Abstract

The dispersion of the fifth-order nonlinear optical susceptibility χ113333(5)(ω; ω, 0, 0, 0, 0) of a spin-coated polydiacetylene film (poly(BPOD), i.e., poly{[[8-butoxy carbonyl] methyl urethanyl]1-(5-pyrimidyl)-octa-1, 3-diyne}) is determined through electroabsorption spectroscopy. The maximum values of the real and the imaginary parts of χ113333(5)(ω; ω, 0, 0, 0, 0) are 9.87×10-21 esu and 1.28×10-20 esu, respectively. A model is proposed to explain the spectral dispersion of the nonlinear optical susceptibility.

© 2000 Optical Society of America

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  1. H. Shim, M. Liu, C. Hwangbo, and G. I. Stegeman, “Four-photon absorption in the single-crystal polymer bis(paratoluene) sulfonate,” Opt. Lett. 23, 430–432 (1998).
    [CrossRef]
  2. F. Kajzar, J. Messier, J. Zyss, and I. Ledoux, “Nonlinear interferometry in Langmuir–Blodgett multilayers of polydiacetylene,” Opt. Commun. 45, 133–137 (1983).
    [CrossRef]
  3. G. M. Carter, Y. J. Chen, and S. K. Tripathy, “Intensity-dependent index of refraction in multilayers of polydiacetylene,” Appl. Phys. Lett. 43, 891–893 (1983).
    [CrossRef]
  4. C. Sauteret, J. P. Hermann, R. Frey, F. Pradere, J. Ducuing, R. H. Baughman, and R. R. Chance, “Optical nonlinearities in one-dimensional-conjugated polymer crystals,” Phys. Rev. Lett. 36, 956–959 (1976).
    [CrossRef]
  5. B. J. Orchard and S. K. Tripathy, “Molecular structure and electronic property modification of poly(diacetylenes),” Macromolecules 19, 1844–1850 (1986).
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  6. S. B. Clough, S. Kumar, X. F. Sun, S. K. Tripathy, H. Matsuda, H. Nakanishi, S. Okada, and M. Kato, Nonlinear Optics of Organics and Semiconductors (Springer-Verlag, Berlin, 1989), pp. 149–154.
  7. W. H. Kim, N. B. Kodali, J. Kumar, and S. K. Tripathy, “A novel, soluble poly(diacetylene) containing an aromatic substituent,” Macromolecules 27, 1819–1824 (1994).
    [CrossRef]
  8. Y. Kawabe, F. Jarka, N. Peygambarian, D. Guo, S. Mazumdar, S. N. Dixit, and F. Kajzar, “Roles of band states and two-photon transitions in the electroabsorption of a polydiacetylene,” Phys. Rev. B 44, 6530–6533 (1991).
    [CrossRef]
  9. C. Heldmann, L. Brombacher, D. Neher, and M. Graf, “Dispersion of the electro-optical response in poled polymer films determined by Stark spectroscopy,” Thin Solid Films 261, 241–247 (1995).
    [CrossRef]
  10. K. Yang, W. Kim, J. Kumar, L. Li, and S. Tripathy, “Dispersion of χ(3) in polydiacetylene films from electroabsorption spectroscopy,” Opt. Commun. 144, 252–258 (1997).
    [CrossRef]
  11. K. Yang, D.-W. Cheong, S. Tripathy, and J. Kumar, “Dispersion of electroabsorption susceptibilities: application to a polymeric Langmuir–Blodgett film,” Opt. Commun. 144, 259–264 (1997).
    [CrossRef]
  12. K. Yang, X. Wang, A. Jain, L. Li, S. Tripathy, and J. Kumar, “Electroabsorption investigation of a nonlinear optical azo polymer,” Nonlinear Opt. 19, 215–226 (1998).
  13. K. Yang, S. Balasubramanian, X. Wang, J. Kumar, and S. Tripathy, “Electroabsorption spectroscopy study of an azopolymer film fabricated by electrostatic adsorption,” Appl. Phys. Lett. 73, 3345–3347 (1998).
    [CrossRef]
  14. C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734–1736 (1990).
    [CrossRef]
  15. J. S. Schildkraut, “Determination of the electrooptic coefficient of a poled polymer film,” Appl. Opt. 29, 2839–2841 (1990).
    [CrossRef] [PubMed]
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    [CrossRef]
  17. M. Sigelle and R. Hierle, “Determination of the electrooptic coefficients of 3-methyl 4-nitropyridine 1-oxide by an interferometric phase-modulation technique,” J. Appl. Phys. 52, 4199–4204 (1981).
    [CrossRef]
  18. R. A. Norwood, M. G. Kuzyk, and R. A. Keosian, “Electro-optic tensor ratio determination of side-chain copolymers with electro-optic interferometry,” J. Appl. Phys. 75, 1869–1874 (1994).
    [CrossRef]
  19. K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
    [CrossRef]
  20. M. G. Kuzyk and C. W. Dirk, “Quick and simple method to measure third-order nonlinear optical properties of dye-doped polymer films,” Appl. Phys. Lett. 54, 1628–1630 (1989).
    [CrossRef]
  21. M. G. Kuzyk, K. D. Singer, H. E. Zahn, and L. A. King, “Second-order nonlinear optical tensor properties of poled films under stress,” J. Opt. Soc. Am. B 6, 742–752 (1989).
    [CrossRef]
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    [CrossRef]
  23. 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, 531–543 (1995).
    [CrossRef]
  24. K. S. Mathis, M. G. Kuzyk, C. W. Dirk, A. Tan, S. Martinez, and G. Gampos, “Mechanism of the nonlinear optical properties of squaraine dyes in poly(methyl methacrylate) polymer,” J. Opt. Soc. Am. B 15, 871–883 (1998).
    [CrossRef]
  25. F. Qiu, K. Misawa, X. Cheng, A. Ueki, and T. Kobayashi, “Determination of complex tensor components of electro-optic constants of dye-doped polymer films with a Mach–Zehnder interferometer,” Appl. Phys. Lett. 65, 1605–1607 (1994).
    [CrossRef]
  26. H. Ono, K. Misawa, K. Minoshima, A. Ueki, and T. Kobayashi, “Complex electro-optic constants of dye-doped polymer films determined with a Mach–Zehnder interferometer,” J. Appl. Phys. 77, 4935–4940 (1995).
    [CrossRef]
  27. N. Butcher and D. Colter, The Element of Nonlinear Optics (Cambridge University, Cambridge, UK, 1991), Chap. 2.
  28. R. W. Boyd, Nonlinear Optics (Academic, London, 1992), Chap. 1.

1998

H. Shim, M. Liu, C. Hwangbo, and G. I. Stegeman, “Four-photon absorption in the single-crystal polymer bis(paratoluene) sulfonate,” Opt. Lett. 23, 430–432 (1998).
[CrossRef]

K. Yang, X. Wang, A. Jain, L. Li, S. Tripathy, and J. Kumar, “Electroabsorption investigation of a nonlinear optical azo polymer,” Nonlinear Opt. 19, 215–226 (1998).

K. Yang, S. Balasubramanian, X. Wang, J. Kumar, and S. Tripathy, “Electroabsorption spectroscopy study of an azopolymer film fabricated by electrostatic adsorption,” Appl. Phys. Lett. 73, 3345–3347 (1998).
[CrossRef]

K. S. Mathis, M. G. Kuzyk, C. W. Dirk, A. Tan, S. Martinez, and G. Gampos, “Mechanism of the nonlinear optical properties of squaraine dyes in poly(methyl methacrylate) polymer,” J. Opt. Soc. Am. B 15, 871–883 (1998).
[CrossRef]

1997

K. Yang, W. Kim, J. Kumar, L. Li, and S. Tripathy, “Dispersion of χ(3) in polydiacetylene films from electroabsorption spectroscopy,” Opt. Commun. 144, 252–258 (1997).
[CrossRef]

K. Yang, D.-W. Cheong, S. Tripathy, and J. Kumar, “Dispersion of electroabsorption susceptibilities: application to a polymeric Langmuir–Blodgett film,” Opt. Commun. 144, 259–264 (1997).
[CrossRef]

1995

C. Heldmann, L. Brombacher, D. Neher, and M. Graf, “Dispersion of the electro-optical response in poled polymer films determined by Stark spectroscopy,” Thin Solid Films 261, 241–247 (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, 531–543 (1995).
[CrossRef]

H. Ono, K. Misawa, K. Minoshima, A. Ueki, and T. Kobayashi, “Complex electro-optic constants of dye-doped polymer films determined with a Mach–Zehnder interferometer,” J. Appl. Phys. 77, 4935–4940 (1995).
[CrossRef]

1994

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, 80–91 (1994).
[CrossRef]

F. Qiu, K. Misawa, X. Cheng, A. Ueki, and T. Kobayashi, “Determination of complex tensor components of electro-optic constants of dye-doped polymer films with a Mach–Zehnder interferometer,” Appl. Phys. Lett. 65, 1605–1607 (1994).
[CrossRef]

R. A. Norwood, M. G. Kuzyk, and R. A. Keosian, “Electro-optic tensor ratio determination of side-chain copolymers with electro-optic interferometry,” J. Appl. Phys. 75, 1869–1874 (1994).
[CrossRef]

W. H. Kim, N. B. Kodali, J. Kumar, and S. K. Tripathy, “A novel, soluble poly(diacetylene) containing an aromatic substituent,” Macromolecules 27, 1819–1824 (1994).
[CrossRef]

1991

Y. Kawabe, F. Jarka, N. Peygambarian, D. Guo, S. Mazumdar, S. N. Dixit, and F. Kajzar, “Roles of band states and two-photon transitions in the electroabsorption of a polydiacetylene,” Phys. Rev. B 44, 6530–6533 (1991).
[CrossRef]

P. Rohl, B. Andress, and J. Nordmann, “Electro-optic determination of second and third order susceptibilities in poled polymer films,” Appl. Phys. Lett. 59, 2793–2795 (1991).
[CrossRef]

1990

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734–1736 (1990).
[CrossRef]

J. S. Schildkraut, “Determination of the electrooptic coefficient of a poled polymer film,” Appl. Opt. 29, 2839–2841 (1990).
[CrossRef] [PubMed]

1989

M. G. Kuzyk and C. W. Dirk, “Quick and simple method to measure third-order nonlinear optical properties of dye-doped polymer films,” Appl. Phys. Lett. 54, 1628–1630 (1989).
[CrossRef]

M. G. Kuzyk, K. D. Singer, H. E. Zahn, and L. A. King, “Second-order nonlinear optical tensor properties of poled films under stress,” J. Opt. Soc. Am. B 6, 742–752 (1989).
[CrossRef]

1988

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[CrossRef]

1986

B. J. Orchard and S. K. Tripathy, “Molecular structure and electronic property modification of poly(diacetylenes),” Macromolecules 19, 1844–1850 (1986).
[CrossRef]

1983

F. Kajzar, J. Messier, J. Zyss, and I. Ledoux, “Nonlinear interferometry in Langmuir–Blodgett multilayers of polydiacetylene,” Opt. Commun. 45, 133–137 (1983).
[CrossRef]

G. M. Carter, Y. J. Chen, and S. K. Tripathy, “Intensity-dependent index of refraction in multilayers of polydiacetylene,” Appl. Phys. Lett. 43, 891–893 (1983).
[CrossRef]

1981

M. Sigelle and R. Hierle, “Determination of the electrooptic coefficients of 3-methyl 4-nitropyridine 1-oxide by an interferometric phase-modulation technique,” J. Appl. Phys. 52, 4199–4204 (1981).
[CrossRef]

1976

C. Sauteret, J. P. Hermann, R. Frey, F. Pradere, J. Ducuing, R. H. Baughman, and R. R. Chance, “Optical nonlinearities in one-dimensional-conjugated polymer crystals,” Phys. Rev. Lett. 36, 956–959 (1976).
[CrossRef]

Andress, B.

P. Rohl, B. Andress, and J. Nordmann, “Electro-optic determination of second and third order susceptibilities in poled polymer films,” Appl. Phys. Lett. 59, 2793–2795 (1991).
[CrossRef]

Balasubramanian, S.

K. Yang, S. Balasubramanian, X. Wang, J. Kumar, and S. Tripathy, “Electroabsorption spectroscopy study of an azopolymer film fabricated by electrostatic adsorption,” Appl. Phys. Lett. 73, 3345–3347 (1998).
[CrossRef]

Baughman, R. H.

C. Sauteret, J. P. Hermann, R. Frey, F. Pradere, J. Ducuing, R. H. Baughman, and R. R. Chance, “Optical nonlinearities in one-dimensional-conjugated polymer crystals,” Phys. Rev. Lett. 36, 956–959 (1976).
[CrossRef]

Brombacher, L.

C. Heldmann, L. Brombacher, D. Neher, and M. Graf, “Dispersion of the electro-optical response in poled polymer films determined by Stark spectroscopy,” Thin Solid Films 261, 241–247 (1995).
[CrossRef]

Brown, T. M.

Carter, G. M.

G. M. Carter, Y. J. Chen, and S. K. Tripathy, “Intensity-dependent index of refraction in multilayers of polydiacetylene,” Appl. Phys. Lett. 43, 891–893 (1983).
[CrossRef]

Chance, R. R.

C. Sauteret, J. P. Hermann, R. Frey, F. Pradere, J. Ducuing, R. H. Baughman, and R. R. Chance, “Optical nonlinearities in one-dimensional-conjugated polymer crystals,” Phys. Rev. Lett. 36, 956–959 (1976).
[CrossRef]

Chen, Y. J.

G. M. Carter, Y. J. Chen, and S. K. Tripathy, “Intensity-dependent index of refraction in multilayers of polydiacetylene,” Appl. Phys. Lett. 43, 891–893 (1983).
[CrossRef]

Cheng, X.

F. Qiu, K. Misawa, X. Cheng, A. Ueki, and T. Kobayashi, “Determination of complex tensor components of electro-optic constants of dye-doped polymer films with a Mach–Zehnder interferometer,” Appl. Phys. Lett. 65, 1605–1607 (1994).
[CrossRef]

Cheong, D.-W.

K. Yang, D.-W. Cheong, S. Tripathy, and J. Kumar, “Dispersion of electroabsorption susceptibilities: application to a polymeric Langmuir–Blodgett film,” Opt. Commun. 144, 259–264 (1997).
[CrossRef]

Comizzoli, R. B.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[CrossRef]

Dirk, C. W.

Dixit, S. N.

Y. Kawabe, F. Jarka, N. Peygambarian, D. Guo, S. Mazumdar, S. N. Dixit, and F. Kajzar, “Roles of band states and two-photon transitions in the electroabsorption of a polydiacetylene,” Phys. Rev. B 44, 6530–6533 (1991).
[CrossRef]

Ducuing, J.

C. Sauteret, J. P. Hermann, R. Frey, F. Pradere, J. Ducuing, R. H. Baughman, and R. R. Chance, “Optical nonlinearities in one-dimensional-conjugated polymer crystals,” Phys. Rev. Lett. 36, 956–959 (1976).
[CrossRef]

Frey, R.

C. Sauteret, J. P. Hermann, R. Frey, F. Pradere, J. Ducuing, R. H. Baughman, and R. R. Chance, “Optical nonlinearities in one-dimensional-conjugated polymer crystals,” Phys. Rev. Lett. 36, 956–959 (1976).
[CrossRef]

Gampos, G.

Graf, M.

C. Heldmann, L. Brombacher, D. Neher, and M. Graf, “Dispersion of the electro-optical response in poled polymer films determined by Stark spectroscopy,” Thin Solid Films 261, 241–247 (1995).
[CrossRef]

Guo, D.

Y. Kawabe, F. Jarka, N. Peygambarian, D. Guo, S. Mazumdar, S. N. Dixit, and F. Kajzar, “Roles of band states and two-photon transitions in the electroabsorption of a polydiacetylene,” Phys. Rev. B 44, 6530–6533 (1991).
[CrossRef]

Heldmann, C.

C. Heldmann, L. Brombacher, D. Neher, and M. Graf, “Dispersion of the electro-optical response in poled polymer films determined by Stark spectroscopy,” Thin Solid Films 261, 241–247 (1995).
[CrossRef]

Hermann, J. P.

C. Sauteret, J. P. Hermann, R. Frey, F. Pradere, J. Ducuing, R. H. Baughman, and R. R. Chance, “Optical nonlinearities in one-dimensional-conjugated polymer crystals,” Phys. Rev. Lett. 36, 956–959 (1976).
[CrossRef]

Hierle, R.

M. Sigelle and R. Hierle, “Determination of the electrooptic coefficients of 3-methyl 4-nitropyridine 1-oxide by an interferometric phase-modulation technique,” J. Appl. Phys. 52, 4199–4204 (1981).
[CrossRef]

Holland, W. R.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[CrossRef]

Hwangbo, C.

Jain, A.

K. Yang, X. Wang, A. Jain, L. Li, S. Tripathy, and J. Kumar, “Electroabsorption investigation of a nonlinear optical azo polymer,” Nonlinear Opt. 19, 215–226 (1998).

Jarka, F.

Y. Kawabe, F. Jarka, N. Peygambarian, D. Guo, S. Mazumdar, S. N. Dixit, and F. Kajzar, “Roles of band states and two-photon transitions in the electroabsorption of a polydiacetylene,” Phys. Rev. B 44, 6530–6533 (1991).
[CrossRef]

Kajzar, F.

Y. Kawabe, F. Jarka, N. Peygambarian, D. Guo, S. Mazumdar, S. N. Dixit, and F. Kajzar, “Roles of band states and two-photon transitions in the electroabsorption of a polydiacetylene,” Phys. Rev. B 44, 6530–6533 (1991).
[CrossRef]

F. Kajzar, J. Messier, J. Zyss, and I. Ledoux, “Nonlinear interferometry in Langmuir–Blodgett multilayers of polydiacetylene,” Opt. Commun. 45, 133–137 (1983).
[CrossRef]

Katz, H. E.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[CrossRef]

Kawabe, Y.

Y. Kawabe, F. Jarka, N. Peygambarian, D. Guo, S. Mazumdar, S. N. Dixit, and F. Kajzar, “Roles of band states and two-photon transitions in the electroabsorption of a polydiacetylene,” Phys. Rev. B 44, 6530–6533 (1991).
[CrossRef]

Keosian, R. A.

R. A. Norwood, M. G. Kuzyk, and R. A. Keosian, “Electro-optic tensor ratio determination of side-chain copolymers with electro-optic interferometry,” J. Appl. Phys. 75, 1869–1874 (1994).
[CrossRef]

Kim, W.

K. Yang, W. Kim, J. Kumar, L. Li, and S. Tripathy, “Dispersion of χ(3) in polydiacetylene films from electroabsorption spectroscopy,” Opt. Commun. 144, 252–258 (1997).
[CrossRef]

Kim, W. H.

W. H. Kim, N. B. Kodali, J. Kumar, and S. K. Tripathy, “A novel, soluble poly(diacetylene) containing an aromatic substituent,” Macromolecules 27, 1819–1824 (1994).
[CrossRef]

King, L. A.

Kobayashi, T.

H. Ono, K. Misawa, K. Minoshima, A. Ueki, and T. Kobayashi, “Complex electro-optic constants of dye-doped polymer films determined with a Mach–Zehnder interferometer,” J. Appl. Phys. 77, 4935–4940 (1995).
[CrossRef]

F. Qiu, K. Misawa, X. Cheng, A. Ueki, and T. Kobayashi, “Determination of complex tensor components of electro-optic constants of dye-doped polymer films with a Mach–Zehnder interferometer,” Appl. Phys. Lett. 65, 1605–1607 (1994).
[CrossRef]

Kodali, N. B.

W. H. Kim, N. B. Kodali, J. Kumar, and S. K. Tripathy, “A novel, soluble poly(diacetylene) containing an aromatic substituent,” Macromolecules 27, 1819–1824 (1994).
[CrossRef]

Kumar, J.

K. Yang, X. Wang, A. Jain, L. Li, S. Tripathy, and J. Kumar, “Electroabsorption investigation of a nonlinear optical azo polymer,” Nonlinear Opt. 19, 215–226 (1998).

K. Yang, S. Balasubramanian, X. Wang, J. Kumar, and S. Tripathy, “Electroabsorption spectroscopy study of an azopolymer film fabricated by electrostatic adsorption,” Appl. Phys. Lett. 73, 3345–3347 (1998).
[CrossRef]

K. Yang, D.-W. Cheong, S. Tripathy, and J. Kumar, “Dispersion of electroabsorption susceptibilities: application to a polymeric Langmuir–Blodgett film,” Opt. Commun. 144, 259–264 (1997).
[CrossRef]

K. Yang, W. Kim, J. Kumar, L. Li, and S. Tripathy, “Dispersion of χ(3) in polydiacetylene films from electroabsorption spectroscopy,” Opt. Commun. 144, 252–258 (1997).
[CrossRef]

W. H. Kim, N. B. Kodali, J. Kumar, and S. K. Tripathy, “A novel, soluble poly(diacetylene) containing an aromatic substituent,” Macromolecules 27, 1819–1824 (1994).
[CrossRef]

Kuzyk, M. G.

K. S. Mathis, M. G. Kuzyk, C. W. Dirk, A. Tan, S. Martinez, and G. Gampos, “Mechanism of the nonlinear optical properties of squaraine dyes in poly(methyl methacrylate) polymer,” J. Opt. Soc. Am. B 15, 871–883 (1998).
[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, 531–543 (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, 80–91 (1994).
[CrossRef]

R. A. Norwood, M. G. Kuzyk, and R. A. Keosian, “Electro-optic tensor ratio determination of side-chain copolymers with electro-optic interferometry,” J. Appl. Phys. 75, 1869–1874 (1994).
[CrossRef]

M. G. Kuzyk and C. W. Dirk, “Quick and simple method to measure third-order nonlinear optical properties of dye-doped polymer films,” Appl. Phys. Lett. 54, 1628–1630 (1989).
[CrossRef]

M. G. Kuzyk, K. D. Singer, H. E. Zahn, and L. A. King, “Second-order nonlinear optical tensor properties of poled films under stress,” J. Opt. Soc. Am. B 6, 742–752 (1989).
[CrossRef]

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[CrossRef]

Lalama, S. J.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[CrossRef]

Ledoux, I.

F. Kajzar, J. Messier, J. Zyss, and I. Ledoux, “Nonlinear interferometry in Langmuir–Blodgett multilayers of polydiacetylene,” Opt. Commun. 45, 133–137 (1983).
[CrossRef]

Li, L.

K. Yang, X. Wang, A. Jain, L. Li, S. Tripathy, and J. Kumar, “Electroabsorption investigation of a nonlinear optical azo polymer,” Nonlinear Opt. 19, 215–226 (1998).

K. Yang, W. Kim, J. Kumar, L. Li, and S. Tripathy, “Dispersion of χ(3) in polydiacetylene films from electroabsorption spectroscopy,” Opt. Commun. 144, 252–258 (1997).
[CrossRef]

Liu, M.

Man, H. T.

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734–1736 (1990).
[CrossRef]

Martinez, S.

Mathis, K. S.

Mazumdar, S.

Y. Kawabe, F. Jarka, N. Peygambarian, D. Guo, S. Mazumdar, S. N. Dixit, and F. Kajzar, “Roles of band states and two-photon transitions in the electroabsorption of a polydiacetylene,” Phys. Rev. B 44, 6530–6533 (1991).
[CrossRef]

Messier, J.

F. Kajzar, J. Messier, J. Zyss, and I. Ledoux, “Nonlinear interferometry in Langmuir–Blodgett multilayers of polydiacetylene,” Opt. Commun. 45, 133–137 (1983).
[CrossRef]

Minoshima, K.

H. Ono, K. Misawa, K. Minoshima, A. Ueki, and T. Kobayashi, “Complex electro-optic constants of dye-doped polymer films determined with a Mach–Zehnder interferometer,” J. Appl. Phys. 77, 4935–4940 (1995).
[CrossRef]

Misawa, K.

H. Ono, K. Misawa, K. Minoshima, A. Ueki, and T. Kobayashi, “Complex electro-optic constants of dye-doped polymer films determined with a Mach–Zehnder interferometer,” J. Appl. Phys. 77, 4935–4940 (1995).
[CrossRef]

F. Qiu, K. Misawa, X. Cheng, A. Ueki, and T. Kobayashi, “Determination of complex tensor components of electro-optic constants of dye-doped polymer films with a Mach–Zehnder interferometer,” Appl. Phys. Lett. 65, 1605–1607 (1994).
[CrossRef]

Neher, D.

C. Heldmann, L. Brombacher, D. Neher, and M. Graf, “Dispersion of the electro-optical response in poled polymer films determined by Stark spectroscopy,” Thin Solid Films 261, 241–247 (1995).
[CrossRef]

Nordmann, J.

P. Rohl, B. Andress, and J. Nordmann, “Electro-optic determination of second and third order susceptibilities in poled polymer films,” Appl. Phys. Lett. 59, 2793–2795 (1991).
[CrossRef]

Norwood, R. A.

R. A. Norwood, M. G. Kuzyk, and R. A. Keosian, “Electro-optic tensor ratio determination of side-chain copolymers with electro-optic interferometry,” J. Appl. Phys. 75, 1869–1874 (1994).
[CrossRef]

Ono, H.

H. Ono, K. Misawa, K. Minoshima, A. Ueki, and T. Kobayashi, “Complex electro-optic constants of dye-doped polymer films determined with a Mach–Zehnder interferometer,” J. Appl. Phys. 77, 4935–4940 (1995).
[CrossRef]

Orchard, B. J.

B. J. Orchard and S. K. Tripathy, “Molecular structure and electronic property modification of poly(diacetylenes),” Macromolecules 19, 1844–1850 (1986).
[CrossRef]

Peygambarian, N.

Y. Kawabe, F. Jarka, N. Peygambarian, D. Guo, S. Mazumdar, S. N. Dixit, and F. Kajzar, “Roles of band states and two-photon transitions in the electroabsorption of a polydiacetylene,” Phys. Rev. B 44, 6530–6533 (1991).
[CrossRef]

Poga, C.

Pradere, F.

C. Sauteret, J. P. Hermann, R. Frey, F. Pradere, J. Ducuing, R. H. Baughman, and R. R. Chance, “Optical nonlinearities in one-dimensional-conjugated polymer crystals,” Phys. Rev. Lett. 36, 956–959 (1976).
[CrossRef]

Qiu, F.

F. Qiu, K. Misawa, X. Cheng, A. Ueki, and T. Kobayashi, “Determination of complex tensor components of electro-optic constants of dye-doped polymer films with a Mach–Zehnder interferometer,” Appl. Phys. Lett. 65, 1605–1607 (1994).
[CrossRef]

Rohl, P.

P. Rohl, B. Andress, and J. Nordmann, “Electro-optic determination of second and third order susceptibilities in poled polymer films,” Appl. Phys. Lett. 59, 2793–2795 (1991).
[CrossRef]

Sauteret, C.

C. Sauteret, J. P. Hermann, R. Frey, F. Pradere, J. Ducuing, R. H. Baughman, and R. R. Chance, “Optical nonlinearities in one-dimensional-conjugated polymer crystals,” Phys. Rev. Lett. 36, 956–959 (1976).
[CrossRef]

Schildkraut, J. S.

Schilling, M. L.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[CrossRef]

Shim, H.

Sigelle, M.

M. Sigelle and R. Hierle, “Determination of the electrooptic coefficients of 3-methyl 4-nitropyridine 1-oxide by an interferometric phase-modulation technique,” J. Appl. Phys. 52, 4199–4204 (1981).
[CrossRef]

Singer, K. D.

M. G. Kuzyk, K. D. Singer, H. E. Zahn, and L. A. King, “Second-order nonlinear optical tensor properties of poled films under stress,” J. Opt. Soc. Am. B 6, 742–752 (1989).
[CrossRef]

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[CrossRef]

Sohn, J. E.

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[CrossRef]

Stegeman, G. I.

Tan, A.

Teng, C. C.

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734–1736 (1990).
[CrossRef]

Tripathy, S.

K. Yang, S. Balasubramanian, X. Wang, J. Kumar, and S. Tripathy, “Electroabsorption spectroscopy study of an azopolymer film fabricated by electrostatic adsorption,” Appl. Phys. Lett. 73, 3345–3347 (1998).
[CrossRef]

K. Yang, X. Wang, A. Jain, L. Li, S. Tripathy, and J. Kumar, “Electroabsorption investigation of a nonlinear optical azo polymer,” Nonlinear Opt. 19, 215–226 (1998).

K. Yang, W. Kim, J. Kumar, L. Li, and S. Tripathy, “Dispersion of χ(3) in polydiacetylene films from electroabsorption spectroscopy,” Opt. Commun. 144, 252–258 (1997).
[CrossRef]

K. Yang, D.-W. Cheong, S. Tripathy, and J. Kumar, “Dispersion of electroabsorption susceptibilities: application to a polymeric Langmuir–Blodgett film,” Opt. Commun. 144, 259–264 (1997).
[CrossRef]

Tripathy, S. K.

W. H. Kim, N. B. Kodali, J. Kumar, and S. K. Tripathy, “A novel, soluble poly(diacetylene) containing an aromatic substituent,” Macromolecules 27, 1819–1824 (1994).
[CrossRef]

B. J. Orchard and S. K. Tripathy, “Molecular structure and electronic property modification of poly(diacetylenes),” Macromolecules 19, 1844–1850 (1986).
[CrossRef]

G. M. Carter, Y. J. Chen, and S. K. Tripathy, “Intensity-dependent index of refraction in multilayers of polydiacetylene,” Appl. Phys. Lett. 43, 891–893 (1983).
[CrossRef]

Ueki, A.

H. Ono, K. Misawa, K. Minoshima, A. Ueki, and T. Kobayashi, “Complex electro-optic constants of dye-doped polymer films determined with a Mach–Zehnder interferometer,” J. Appl. Phys. 77, 4935–4940 (1995).
[CrossRef]

F. Qiu, K. Misawa, X. Cheng, A. Ueki, and T. Kobayashi, “Determination of complex tensor components of electro-optic constants of dye-doped polymer films with a Mach–Zehnder interferometer,” Appl. Phys. Lett. 65, 1605–1607 (1994).
[CrossRef]

Wang, X.

K. Yang, S. Balasubramanian, X. Wang, J. Kumar, and S. Tripathy, “Electroabsorption spectroscopy study of an azopolymer film fabricated by electrostatic adsorption,” Appl. Phys. Lett. 73, 3345–3347 (1998).
[CrossRef]

K. Yang, X. Wang, A. Jain, L. Li, S. Tripathy, and J. Kumar, “Electroabsorption investigation of a nonlinear optical azo polymer,” Nonlinear Opt. 19, 215–226 (1998).

Yang, K.

K. Yang, S. Balasubramanian, X. Wang, J. Kumar, and S. Tripathy, “Electroabsorption spectroscopy study of an azopolymer film fabricated by electrostatic adsorption,” Appl. Phys. Lett. 73, 3345–3347 (1998).
[CrossRef]

K. Yang, X. Wang, A. Jain, L. Li, S. Tripathy, and J. Kumar, “Electroabsorption investigation of a nonlinear optical azo polymer,” Nonlinear Opt. 19, 215–226 (1998).

K. Yang, W. Kim, J. Kumar, L. Li, and S. Tripathy, “Dispersion of χ(3) in polydiacetylene films from electroabsorption spectroscopy,” Opt. Commun. 144, 252–258 (1997).
[CrossRef]

K. Yang, D.-W. Cheong, S. Tripathy, and J. Kumar, “Dispersion of electroabsorption susceptibilities: application to a polymeric Langmuir–Blodgett film,” Opt. Commun. 144, 259–264 (1997).
[CrossRef]

Zahn, H. E.

Zyss, J.

F. Kajzar, J. Messier, J. Zyss, and I. Ledoux, “Nonlinear interferometry in Langmuir–Blodgett multilayers of polydiacetylene,” Opt. Commun. 45, 133–137 (1983).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

P. Rohl, B. Andress, and J. Nordmann, “Electro-optic determination of second and third order susceptibilities in poled polymer films,” Appl. Phys. Lett. 59, 2793–2795 (1991).
[CrossRef]

K. Yang, S. Balasubramanian, X. Wang, J. Kumar, and S. Tripathy, “Electroabsorption spectroscopy study of an azopolymer film fabricated by electrostatic adsorption,” Appl. Phys. Lett. 73, 3345–3347 (1998).
[CrossRef]

C. C. Teng and H. T. Man, “Simple reflection technique for measuring the electro-optic coefficient of poled polymers,” Appl. Phys. Lett. 56, 1734–1736 (1990).
[CrossRef]

G. M. Carter, Y. J. Chen, and S. K. Tripathy, “Intensity-dependent index of refraction in multilayers of polydiacetylene,” Appl. Phys. Lett. 43, 891–893 (1983).
[CrossRef]

K. D. Singer, M. G. Kuzyk, W. R. Holland, J. E. Sohn, S. J. Lalama, R. B. Comizzoli, H. E. Katz, and M. L. Schilling, “Electro-optic phase modulation and optical second-harmonic generation in corona-poled polymer films,” Appl. Phys. Lett. 53, 1800–1802 (1988).
[CrossRef]

M. G. Kuzyk and C. W. Dirk, “Quick and simple method to measure third-order nonlinear optical properties of dye-doped polymer films,” Appl. Phys. Lett. 54, 1628–1630 (1989).
[CrossRef]

F. Qiu, K. Misawa, X. Cheng, A. Ueki, and T. Kobayashi, “Determination of complex tensor components of electro-optic constants of dye-doped polymer films with a Mach–Zehnder interferometer,” Appl. Phys. Lett. 65, 1605–1607 (1994).
[CrossRef]

J. Appl. Phys.

H. Ono, K. Misawa, K. Minoshima, A. Ueki, and T. Kobayashi, “Complex electro-optic constants of dye-doped polymer films determined with a Mach–Zehnder interferometer,” J. Appl. Phys. 77, 4935–4940 (1995).
[CrossRef]

M. Sigelle and R. Hierle, “Determination of the electrooptic coefficients of 3-methyl 4-nitropyridine 1-oxide by an interferometric phase-modulation technique,” J. Appl. Phys. 52, 4199–4204 (1981).
[CrossRef]

R. A. Norwood, M. G. Kuzyk, and R. A. Keosian, “Electro-optic tensor ratio determination of side-chain copolymers with electro-optic interferometry,” J. Appl. Phys. 75, 1869–1874 (1994).
[CrossRef]

J. Opt. Soc. Am. B

Macromolecules

B. J. Orchard and S. K. Tripathy, “Molecular structure and electronic property modification of poly(diacetylenes),” Macromolecules 19, 1844–1850 (1986).
[CrossRef]

W. H. Kim, N. B. Kodali, J. Kumar, and S. K. Tripathy, “A novel, soluble poly(diacetylene) containing an aromatic substituent,” Macromolecules 27, 1819–1824 (1994).
[CrossRef]

Nonlinear Opt.

K. Yang, X. Wang, A. Jain, L. Li, S. Tripathy, and J. Kumar, “Electroabsorption investigation of a nonlinear optical azo polymer,” Nonlinear Opt. 19, 215–226 (1998).

Opt. Commun.

F. Kajzar, J. Messier, J. Zyss, and I. Ledoux, “Nonlinear interferometry in Langmuir–Blodgett multilayers of polydiacetylene,” Opt. Commun. 45, 133–137 (1983).
[CrossRef]

K. Yang, W. Kim, J. Kumar, L. Li, and S. Tripathy, “Dispersion of χ(3) in polydiacetylene films from electroabsorption spectroscopy,” Opt. Commun. 144, 252–258 (1997).
[CrossRef]

K. Yang, D.-W. Cheong, S. Tripathy, and J. Kumar, “Dispersion of electroabsorption susceptibilities: application to a polymeric Langmuir–Blodgett film,” Opt. Commun. 144, 259–264 (1997).
[CrossRef]

Opt. Lett.

Phys. Rev. B

Y. Kawabe, F. Jarka, N. Peygambarian, D. Guo, S. Mazumdar, S. N. Dixit, and F. Kajzar, “Roles of band states and two-photon transitions in the electroabsorption of a polydiacetylene,” Phys. Rev. B 44, 6530–6533 (1991).
[CrossRef]

Phys. Rev. Lett.

C. Sauteret, J. P. Hermann, R. Frey, F. Pradere, J. Ducuing, R. H. Baughman, and R. R. Chance, “Optical nonlinearities in one-dimensional-conjugated polymer crystals,” Phys. Rev. Lett. 36, 956–959 (1976).
[CrossRef]

Thin Solid Films

C. Heldmann, L. Brombacher, D. Neher, and M. Graf, “Dispersion of the electro-optical response in poled polymer films determined by Stark spectroscopy,” Thin Solid Films 261, 241–247 (1995).
[CrossRef]

Other

S. B. Clough, S. Kumar, X. F. Sun, S. K. Tripathy, H. Matsuda, H. Nakanishi, S. Okada, and M. Kato, Nonlinear Optics of Organics and Semiconductors (Springer-Verlag, Berlin, 1989), pp. 149–154.

N. Butcher and D. Colter, The Element of Nonlinear Optics (Cambridge University, Cambridge, UK, 1991), Chap. 2.

R. W. Boyd, Nonlinear Optics (Academic, London, 1992), Chap. 1.

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Figures (6)

Fig. 1
Fig. 1

Curve a is the dispersion of ΔI4Ω/I, and curve b is ΔI4Ω/I-ΔIC4Ω/I, the result after χ(3) correction.

Fig. 2
Fig. 2

Dispersion of χ11(1)(ω; ω): curve a is the real part; curve b is the imaginary part. The separation between adjacent data points is 1 nm.

Fig. 3
Fig. 3

Dispersion of χ113333(5)(ω; ω, 0, 0, 0, 0): curve a is the real part; curve b is the imaginary part. Uncertainty: 6.4×10-22esu. The separation between adjacent data points is 1 nm.

Fig. 4
Fig. 4

Dispersion of χ1133(3)(ω; ω, 0, 0); curve a is the real part; curve b is the imaginary part. Uncertainty: 5.2×10-13 esu. The separation between adjacent data points is 1 nm.

Fig. 5
Fig. 5

Data-fitting results from Eq. (4.42). Curves a1 and b1 are (a) the real and (b) the imaginary parts of the left side of the equation. Curves a2 and b2 are (a) the real and (b) the imaginary parts of the right side of the equation.

Fig. 6
Fig. 6

Data-fitting results from Eq. (4.60). Curves a1 and b1 are (a) the real and (b) the imaginary parts of the left side of the equation. Curves a2 and b2 are (a) the real and (b) the imaginary parts of the right side of the equation.

Equations (101)

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2E(r)+ω2c2n˜2E(r)=-4πω2c2P,
Pi=n=2njχijzz(n)(ω; ω, 0,, 0)ejE0Eacn-1 exp(ik·r),
2eˆ·E(r)+ω2c2n˜2eˆ·E(r)=-4πω2c2eˆ·P,
eˆ·P=n=2nχeff(n)Eacn-1eˆ·E(r),
χeff(n)=ijχijzz(n)(ω; ω, 0,, 0)eiej.
2eˆ·E(r)+ω2c2n˜2eˆ·E(r)=0,
n˜2=n˜2+4πn=2nχeff(n)Eacn-1.
k·k=ω2c2n˜2.
k=(0, 0, k)=kzˆ,
ΔII=|exp(iktk)|Eac02|exp(iktk)|Eac=02-1,
ΔII=-4π ωctkn=2nEacn-1 Imχ1133(n)n˜+ΔICI,
ΔICI=124π ωctkn=2nEacn-1 Imχ1133(n)n˜2+ωctk Im1n˜32πn=2nEacn-1χ1133(n)2
Eac2=12Eaco2 cos(2Ωt)+12Eaco2,
Eac4=14Eaco41+2 cos(2Ωt)+12[1+cos(4Ωt)],
ΔI2ΩI=-2π ωctkEaco2×3 Imχ1133(3)n˜,
ΔI4ΩI=-π2ωctkEaco4×5 Imχ113333(5)n˜+ΔIC4ΩI,
ΔIC4ΩI=14Eaco42π ωctk3 Imχ1133(3)n˜2+9π22ωctkEaco4 Im[χ1133(3)]2n˜3,
Reχ1133(n)(ω)n˜=2πωiωf ωdωω2-ω2Imχ1133(n)(ω)n˜,
ψn=ψn+m=1EacsmknBnk(m)ψk,
En=En+m=1m=EacsmDn(m),
Bnk(1)=-μknEn-Ek,
Bnk(2)=mk μkmμmn(En-Ek)(En-Em)-μknμnn(En-Ek)2-δnk2mn μnmμmn(En-Em)2,
Dn(1)=-μnn,
Dn(2)=kn μnkμknEn-Ek,
μmk=-eψm*sψkds.
p(ω)=λ(1)(ω; ω)Es(ω),
λ(1)(ω; ω)=-1ngμgnμng1ωng-ω-iγng+1ωng+ω+iγng,
ωng=-1(En-Eg),
γng=12(Γn+Γg)=12Γn.
p(ω)=λ(1)(ω; ω)Es(ω),
λ(1)(ω; ω)=-1ngμgnμng1ωng-ω-iγng+1ωng+ω+iγng,
Dn(m)=0,
μnk=μnk+m=evenAnk(m)Eacsm,
μnk=m=oddAnk(m)Eacsm,
Ank(m)=k2kBkk2(m)μnk2+k1nBnk1(m)*μk1k+l=-m/2+2,-m/2+4,,m/2-2k1n,k2kBnk1(m/2+l)*×Bkk2(m/2-l)μk1k2.
μgnμng=μgnμng+m=evenCng(m)Eacsm,
Cng(m)=μgnAng(m)+Agn(m)μng+l=-m/2+2,-m/2+4m/2-2Agn(m/2+l)Ang(m/2-l),
ωng=ωng+m=evenGng(m)Eacsm,
Gng(m)=-1[Dn(m)-Dg(m)].
Γn=Ek<EnΓkn,
γng=γng+m=evenFng(m)Eacsm.
λ(1)(ω; ω)=λ(1)(ω; ω)+λ(3)(ω; ω, 0, 0)Eacs2+λ(5)(ω; ω, 0, 0, 0, 0)Eacs4+ ,
λ(3)(ω; ω, 0, 0)
=-1ngCng(2)1ωng-ω-iγng+1ωng+ω+iγng+-1ngμgnμng-Gng(2)+iFng(2)(ωng-ω-iγng)2-Gng(2)+iFng(2)(ωng+ω+iggng)2,
λ(5)(ω; ω, 0, 0, 0, 0)
=-1ngCng(4)1ωng-ω-iγng+1ωng+ω+iγng+-1ngCng(2)-Gng(2)+iFng(2)(ωng-ω-iγng)2-Gng(2)+iFng(2)(ωng+ω+iγng)2+-1ngμgnμng×-Gng(4)+iFng(4)(ωng-ω-iγng)2-Gng(4)+iFng(4)(ωng+ω+iγng)2+-1ngμgnμng×[Gng(2)-iFng(2)]2(ωng-ω-iγng)3+[Gng(2)+iFng(2)]2(ωng+ω+iγng)3.
χ11(1)(ω; ω)
=N2λ(1)(ω; ω)lsin2 αo,
χ1133(1)(ω; ω, 0, 0)
=N2λ(3)(ω; ω, 0, 0)lcos2 α sin2 αo,
χ113333(5)(ω; ω, 0, 0, 0, 0)
=N2λ(5)(ω; ω, 0, 0, 0, 0)lcos4 α sin2 αo,
λ(1)(ω; ω)
=-1μ01μ10n=1,21ωn0-ω-iγn0,
λ(3)(ω; ω, 0, 0)
=-1C10(2)n=1,21ωn0-ω-iγn0+-1μ01μ10×[-G10(2)+iF10(2)]n=1,21(ωn0-ω-iγn0)2,
λ(5)(ω; ω, 0, 0, 0, 0)
=-1C10(4)n=1,21ωn0-ω-iγn0+-1C10(2)×[-G10(2)+iF10(2)]n=1,21(ωn0-ω-iγn0)2+-1μ01μ10[-G10(4)+iF10(4)]×n=1,21(ωn0-ω-iγn0)2+-1μ01μ10[Gng(2)-iFng(2)]2×n=1,21(ωn0-ω-iγn0)3.
1(ωn0-ω-iγn0)3=12ddω1(ωn0-ω-iγn0)2,
1(ωn0-ω-iγn0)2=ddω1ωn0-ω-iγn0,
λ(5)(ω; ω, 0, 0, 0, 0)=q ddω[λ(3)(ω; ω, 0, 0)]+sλ(3)(ω; ω, 0, 0)+pλ(1)(ω; ω),
q=12[-G10(2)+iF10(2)],
s=-G10(4)+iF10(4)-G10(2)+iF10(2)+C10(2)2μ01μ10,
p=C10(4)-sC10(2)μ01μ10.
χ113333(5)(ω; ω, 0, 0, 0, 0)
=q ddω[χ1133(3)(ω; ω, 0, 0)]+sχ1133(3)(ω; ω, 0, 0)
+pχ11(1)(ω; ω),
q=q cos4 α sin2 αocos2 α sin2 αo,
s=s cos4 α sin2 αocos2 α sin2 αo,
p=p cos4 α sin2 αosin2 αo,
ωiωdωχ113333(5)(ω; ω, 0, 0, 0, 0)
=q[χ1133(3)(ω; ω, 0, 0)-χ1133(3)(ωi; ωi, 0, 0)]
+sωiωdωχ1133(3)(ω; ω, 0, 0)
+pωiωdωχ11(1)(ω; ω).
q=2.35×104+i2.01×104esu,
s=3.82×10-12-i4.60×10-11esu,
p=-8.38×10-23+i2.21×10-22esu.
Dn(2)|μn3|2En-E3<0
|D0(2)||Dn(2)|
Gn0(2)=-1[Dn(2)-D0(2)]<0(n=1, 2),
Re[q]>0,
μ30=μ03=0,
λ(1)(ω; ω)=0,
λ(3)(ω; ω, 0, 0)=-1C30(2) 1ω30-ω-iγ30,
λ(5)(ω; ω, 0, 0, 0, 0)
=-1C30(4) 1ω30-ω-iγ30+-1C30(2)×[-G30(2)+iF30(2)] 1(ω30-ω-iγ30)2,
λ(5)(ω; ω, 0, 0, 0, 0)
=q3 ddω[λ(3)(ω; ω, 0, 0)]+s3λ(3)(ω; ω, 0, 0),
q3=12[-G30(2)+iF30(2)],
s3=C30(4)/C30(2),
χ113333(5)(ω; ω, 0, 0, 0, 0)=q3 ddω[χ1133(3)(ω; ω, 0, 0)]+s3χ1133(3)(ω; ω, 0, 0),
q3=q3 cos4 α sin2 αocos2 α sin2 αo,
s3=s3 cos4 α sin2 αocos2 α sin2 αo,
ωiωdωχ113333(5)(ω; ω, 0, 0, 0, 0)
=q3[χ1133(3)(ω; ω, 0, 0)-χ1133(3)(ωi; ωi, 0, 0)]+s3ωiωdωχ1133(3)(ω; ω, 0, 0).
q3=-1.44×105-i5.52×104esu,
s3=-6.49×10-10esu.
D3(2)k=1,2 |μk3|2E3-Ek>0.
|D0(2)||D3(2)|.
G30(2)=-1[D3(2)-D0(2)]>0,
Re[q3]<0,

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