Abstract

An experimental analysis technique is described for accurate extraction of the coherence length and the complex third-order nonlinear susceptibility χ(3) in films or bulk optical glasses from the Maker fringes obtained by third-harmonic generation measurements. This method permits calculation of the third-order susceptibility of a sample without the need for assumptions as to the magnitude or the phase of the nonlinearity relative to a reference material such as the substrate. To illustrate the utility of the method we study spin-coated films of copper 2,3,9,10,16,17,23,24-octa(1,4,7,10-tetraoxaundecyl)phthalocyanine.

© 1998 Optical Society of America

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  1. F. Kajzar and J. Messier, “Cubic effects in polydiacetylene solutions and films,” in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, Orlando, Fla., 1987), Vol. 2, pp. 51–83.
  2. J. W. Perry, “Nonlinear optical properties of molecules and materials,” in Materials for Nonlinear Optics, S. R. Marder, J. E. Sohn, and G. D. Stucky, eds. Vol. 455 of ACS Symposium Series (American Chemical Society, Washington, D.C., 1991), pp. 67–88.
    [CrossRef]
  3. P. N. Prasad and D. J. Williams, “A survey of third-order nonlinear optical materials,” in Introduction to Nonlinear Optical Effects in Molecules and Polymers (Wiley, New York, 1991), Chap. 10, pp. 222–251.
  4. F. Kajzar, J. Messier, and C. Rosilio, “Nonlinear optical properties of thin films of polysilane,” J. Appl. Phys. 60, 3040–3044 (1986).
    [CrossRef]
  5. J. B. Van Beek, F. Kajzar, and A. C. Albrecht, “Third-harmonic generation from all-trans β-carotene in polystyrene thin films: multiple reflection effects and the onset of a two-photon resonance,” Chem. Phys. 161, 299–311 (1992).
    [CrossRef]
  6. N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
    [CrossRef]
  7. F. Kajzar and J. Messier, “Third-harmonic generation in liquids,” Phys. Rev. A 32, 2352–2363 (1985).
    [CrossRef] [PubMed]
  8. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
    [CrossRef]
  9. J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. 41, 1667–1681 (1970);S. K. Kurtz, “Measurement of nonlinear optical susceptibilities,” in Quantum Electronics, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, pp. 209–281.
    [CrossRef]
  10. Zhong Hua Zhou, H. Nasu, T. Hashimoto, and K. Kamiya, “Non-linear optical properties and structure of Na2S–GeS2 glasses,” J. Non-Cryst. Solids 215, 61–67 (1997).
    [CrossRef]
  11. G. R. Meredith, “Cascading in optical third-harmonic generation by crystalline quartz,” Phys. Rev. B 24, 5522–5532 (1981).
    [CrossRef]
  12. K. Kubodera and H. Kobayashi, “Determination of third-order nonlinear optical susceptibilities for organic materials by third harmonic generation,” Mol. Cryst. Liq. Cryst. 182A, 103–113 (1990).
  13. G. R. Meredith, B. Buchalter, and C. Hanzlik, “Third-order optical susceptibility determination by third harmonic generation. I,” J. Chem. Phys. 78, 1533–1551 (1983).
    [CrossRef]
  14. F. Kajzar and J. Messier, “Resonance enhancement in cubic susceptibility of Langmuir–Blodgett multilayers of polydiacetylene,” Thin Solid Films 132, 11–19 (1985).
    [CrossRef]
  15. G. J. Clarkson, N. B. McKeown, and K. E. Treacher, “Synthesis and characterisation of some novel phthalocyanines containing both oligo(ethyleneoxy) and alkyl or alkoxy side-chains: novel unsymmetrical discotic mesogens,” J. Chem. Soc. Perkin Trans. 1, 1817–1823 (1995).
    [CrossRef]
  16. J. Messier, “Third-order nonlinear susceptibility in semiconducting polymers,” in Nonlinear Optical Effects in Organic Polymers, J. Messier, P. Prasad, and D. Ulrich, eds. (Kluwer, Dordrecht, The Netherlands, 1989), pp. 47–60.
  17. T. Wada, T. Masuda, and H. Sasabe, “Third-order nonlinear optical properties of substituted polyphenylacetylenes,” Mol. Cryst. Liq. Cryst. 247, 139–147 (1994).
    [CrossRef]
  18. H. Kanbara, T. Maruno, A. Yamashita, S. Matsumoto, T. Hayashi, H. Konami, and N. Tanaka, “Third-order nonlinear optical properties of phthalocyanine and fullerene,” J. Appl. Phys. 80, 3674–3682 (1996).
    [CrossRef]
  19. J.-I. Lee, D.-H. Hwang, and H.-K. Shim, “Optical third harmonic generation of poly(2-alkoxy-1,4-phenylenevinylene)’s,” Mol. Cryst. Liq. Cryst. 247, 121–128 (1994).
    [CrossRef]
  20. H. Kobayashi, H. Kanbara, M. Koga, and K. Kubodera, “Third-order nonlinear optical properties of As2S3 chalcogenide glass,” J. Appl. Phys. 74, 3683–3687 (1993);T. Kanetake, K. Ishikawa, T. Hasegawa, T. Koda, K. Takeda, M. Hasegawa, K. Kubodera, and H. Kobayashi, “Nonlinear optical properties of highly oriented polydiacetylene evaporated films,” Appl. Phys. Lett. 54, 2287–2289 (1989).
    [CrossRef]
  21. F. Kajzar and M. Zagorska, “Third-order nonlinear optical properties of functionalized polymers,” Nonlin. Opt. 6, 181–192 (1993).

1997 (1)

Zhong Hua Zhou, H. Nasu, T. Hashimoto, and K. Kamiya, “Non-linear optical properties and structure of Na2S–GeS2 glasses,” J. Non-Cryst. Solids 215, 61–67 (1997).
[CrossRef]

1996 (1)

H. Kanbara, T. Maruno, A. Yamashita, S. Matsumoto, T. Hayashi, H. Konami, and N. Tanaka, “Third-order nonlinear optical properties of phthalocyanine and fullerene,” J. Appl. Phys. 80, 3674–3682 (1996).
[CrossRef]

1995 (1)

G. J. Clarkson, N. B. McKeown, and K. E. Treacher, “Synthesis and characterisation of some novel phthalocyanines containing both oligo(ethyleneoxy) and alkyl or alkoxy side-chains: novel unsymmetrical discotic mesogens,” J. Chem. Soc. Perkin Trans. 1, 1817–1823 (1995).
[CrossRef]

1994 (2)

T. Wada, T. Masuda, and H. Sasabe, “Third-order nonlinear optical properties of substituted polyphenylacetylenes,” Mol. Cryst. Liq. Cryst. 247, 139–147 (1994).
[CrossRef]

J.-I. Lee, D.-H. Hwang, and H.-K. Shim, “Optical third harmonic generation of poly(2-alkoxy-1,4-phenylenevinylene)’s,” Mol. Cryst. Liq. Cryst. 247, 121–128 (1994).
[CrossRef]

1993 (2)

H. Kobayashi, H. Kanbara, M. Koga, and K. Kubodera, “Third-order nonlinear optical properties of As2S3 chalcogenide glass,” J. Appl. Phys. 74, 3683–3687 (1993);T. Kanetake, K. Ishikawa, T. Hasegawa, T. Koda, K. Takeda, M. Hasegawa, K. Kubodera, and H. Kobayashi, “Nonlinear optical properties of highly oriented polydiacetylene evaporated films,” Appl. Phys. Lett. 54, 2287–2289 (1989).
[CrossRef]

F. Kajzar and M. Zagorska, “Third-order nonlinear optical properties of functionalized polymers,” Nonlin. Opt. 6, 181–192 (1993).

1992 (2)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

J. B. Van Beek, F. Kajzar, and A. C. Albrecht, “Third-harmonic generation from all-trans β-carotene in polystyrene thin films: multiple reflection effects and the onset of a two-photon resonance,” Chem. Phys. 161, 299–311 (1992).
[CrossRef]

1990 (1)

K. Kubodera and H. Kobayashi, “Determination of third-order nonlinear optical susceptibilities for organic materials by third harmonic generation,” Mol. Cryst. Liq. Cryst. 182A, 103–113 (1990).

1986 (1)

F. Kajzar, J. Messier, and C. Rosilio, “Nonlinear optical properties of thin films of polysilane,” J. Appl. Phys. 60, 3040–3044 (1986).
[CrossRef]

1985 (2)

F. Kajzar and J. Messier, “Third-harmonic generation in liquids,” Phys. Rev. A 32, 2352–2363 (1985).
[CrossRef] [PubMed]

F. Kajzar and J. Messier, “Resonance enhancement in cubic susceptibility of Langmuir–Blodgett multilayers of polydiacetylene,” Thin Solid Films 132, 11–19 (1985).
[CrossRef]

1983 (1)

G. R. Meredith, B. Buchalter, and C. Hanzlik, “Third-order optical susceptibility determination by third harmonic generation. I,” J. Chem. Phys. 78, 1533–1551 (1983).
[CrossRef]

1981 (1)

G. R. Meredith, “Cascading in optical third-harmonic generation by crystalline quartz,” Phys. Rev. B 24, 5522–5532 (1981).
[CrossRef]

1970 (1)

J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. 41, 1667–1681 (1970);S. K. Kurtz, “Measurement of nonlinear optical susceptibilities,” in Quantum Electronics, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, pp. 209–281.
[CrossRef]

1962 (1)

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

Albrecht, A. C.

J. B. Van Beek, F. Kajzar, and A. C. Albrecht, “Third-harmonic generation from all-trans β-carotene in polystyrene thin films: multiple reflection effects and the onset of a two-photon resonance,” Chem. Phys. 161, 299–311 (1992).
[CrossRef]

Bloembergen, N.

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

Buchalter, B.

G. R. Meredith, B. Buchalter, and C. Hanzlik, “Third-order optical susceptibility determination by third harmonic generation. I,” J. Chem. Phys. 78, 1533–1551 (1983).
[CrossRef]

Byer, R. L.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Clarkson, G. J.

G. J. Clarkson, N. B. McKeown, and K. E. Treacher, “Synthesis and characterisation of some novel phthalocyanines containing both oligo(ethyleneoxy) and alkyl or alkoxy side-chains: novel unsymmetrical discotic mesogens,” J. Chem. Soc. Perkin Trans. 1, 1817–1823 (1995).
[CrossRef]

Fejer, M. M.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Hanzlik, C.

G. R. Meredith, B. Buchalter, and C. Hanzlik, “Third-order optical susceptibility determination by third harmonic generation. I,” J. Chem. Phys. 78, 1533–1551 (1983).
[CrossRef]

Hashimoto, T.

Zhong Hua Zhou, H. Nasu, T. Hashimoto, and K. Kamiya, “Non-linear optical properties and structure of Na2S–GeS2 glasses,” J. Non-Cryst. Solids 215, 61–67 (1997).
[CrossRef]

Hayashi, T.

H. Kanbara, T. Maruno, A. Yamashita, S. Matsumoto, T. Hayashi, H. Konami, and N. Tanaka, “Third-order nonlinear optical properties of phthalocyanine and fullerene,” J. Appl. Phys. 80, 3674–3682 (1996).
[CrossRef]

Hwang, D.-H.

J.-I. Lee, D.-H. Hwang, and H.-K. Shim, “Optical third harmonic generation of poly(2-alkoxy-1,4-phenylenevinylene)’s,” Mol. Cryst. Liq. Cryst. 247, 121–128 (1994).
[CrossRef]

Jerphagnon, J.

J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. 41, 1667–1681 (1970);S. K. Kurtz, “Measurement of nonlinear optical susceptibilities,” in Quantum Electronics, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, pp. 209–281.
[CrossRef]

Jundt, D. H.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Kajzar, F.

F. Kajzar and M. Zagorska, “Third-order nonlinear optical properties of functionalized polymers,” Nonlin. Opt. 6, 181–192 (1993).

J. B. Van Beek, F. Kajzar, and A. C. Albrecht, “Third-harmonic generation from all-trans β-carotene in polystyrene thin films: multiple reflection effects and the onset of a two-photon resonance,” Chem. Phys. 161, 299–311 (1992).
[CrossRef]

F. Kajzar, J. Messier, and C. Rosilio, “Nonlinear optical properties of thin films of polysilane,” J. Appl. Phys. 60, 3040–3044 (1986).
[CrossRef]

F. Kajzar and J. Messier, “Third-harmonic generation in liquids,” Phys. Rev. A 32, 2352–2363 (1985).
[CrossRef] [PubMed]

F. Kajzar and J. Messier, “Resonance enhancement in cubic susceptibility of Langmuir–Blodgett multilayers of polydiacetylene,” Thin Solid Films 132, 11–19 (1985).
[CrossRef]

F. Kajzar and J. Messier, “Cubic effects in polydiacetylene solutions and films,” in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, Orlando, Fla., 1987), Vol. 2, pp. 51–83.

Kamiya, K.

Zhong Hua Zhou, H. Nasu, T. Hashimoto, and K. Kamiya, “Non-linear optical properties and structure of Na2S–GeS2 glasses,” J. Non-Cryst. Solids 215, 61–67 (1997).
[CrossRef]

Kanbara, H.

H. Kanbara, T. Maruno, A. Yamashita, S. Matsumoto, T. Hayashi, H. Konami, and N. Tanaka, “Third-order nonlinear optical properties of phthalocyanine and fullerene,” J. Appl. Phys. 80, 3674–3682 (1996).
[CrossRef]

H. Kobayashi, H. Kanbara, M. Koga, and K. Kubodera, “Third-order nonlinear optical properties of As2S3 chalcogenide glass,” J. Appl. Phys. 74, 3683–3687 (1993);T. Kanetake, K. Ishikawa, T. Hasegawa, T. Koda, K. Takeda, M. Hasegawa, K. Kubodera, and H. Kobayashi, “Nonlinear optical properties of highly oriented polydiacetylene evaporated films,” Appl. Phys. Lett. 54, 2287–2289 (1989).
[CrossRef]

Kobayashi, H.

H. Kobayashi, H. Kanbara, M. Koga, and K. Kubodera, “Third-order nonlinear optical properties of As2S3 chalcogenide glass,” J. Appl. Phys. 74, 3683–3687 (1993);T. Kanetake, K. Ishikawa, T. Hasegawa, T. Koda, K. Takeda, M. Hasegawa, K. Kubodera, and H. Kobayashi, “Nonlinear optical properties of highly oriented polydiacetylene evaporated films,” Appl. Phys. Lett. 54, 2287–2289 (1989).
[CrossRef]

K. Kubodera and H. Kobayashi, “Determination of third-order nonlinear optical susceptibilities for organic materials by third harmonic generation,” Mol. Cryst. Liq. Cryst. 182A, 103–113 (1990).

Koga, M.

H. Kobayashi, H. Kanbara, M. Koga, and K. Kubodera, “Third-order nonlinear optical properties of As2S3 chalcogenide glass,” J. Appl. Phys. 74, 3683–3687 (1993);T. Kanetake, K. Ishikawa, T. Hasegawa, T. Koda, K. Takeda, M. Hasegawa, K. Kubodera, and H. Kobayashi, “Nonlinear optical properties of highly oriented polydiacetylene evaporated films,” Appl. Phys. Lett. 54, 2287–2289 (1989).
[CrossRef]

Konami, H.

H. Kanbara, T. Maruno, A. Yamashita, S. Matsumoto, T. Hayashi, H. Konami, and N. Tanaka, “Third-order nonlinear optical properties of phthalocyanine and fullerene,” J. Appl. Phys. 80, 3674–3682 (1996).
[CrossRef]

Kubodera, K.

H. Kobayashi, H. Kanbara, M. Koga, and K. Kubodera, “Third-order nonlinear optical properties of As2S3 chalcogenide glass,” J. Appl. Phys. 74, 3683–3687 (1993);T. Kanetake, K. Ishikawa, T. Hasegawa, T. Koda, K. Takeda, M. Hasegawa, K. Kubodera, and H. Kobayashi, “Nonlinear optical properties of highly oriented polydiacetylene evaporated films,” Appl. Phys. Lett. 54, 2287–2289 (1989).
[CrossRef]

K. Kubodera and H. Kobayashi, “Determination of third-order nonlinear optical susceptibilities for organic materials by third harmonic generation,” Mol. Cryst. Liq. Cryst. 182A, 103–113 (1990).

Kurtz, S. K.

J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. 41, 1667–1681 (1970);S. K. Kurtz, “Measurement of nonlinear optical susceptibilities,” in Quantum Electronics, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, pp. 209–281.
[CrossRef]

Lee, J.-I.

J.-I. Lee, D.-H. Hwang, and H.-K. Shim, “Optical third harmonic generation of poly(2-alkoxy-1,4-phenylenevinylene)’s,” Mol. Cryst. Liq. Cryst. 247, 121–128 (1994).
[CrossRef]

Magel, G. A.

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

Maruno, T.

H. Kanbara, T. Maruno, A. Yamashita, S. Matsumoto, T. Hayashi, H. Konami, and N. Tanaka, “Third-order nonlinear optical properties of phthalocyanine and fullerene,” J. Appl. Phys. 80, 3674–3682 (1996).
[CrossRef]

Masuda, T.

T. Wada, T. Masuda, and H. Sasabe, “Third-order nonlinear optical properties of substituted polyphenylacetylenes,” Mol. Cryst. Liq. Cryst. 247, 139–147 (1994).
[CrossRef]

Matsumoto, S.

H. Kanbara, T. Maruno, A. Yamashita, S. Matsumoto, T. Hayashi, H. Konami, and N. Tanaka, “Third-order nonlinear optical properties of phthalocyanine and fullerene,” J. Appl. Phys. 80, 3674–3682 (1996).
[CrossRef]

McKeown, N. B.

G. J. Clarkson, N. B. McKeown, and K. E. Treacher, “Synthesis and characterisation of some novel phthalocyanines containing both oligo(ethyleneoxy) and alkyl or alkoxy side-chains: novel unsymmetrical discotic mesogens,” J. Chem. Soc. Perkin Trans. 1, 1817–1823 (1995).
[CrossRef]

Meredith, G. R.

G. R. Meredith, B. Buchalter, and C. Hanzlik, “Third-order optical susceptibility determination by third harmonic generation. I,” J. Chem. Phys. 78, 1533–1551 (1983).
[CrossRef]

G. R. Meredith, “Cascading in optical third-harmonic generation by crystalline quartz,” Phys. Rev. B 24, 5522–5532 (1981).
[CrossRef]

Messier, J.

F. Kajzar, J. Messier, and C. Rosilio, “Nonlinear optical properties of thin films of polysilane,” J. Appl. Phys. 60, 3040–3044 (1986).
[CrossRef]

F. Kajzar and J. Messier, “Third-harmonic generation in liquids,” Phys. Rev. A 32, 2352–2363 (1985).
[CrossRef] [PubMed]

F. Kajzar and J. Messier, “Resonance enhancement in cubic susceptibility of Langmuir–Blodgett multilayers of polydiacetylene,” Thin Solid Films 132, 11–19 (1985).
[CrossRef]

F. Kajzar and J. Messier, “Cubic effects in polydiacetylene solutions and films,” in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, Orlando, Fla., 1987), Vol. 2, pp. 51–83.

J. Messier, “Third-order nonlinear susceptibility in semiconducting polymers,” in Nonlinear Optical Effects in Organic Polymers, J. Messier, P. Prasad, and D. Ulrich, eds. (Kluwer, Dordrecht, The Netherlands, 1989), pp. 47–60.

Nasu, H.

Zhong Hua Zhou, H. Nasu, T. Hashimoto, and K. Kamiya, “Non-linear optical properties and structure of Na2S–GeS2 glasses,” J. Non-Cryst. Solids 215, 61–67 (1997).
[CrossRef]

Perry, J. W.

J. W. Perry, “Nonlinear optical properties of molecules and materials,” in Materials for Nonlinear Optics, S. R. Marder, J. E. Sohn, and G. D. Stucky, eds. Vol. 455 of ACS Symposium Series (American Chemical Society, Washington, D.C., 1991), pp. 67–88.
[CrossRef]

Pershan, P. S.

N. Bloembergen and P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 128, 606–622 (1962).
[CrossRef]

Prasad, P. N.

P. N. Prasad and D. J. Williams, “A survey of third-order nonlinear optical materials,” in Introduction to Nonlinear Optical Effects in Molecules and Polymers (Wiley, New York, 1991), Chap. 10, pp. 222–251.

Rosilio, C.

F. Kajzar, J. Messier, and C. Rosilio, “Nonlinear optical properties of thin films of polysilane,” J. Appl. Phys. 60, 3040–3044 (1986).
[CrossRef]

Sasabe, H.

T. Wada, T. Masuda, and H. Sasabe, “Third-order nonlinear optical properties of substituted polyphenylacetylenes,” Mol. Cryst. Liq. Cryst. 247, 139–147 (1994).
[CrossRef]

Shim, H.-K.

J.-I. Lee, D.-H. Hwang, and H.-K. Shim, “Optical third harmonic generation of poly(2-alkoxy-1,4-phenylenevinylene)’s,” Mol. Cryst. Liq. Cryst. 247, 121–128 (1994).
[CrossRef]

Tanaka, N.

H. Kanbara, T. Maruno, A. Yamashita, S. Matsumoto, T. Hayashi, H. Konami, and N. Tanaka, “Third-order nonlinear optical properties of phthalocyanine and fullerene,” J. Appl. Phys. 80, 3674–3682 (1996).
[CrossRef]

Treacher, K. E.

G. J. Clarkson, N. B. McKeown, and K. E. Treacher, “Synthesis and characterisation of some novel phthalocyanines containing both oligo(ethyleneoxy) and alkyl or alkoxy side-chains: novel unsymmetrical discotic mesogens,” J. Chem. Soc. Perkin Trans. 1, 1817–1823 (1995).
[CrossRef]

Van Beek, J. B.

J. B. Van Beek, F. Kajzar, and A. C. Albrecht, “Third-harmonic generation from all-trans β-carotene in polystyrene thin films: multiple reflection effects and the onset of a two-photon resonance,” Chem. Phys. 161, 299–311 (1992).
[CrossRef]

Wada, T.

T. Wada, T. Masuda, and H. Sasabe, “Third-order nonlinear optical properties of substituted polyphenylacetylenes,” Mol. Cryst. Liq. Cryst. 247, 139–147 (1994).
[CrossRef]

Williams, D. J.

P. N. Prasad and D. J. Williams, “A survey of third-order nonlinear optical materials,” in Introduction to Nonlinear Optical Effects in Molecules and Polymers (Wiley, New York, 1991), Chap. 10, pp. 222–251.

Yamashita, A.

H. Kanbara, T. Maruno, A. Yamashita, S. Matsumoto, T. Hayashi, H. Konami, and N. Tanaka, “Third-order nonlinear optical properties of phthalocyanine and fullerene,” J. Appl. Phys. 80, 3674–3682 (1996).
[CrossRef]

Zagorska, M.

F. Kajzar and M. Zagorska, “Third-order nonlinear optical properties of functionalized polymers,” Nonlin. Opt. 6, 181–192 (1993).

Zhou, Zhong Hua

Zhong Hua Zhou, H. Nasu, T. Hashimoto, and K. Kamiya, “Non-linear optical properties and structure of Na2S–GeS2 glasses,” J. Non-Cryst. Solids 215, 61–67 (1997).
[CrossRef]

Chem. Phys. (1)

J. B. Van Beek, F. Kajzar, and A. C. Albrecht, “Third-harmonic generation from all-trans β-carotene in polystyrene thin films: multiple reflection effects and the onset of a two-photon resonance,” Chem. Phys. 161, 299–311 (1992).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, “Quasi-phase-matched second harmonic generation: tuning and tolerances,” IEEE J. Quantum Electron. 28, 2631–2654 (1992).
[CrossRef]

J. Appl. Phys. (4)

J. Jerphagnon and S. K. Kurtz, “Maker fringes: a detailed comparison of theory and experiment for isotropic and uniaxial crystals,” J. Appl. Phys. 41, 1667–1681 (1970);S. K. Kurtz, “Measurement of nonlinear optical susceptibilities,” in Quantum Electronics, H. Rabin and C. L. Tang, eds. (Academic, New York, 1975), Vol. 1, pp. 209–281.
[CrossRef]

F. Kajzar, J. Messier, and C. Rosilio, “Nonlinear optical properties of thin films of polysilane,” J. Appl. Phys. 60, 3040–3044 (1986).
[CrossRef]

H. Kanbara, T. Maruno, A. Yamashita, S. Matsumoto, T. Hayashi, H. Konami, and N. Tanaka, “Third-order nonlinear optical properties of phthalocyanine and fullerene,” J. Appl. Phys. 80, 3674–3682 (1996).
[CrossRef]

H. Kobayashi, H. Kanbara, M. Koga, and K. Kubodera, “Third-order nonlinear optical properties of As2S3 chalcogenide glass,” J. Appl. Phys. 74, 3683–3687 (1993);T. Kanetake, K. Ishikawa, T. Hasegawa, T. Koda, K. Takeda, M. Hasegawa, K. Kubodera, and H. Kobayashi, “Nonlinear optical properties of highly oriented polydiacetylene evaporated films,” Appl. Phys. Lett. 54, 2287–2289 (1989).
[CrossRef]

J. Chem. Phys. (1)

G. R. Meredith, B. Buchalter, and C. Hanzlik, “Third-order optical susceptibility determination by third harmonic generation. I,” J. Chem. Phys. 78, 1533–1551 (1983).
[CrossRef]

J. Chem. Soc. Perkin Trans. (1)

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J. Non-Cryst. Solids (1)

Zhong Hua Zhou, H. Nasu, T. Hashimoto, and K. Kamiya, “Non-linear optical properties and structure of Na2S–GeS2 glasses,” J. Non-Cryst. Solids 215, 61–67 (1997).
[CrossRef]

Mol. Cryst. Liq. Cryst. (3)

J.-I. Lee, D.-H. Hwang, and H.-K. Shim, “Optical third harmonic generation of poly(2-alkoxy-1,4-phenylenevinylene)’s,” Mol. Cryst. Liq. Cryst. 247, 121–128 (1994).
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Nonlin. Opt. (1)

F. Kajzar and M. Zagorska, “Third-order nonlinear optical properties of functionalized polymers,” Nonlin. Opt. 6, 181–192 (1993).

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Figures (5)

Fig. 1
Fig. 1

Experimental Maker fringes of the third-harmonic generated, an analysis of the positions of the minima for (a) a fused-silica substrate in vacuum and (b) a microscope slide in vacuum.

Fig. 2
Fig. 2

Experimental configuration for the measurement of Maker fringes in THG. HP, high-pass filter; OPO, optical parametric oscillator; ND, neutral density, PMT, photomultiplier tube.

Fig. 3
Fig. 3

Effect of air on THG: top, Maker fringe pattern and residuals to the model from a fused-silica sample in vacuum; bottom, corresponding pattern and residuals from the same sample immersed in air.

Fig. 4
Fig. 4

Harmonic signal from top, a bare substrate and bottom, a substrate coated on one side with a spin-coated film of (TOU)CuPc.

Fig. 5
Fig. 5

Orientation of a sample comprising a substrate coated on one side with a nonlinear film. PMT, photomultiplier tube.

Tables (2)

Tables Icon

Table 1 Comparison of Coherence-Length Values Calculated from Dispersion Data and from Maker Fringe Experiments

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Table 2 Parameters of the (TOU)CuPc Film a

Equations (46)

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E3t3ω=E2b3ωA exp(ik2t3ωl){exp[i(k2b3ω-k2t3ω)l]-1},
E2b3ω=4πP2NLΔε
P2NL=¼χ(3)(-3ω; ω, ω, ω)(E2ω)3,
E2b3ω=πχ(3)Δε (E2ω)=πχ(3)Δε (t12ωEω)3,
A=N23ω+N2ωN23ω+N33ω,Njω,3ω=njω,3ω cos θjω, 3ω,
j=2, 3,
t12ω=2n1 cos θ1n1 cos θ1+n2ω cos θ2ω,
I3ωχ(3)Δε2(Iω)3A2(t12ω)6×expi 6πλ (nω cos θω-n3ω cos θ3ω)l-12χ(3)Δε2(Iω)3A2(t12ω)6×sin26πλ (nω cos θω-n3ω cos θ3ω)l2.
(3π/λ)(n3ω cos θ3ω-nω cos θω)L=mπ,
L=(mλ/3)(n3ω cos θ3ω-nω cos θω)-1.
nω sin θω=n3ω sin θ3ω,
L=mλ3n3ω 1-nωn3ω sin θω21/2-nωn3ω cos θω-1.
L=L0 cos θω1+n3ω-nω2n3ω tan2 θω,
L0=mλ3(n3ω-nω)=2mlC.
lC=λ6(n3ω-nω).
y=cos θω1+n3ω-nω2n3ω tan2 θω-1
y=kx+b,
k=dydx=2lCL
lC=d2(j-i) 1(1-sin2 θj/nω2)1/2-1(1-sin2 θi/nω2)1/2.
E3ω(r, t)=jTjEj3ω(r, t),
I3ω=cε(ω)8π jTjEj3ω(r, t)2.
I3ω|ES3ω+C(χ(3)/Δε)A{T3ω exp[i(ψ+α)]-Tω3 exp[-i(ψ+β)]}(Eω)3|2,
Tω=t12ωt23ω,
T3ω=t233ω,
t12ω=2n1 cos θ1n1 cos θ1+n2ω cos θ2ω,
t23ω=2n2ω cos θ2ωn2ω cos θ2ω+n3 cos θ3,
t233ω=2n23ω cos θ23ωn23ω cos θ23ω+n3 cos θ3.
I3ω=Bχ(3)ΔεS2 f(λ3ω)(Iω)3|A(t12ω)3 exp(iψS3ω)×{exp[i(ψSω-ψS3ω)]-1}|2,
ψS3ω=kS3ωl=3ω/cnS3ωl cos θS3ω,
ψSω=3kSωl=3ω/cnSωl cos θSω,
θ3ω=arcsinsin θvacuumn3ω,
θω=arcsinsin θvacuumnω.
I3ω=Bf(λ3ω)χ(3)ΔεS2(Iω)3|A(t12ω)3× exp(iψS3ω){exp[i(ψSω-ψS3ω)]-1}+C{t233ω exp[i(ψ+α)]-(t12ωt23ω)3 exp[-i(ψ+β)]}|2,
C=χ(3)ΔεA/χ(3)ΔεSC
I3ω|ES3ω(t12ω)3 exp(iψPω)+EP3ωt343ω exp(iψS3ω)|2|[χ(3)/Δε]SESω(t12ω)3 exp(iψPω)exp(iψS3ω)A1×[exp(iΔψS)-1]+(χ(3)/Δε)PEPωt343ω exp(iψS3ω)×exp(iψP3ω)A2[exp(iΔψP)-1]|2|exp[i(ψS3ω+ψPω)](χ(3)/Δε)S(Eω)3×{T1[exp(iΔψS)-1]+ρ exp(iϕ)T2[1-exp(-iΔψP)]}|2,
I3ω=Bχ(3)ΔεS2 f(λ3ω)(Iω)3|exp[i(ψS3ω+ψPω)]×{T1[exp(iΔψS)-1]+ρ exp(iϕ)T2[1-exp(-iΔψP)]}|2
T1=(t12ωt23ω)3 N23ω+N2ωN23ω+N33ω,
T2=(t12ω)3t343ω N33ω+N3ωN33ω+N43ω;
Njω,3ω=njω,3ω cos θjω,3ω.
I3ω=Bf(λ3ω)χ(3)ΔεS2(Iω)3|exp[i(ψS3ω+ψPω)]×{T1[exp(iΔψS)-1]+ρ exp(iϕ)T2[1-exp(-iΔψP)]}+C{t233ωt343ω exp[i(ψ+α)]-(t12ωt23ωt34ω)3 exp[-i(ψ+β)]}|2,
ρeiϕ=χ(3)Δεfilm/χ(3)ΔεS,
C=χ(3)Δεair/χ(3)ΔεS.
I3ω=(64π4/c2)[Aχ(3)]2(Iω)3fa,
fa={[1-exp(-α3ωd/2)]2+(Δψ)2 exp(-α3ωd/2)}[(n3ω2-nω2-k3ω2)2+(2n3ωk3ω)2],
χ(3)=χS(3)2πlC,SlI3ωIS3ω1/2
χ(3)=χS(3)2πlC,S α/21-exp(-αl/2) I3ωIS3ω1/2.

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