,” J. Appl. Phys. 75, 1270 (1994).
[CrossRef]

Zyss, J.

C. W. Dirk, W. C. Herndon, F. Cervantes-Lee, H. Selnau, S. Martinez, P. Kalamegham, A. Tan, G. Campos, M. Velez, J. Zyss, I. Ledoux, and L. Cheng, “Squarylium dyes: structural factors pertaining to the negative third-order nonlinear optical response,” J. Am. Chem. Soc. 117, 2214 (1995).
[CrossRef]

Chem. Mater.

C. W. Dirk and M. G. Kuzyk, “Squarylium dye-doped polymer systems as quadratic electrooptic materials,” Chem. Mater. 2, 4 (1990).
[CrossRef]

Chem. Phys.

R. W. Bigelow and H. Freund, “An MNDO and CNDO/S(S+DES CI) study on the structural and electronic properties of a model squaraine dye and related cyanine,” Chem. Phys. 107, 159 (1986).
[CrossRef]

Int. J. Quantum Chem.

C. W. Dirk, L.-T. Cheng, and M. G. Kuzyk, “A simplified three-level model describing the molecular third-order nonlinear optical susceptibility,” Int. J. Quantum Chem. 43, 27 (1992).
[CrossRef]

J. Am. Chem. Soc.

C. W. Dirk, W. C. Herndon, F. Cervantes-Lee, H. Selnau, S. Martinez, P. Kalamegham, A. Tan, G. Campos, M. Velez, J. Zyss, I. Ledoux, and L. Cheng, “Squarylium dyes: structural factors pertaining to the negative third-order nonlinear optical response,” J. Am. Chem. Soc. 117, 2214 (1995).
[CrossRef]

J. Appl. Phys.

K. Zimmerman, F. Ghebremichael, and M. G. Kuzyk, “Electric-field-induced polarization current studies in guest–host polymers,” J. Appl. Phys. 75, 1270 (1994).
[CrossRef]

J. Opt. Soc. Am. B

Mater. Res. Soc. Symp. Proc.

J. C. Luong, N. F. Borrelli, and A. R. Olszewski, “Quadratic electro-optical characterization of molecular nonlinear optical materials,” Mater. Res. Soc. Symp. Proc. 109, 251 (1988).
[CrossRef]

Mol. Phys.

B. J. Orr and J. F. Ward, “Perturbation theory of the non-linear optical polarization of an isolated system,” Mol. Phys. 20, 513 (1971).
[CrossRef]

Nonlinear Opt.

Q. L. Zhou, R. F. Shi, O. Zamani-Khamari, and A. F. Garito, “Negative third-order optical responses in squaraines,” Nonlinear Opt. 6, 145 (1993).

Opt. Lett.

Phys. Rev. A

M. G. Kuzyk and C. W. Dirk, “Effects of centrosymmetry on the nonresonant electronic third-order nonlinear optical susceptibility,” Phys. Rev. A 41, 5098 (1990).
[CrossRef] [PubMed]

Phys. Rev. B

C. W. Dirk and M. G. Kuzyk, “Damping corrections and the calculation of optical nonlinearities in organic molecules,” Phys. Rev. B 41, 1636 (1990).
[CrossRef]

Science

S. Marder, J. W. Perry, G. Bourhill, C. B. Gorman, B. G. Tiemann, and K. Mansour, “Relation between bond-length alternation and second electronic hyperpolarizability of conjugated organic molecules,” Science 261, 186 (1993).
[CrossRef] [PubMed]

Other

J. Zyss, “Nonlinear organic materials for integrated optics: a review,” J. Molec. Electron. 1, 25 (1985).

C. Poga, “Mechanisms of the third-order nonlinear optical response in dye-doped polymers,” Ph.D. dissertation (Washington State University, Pullman, Wash., 1994).

R. W. Boyd, Nonlinear Optics (Academic, San Diego, Calif., 1992).

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

M. G. Kuzyk and C. Poga, “Quadratic electro-optics of guest–host polymers,” in Molecular Nonlinear Optics: Materials, Physics, and Devices, J. Zyss, ed. (Academic, San Diego, Calif., 1993), pp. 299–337.

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Figures (18)

Fig. 1
Fig. 1

Comparison of squaraine absorption spectra normalized by their number densities.

Fig. 2
Fig. 2

Dispersion of Im(D11), Im(D121), and the molecular reorientation term relative to probe wavelength.

Fig. 3
Fig. 3

Variation in pressure and temperature during the sample pressing procedure.

Fig. 4
Fig. 4

Diagram of the QEA experiment.

Fig. 5
Fig. 5

(a) Magnitude (square meters per square volt) of the QEA spectrum of 0.5% TSQ at room temperature and modulating frequency Ω=1.5 kHz. (b) Relative phase between the signal and the applied voltage.

Fig. 6
Fig. 6

QEA spectrum (points) and three-level model curves: theoretical fit (dashed curve) and best fit (solid curve) for BSQ.

Fig. 7
Fig. 7

Nonlinear spectrum and three-level model fits for PSQ.

Fig. 8
Fig. 8

Nonlinear spectrum and three-level model for 0.5% TSQ.

Fig. 9
Fig. 9

QEA spectrum and three-level model fit for HSQ.

Fig. 10
Fig. 10

QEA spectrum and three-level model fit for PYSQ.

Fig. 11
Fig. 11

Nonlinear spectrum of ISQ versus three-level model and four-level model 1.

Fig. 12
Fig. 12

Comparison of the dispersion terms used in the PYSQ three- and four-level 1 models.

Fig. 13
Fig. 13

Four-level model 1 for PYSQ as μ13 is varied.

Fig. 14
Fig. 14

Four-level model 2 of PYSQ using two one-photon states, with increasing transition widths (in millielectron volts).

Fig. 15
Fig. 15

BSQ three-level model including molecular reorientation.

Fig. 16
Fig. 16

Comparison of the three-level models (original and cis–trans) for BSQ.

Fig. 17
Fig. 17

Contributions of the ISQ cis and trans isomers to Im[χ(3)] for the cis–trans model.

Fig. 18
Fig. 18

Comparison of the three-level models (original and cis–trans) for ISQ.

Tables (6)

Tables Icon

Table 1 Transition Values of Squaraine Dyes as Determined by Absorption Spectroscopy

Tables Icon

Table 2 Spectroscopic Designation of the PYSQ Molecule a

Tables Icon

Table 3 Molecular Structures of Squarines

Tables Icon

Table 4 Parameter Values Used in the Three- and Four-Level Models for the PYSQ Dye

Tables Icon

Table 5 Parameters Used in the cis (C)–trans (T) Isomerization Model for BSQ

Tables Icon

Table 6 Parameters Used in the cis (C)–trans (T) Isomerization Model for ISQ

Equations (28)

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

χ(1)(-ω; ω)Nμ1g2Γ1g 1(ω1g-ω)2+Γ1g2-1(ω1g+ω)2+Γ1g2,
a=χ3333(3)χ1133(3)=3purelyelectronic-2purelyreorientational.
γ=K3 l,m,nDl,m,nμglμlmμmnμng-l,nDl,nμglμlgμgnμng,
γ(-ω; ω, 0, 0)=3μ0123 (D121μ122-D11μ012).
Im(γ)3-level=3μ0123 [μ122 Im(D121)-μ012 Im(D11)].
D11(-ωσ; ω1, ω2, ω3)
=I^1,2,3{[(Ω1g-ωσ)(Ω1g-ω3)(Ω1g-ω1)]-1+[(Ω1g-ω3)(Ω1g*+ω2)(Ω1g-ω1)]-1+[(Ω1g*+ωσ)(Ω1g*+ω3)(Ω1g*+ω1)]-1+[(Ω1g*+ω3)(Ω1g-ω2)(Ω1g*+ω1)]-1},
D121(-ωσ; ω1, ω2, ω3)
=I^1,2,3{[(Ω1g-ωσ)(Ω2g-ω1-ω2)(Ω1g-ω1)]-1+[(Ω1g*+ω3)(Ω2g-ω1-ω2)(Ω1g-ω1)]-1+[(Ω1g*+ω1)(Ω2g*+ω1+ω2)(Ω1g-ω3)]-1+[(Ω1g*+ω1)(Ω2g*+ω1+ω2)(Ω1g*+ωσ)]-1},
Im(D11)=16γ1ωω1[-2Γ16-Γ14(2ω2+ω12)-2Γ12ω12(ω2-2ω12)-ω2ω12(4ω12-ω2)+3ω16]3{(ω12+Γ12)[(ω1-ω)2+Γ12][(ω1+ω)2+Γ12]}2,
Im(D121)=2Γ1(ω1ω2-Γ1Γ2)[(ω2-ω)2+Γ22]+2ω1(ω22+Γ22)[Γ1(ω2-ω)+Γ2(ω1-ω)]3(ω12+Γ12)(ω22+Γ22)[(ω1-ω)2+Γ12][(ω2-ω)2+Γ22]
+-2Γ1(ω1ω2-Γ1Γ2)[(ω2+ω)2+Γ22]-2ω1(ω22+Γ22)[Γ1(ω2+ω)+Γ2(ω1+ω)]3(ω12+Γ12)(ω22+Γ22)[(ω1+ω)2+Γ12][(ω2+ω)2+Γ22]
+Γ12Γ2(3ω2-6ωω1+2ω12)+2Γ1(ω-ω1)(ω-ω2)(ω12+Γ12)+[Γ2(ω-ω1)2(ω2-2ωω1+2ω12)]3(ω12+Γ12)[(ω1-ω)2+Γ12]2[(ω2-ω)2+Γ22]
+-Γ12Γ2(3ω2+6ωω1+2ω12)-2Γ1(ω+ω1)(ω+ω2)(ω12+Γ12)-[Γ2(ω+ω1)2(ω2+2ωω1+2ω12)]3(ω12+Γ12)[(ω1+ω)2+Γ12]2[(ω2+ω)2+Γ22],
Im(γ)4-level=3μ0123 [μ122 Im(D121)+μ132 Im(D131)-μ012 Im(D11)].
γ(-ω; ω, 0, 0)
=33 (-μ014D11-2μ012μ012D11-μ014D11+μ012μ122D121+μ01μ12μ21μ10D121+μ01μ12μ21μ10D121+μ012μ122D121),
Im(γ)=33 {[μ012μ122 Im(D121)-μ014 Im(D11)]+[μ012μ122 Im(D121)-μ014 Im(D11)]},
Im[χ(3)(-ω; ω, 0, 0)]N15 Im[γ(-ω; ω, 0, 0)]-43kθ Im[α(-ω; ω)α(0; 0)],
α(ω)=1 n,mρmm(0)μmniμnmjωmn-ω-iΓnm+μmniμnmjωmn+ω+iΓnm,
α(ω)=1 μgliμlgjωlg-ω-iΓlg+μlgiμgljωlg+ω+iΓlgρg(0),
Im[α(-ω; ω)α(0; 0)]
=8μ014ωω012Γ012(ω012+Γ012)[(ω-ω01)2+Γ012][(ω+ω01)2+Γ012],
nij=(n0)ij+(n0)ij32 sijklEk0El0,
Im[χijkl(3)]= Re(n0)Im(n03sijkl).
Im[χ1133(3)]=N15 (fω)2(f0)2 Im(γ),
(fω)=nω2+23(fω)2(f0)27.
(n03s)I=λd4πVrms2 I2ΩIsig,

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