Abstract

A detailed comparison is given of several theoretical expressions commonly used in the determination of the molecular orientation in monolayers by reflection second-harmonic-generation measurements. The experimental data obtained from the Langmuir films of a hemicyanine dye are used to demonstrate that the deduced molecular-orientation angle depends sensitively on the linear dielectric constants of the monolayer. It is also pointed out that an unambiguous determination of the nonlinear susceptibilities of a monolayer by reflection second-harmonic generation requires measurements that use at least three different polarization combinations.

© 1990 Optical Society of America

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References

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  1. Th. Rasing, Y. R. Shen, M. W. Kim, S. G. Grubb, “Observation of molecular reorientation at a two-dimensional-liquid phase transition,” Phys. Rev. Lett. 55, 2903 (1985); Th. Rasing, G. Berkovic, Y. R. Shen, S. G. Grubb, M. W. Kim, “A novel method for measurements of second-order non-linearities of organic molecules,” Chem. Phys. Lett. 130, 1 (1986).
    [CrossRef] [PubMed]
  2. I. R. Girling, N. A. Cade, P. V. Kolinsky, R. J. Jones, I. R. Peterson, M. M. Ahmad, D. B. Neal, M. C. Petty, G. G. Roberts, W. J. Feast, “Second-harmonic generation in mixed hemicyanine: fatty-acid Langmuir–Blodgett monolayers,” J. Opt. Soc. Am. B 4, 950 (1987).
    [CrossRef]
  3. Th. Rasing, Y. R. Shen, Mahn Won Kim, P. Vaint, J. Block, “Orientation of surfactant molecules at a liquid-air interface measured by optical second-harmonic generation,” Phys. Rev. A 31, 537 (1985).
    [CrossRef] [PubMed]
  4. P. Guyot-Sionnest, H. Hsiung, Y. R. Shen, “Surface polar ordering in a liquid crystal observed by optical-harmonic generation,” Phys. Rev. Lett. 57, 2963 (1986).
    [CrossRef] [PubMed]
  5. O. A. Aktsipetrov, N. N. Akhmediev, E. D. Mishina, V. R. Novak, “Second harmonic generation on reflection from a monomolecular Langmuir layer,” JETP Lett. 37, 207 (1983).
  6. K. D. Singer, M. G. Kuzyk, 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]
  7. D. J. Williams, ed., Nonlinear Optical Properties of Organic and Polymeric Materialse, ACS Symp. Ser.233 (1983).
    [CrossRef]
  8. J. Messier, F. Kajzar, P. N. Prasad, D. R. Ulrich, eds., Nonlinear Optical Effects in Organic Polymers, NATO ASI Series E, Vol. 162 (Kluwer, Dordrecht, The Netherlands, 1989).
    [CrossRef]
  9. N. Bloembergen, P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 138, 606 (1962).
    [CrossRef]
  10. T. F. Heinz, H. W. K. Tom, Y. R. Shen, “Determination of molecular orientation of monolayer adsorbates by optical second-harmonic generation,” Phys. Rev. A 28, 1883 (1983).
    [CrossRef]
  11. O. A. Aktsipetrov, N. N. Akhmediev, I. M. Baranova, E. D. Mishina, V. R. Novak, “Structure of Langmuir films by second harmonic reflection,” Sov. Phys. JETP 62, 524 (1985).
  12. P. Guyot-Sionnest, Y. R. Shen, T. F. Heinz, “Comments on “Determination of the nonlinear optical susceptibility χ(2)of surface layers by Dick et al.,” Appl. Phys. B 42, 237 (1987).
    [CrossRef]
  13. Y. R. Shen, The Principles of Nonlinear Optics (Wiley, New York, 1984).
  14. V. Mizrahi, J. E. Sipe, “Phenomenological treatment of surface second-harmonic generation,” J. Opt. Soc. Am. B 5, 660 (1988).
    [CrossRef]
  15. B. Dick, A. Gierulski, G. Marowski, G. A. Reider, “Determination of the nonlinear optical susceptibility χ(2) of surface layers by sum and difference frequency generation in reflection and transmission,” Appl. Phys. B 38, 107 (1985).
    [CrossRef]
  16. Z. Chen, W. Chen, J. B. Zheng, W. C. Wang, Z. M. Zhang, “Surface enhanced SHG study on Langmuir–Blodgett, monomolecular layers,” Opt. Commun. 54, 305 (1985).
    [CrossRef]
  17. G. Marowsky, L. F. Chi, D. Mobius, R. Steinhoff, Y. R. Shen, D. Dorsch, B. Rieger, “Nonlinear optical properties of hemicyanine monolayers and the protonation effect,” Chem. Phys. Lett. 147, 420 (1988).
    [CrossRef]
  18. L. M. Hayden, “Local-field effects in Langmuir-Blodgett films of hemicyanine and behenic acid mixtures,” Phys. Rev. B 38, 3718 (1988).
    [CrossRef]

1988 (3)

G. Marowsky, L. F. Chi, D. Mobius, R. Steinhoff, Y. R. Shen, D. Dorsch, B. Rieger, “Nonlinear optical properties of hemicyanine monolayers and the protonation effect,” Chem. Phys. Lett. 147, 420 (1988).
[CrossRef]

L. M. Hayden, “Local-field effects in Langmuir-Blodgett films of hemicyanine and behenic acid mixtures,” Phys. Rev. B 38, 3718 (1988).
[CrossRef]

V. Mizrahi, J. E. Sipe, “Phenomenological treatment of surface second-harmonic generation,” J. Opt. Soc. Am. B 5, 660 (1988).
[CrossRef]

1987 (3)

1986 (1)

P. Guyot-Sionnest, H. Hsiung, Y. R. Shen, “Surface polar ordering in a liquid crystal observed by optical-harmonic generation,” Phys. Rev. Lett. 57, 2963 (1986).
[CrossRef] [PubMed]

1985 (5)

Th. Rasing, Y. R. Shen, Mahn Won Kim, P. Vaint, J. Block, “Orientation of surfactant molecules at a liquid-air interface measured by optical second-harmonic generation,” Phys. Rev. A 31, 537 (1985).
[CrossRef] [PubMed]

B. Dick, A. Gierulski, G. Marowski, G. A. Reider, “Determination of the nonlinear optical susceptibility χ(2) of surface layers by sum and difference frequency generation in reflection and transmission,” Appl. Phys. B 38, 107 (1985).
[CrossRef]

Z. Chen, W. Chen, J. B. Zheng, W. C. Wang, Z. M. Zhang, “Surface enhanced SHG study on Langmuir–Blodgett, monomolecular layers,” Opt. Commun. 54, 305 (1985).
[CrossRef]

Th. Rasing, Y. R. Shen, M. W. Kim, S. G. Grubb, “Observation of molecular reorientation at a two-dimensional-liquid phase transition,” Phys. Rev. Lett. 55, 2903 (1985); Th. Rasing, G. Berkovic, Y. R. Shen, S. G. Grubb, M. W. Kim, “A novel method for measurements of second-order non-linearities of organic molecules,” Chem. Phys. Lett. 130, 1 (1986).
[CrossRef] [PubMed]

O. A. Aktsipetrov, N. N. Akhmediev, I. M. Baranova, E. D. Mishina, V. R. Novak, “Structure of Langmuir films by second harmonic reflection,” Sov. Phys. JETP 62, 524 (1985).

1983 (2)

T. F. Heinz, H. W. K. Tom, Y. R. Shen, “Determination of molecular orientation of monolayer adsorbates by optical second-harmonic generation,” Phys. Rev. A 28, 1883 (1983).
[CrossRef]

O. A. Aktsipetrov, N. N. Akhmediev, E. D. Mishina, V. R. Novak, “Second harmonic generation on reflection from a monomolecular Langmuir layer,” JETP Lett. 37, 207 (1983).

1962 (1)

N. Bloembergen, P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 138, 606 (1962).
[CrossRef]

Ahmad, M. M.

Akhmediev, N. N.

O. A. Aktsipetrov, N. N. Akhmediev, I. M. Baranova, E. D. Mishina, V. R. Novak, “Structure of Langmuir films by second harmonic reflection,” Sov. Phys. JETP 62, 524 (1985).

O. A. Aktsipetrov, N. N. Akhmediev, E. D. Mishina, V. R. Novak, “Second harmonic generation on reflection from a monomolecular Langmuir layer,” JETP Lett. 37, 207 (1983).

Aktsipetrov, O. A.

O. A. Aktsipetrov, N. N. Akhmediev, I. M. Baranova, E. D. Mishina, V. R. Novak, “Structure of Langmuir films by second harmonic reflection,” Sov. Phys. JETP 62, 524 (1985).

O. A. Aktsipetrov, N. N. Akhmediev, E. D. Mishina, V. R. Novak, “Second harmonic generation on reflection from a monomolecular Langmuir layer,” JETP Lett. 37, 207 (1983).

Baranova, I. M.

O. A. Aktsipetrov, N. N. Akhmediev, I. M. Baranova, E. D. Mishina, V. R. Novak, “Structure of Langmuir films by second harmonic reflection,” Sov. Phys. JETP 62, 524 (1985).

Block, J.

Th. Rasing, Y. R. Shen, Mahn Won Kim, P. Vaint, J. Block, “Orientation of surfactant molecules at a liquid-air interface measured by optical second-harmonic generation,” Phys. Rev. A 31, 537 (1985).
[CrossRef] [PubMed]

Bloembergen, N.

N. Bloembergen, P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 138, 606 (1962).
[CrossRef]

Cade, N. A.

Chen, W.

Z. Chen, W. Chen, J. B. Zheng, W. C. Wang, Z. M. Zhang, “Surface enhanced SHG study on Langmuir–Blodgett, monomolecular layers,” Opt. Commun. 54, 305 (1985).
[CrossRef]

Chen, Z.

Z. Chen, W. Chen, J. B. Zheng, W. C. Wang, Z. M. Zhang, “Surface enhanced SHG study on Langmuir–Blodgett, monomolecular layers,” Opt. Commun. 54, 305 (1985).
[CrossRef]

Chi, L. F.

G. Marowsky, L. F. Chi, D. Mobius, R. Steinhoff, Y. R. Shen, D. Dorsch, B. Rieger, “Nonlinear optical properties of hemicyanine monolayers and the protonation effect,” Chem. Phys. Lett. 147, 420 (1988).
[CrossRef]

Dick, B.

B. Dick, A. Gierulski, G. Marowski, G. A. Reider, “Determination of the nonlinear optical susceptibility χ(2) of surface layers by sum and difference frequency generation in reflection and transmission,” Appl. Phys. B 38, 107 (1985).
[CrossRef]

Dorsch, D.

G. Marowsky, L. F. Chi, D. Mobius, R. Steinhoff, Y. R. Shen, D. Dorsch, B. Rieger, “Nonlinear optical properties of hemicyanine monolayers and the protonation effect,” Chem. Phys. Lett. 147, 420 (1988).
[CrossRef]

Feast, W. J.

Gierulski, A.

B. Dick, A. Gierulski, G. Marowski, G. A. Reider, “Determination of the nonlinear optical susceptibility χ(2) of surface layers by sum and difference frequency generation in reflection and transmission,” Appl. Phys. B 38, 107 (1985).
[CrossRef]

Girling, I. R.

Grubb, S. G.

Th. Rasing, Y. R. Shen, M. W. Kim, S. G. Grubb, “Observation of molecular reorientation at a two-dimensional-liquid phase transition,” Phys. Rev. Lett. 55, 2903 (1985); Th. Rasing, G. Berkovic, Y. R. Shen, S. G. Grubb, M. W. Kim, “A novel method for measurements of second-order non-linearities of organic molecules,” Chem. Phys. Lett. 130, 1 (1986).
[CrossRef] [PubMed]

Guyot-Sionnest, P.

P. Guyot-Sionnest, Y. R. Shen, T. F. Heinz, “Comments on “Determination of the nonlinear optical susceptibility χ(2)of surface layers by Dick et al.,” Appl. Phys. B 42, 237 (1987).
[CrossRef]

P. Guyot-Sionnest, H. Hsiung, Y. R. Shen, “Surface polar ordering in a liquid crystal observed by optical-harmonic generation,” Phys. Rev. Lett. 57, 2963 (1986).
[CrossRef] [PubMed]

Hayden, L. M.

L. M. Hayden, “Local-field effects in Langmuir-Blodgett films of hemicyanine and behenic acid mixtures,” Phys. Rev. B 38, 3718 (1988).
[CrossRef]

Heinz, T. F.

P. Guyot-Sionnest, Y. R. Shen, T. F. Heinz, “Comments on “Determination of the nonlinear optical susceptibility χ(2)of surface layers by Dick et al.,” Appl. Phys. B 42, 237 (1987).
[CrossRef]

T. F. Heinz, H. W. K. Tom, Y. R. Shen, “Determination of molecular orientation of monolayer adsorbates by optical second-harmonic generation,” Phys. Rev. A 28, 1883 (1983).
[CrossRef]

Hsiung, H.

P. Guyot-Sionnest, H. Hsiung, Y. R. Shen, “Surface polar ordering in a liquid crystal observed by optical-harmonic generation,” Phys. Rev. Lett. 57, 2963 (1986).
[CrossRef] [PubMed]

Jones, R. J.

Kim, M. W.

Th. Rasing, Y. R. Shen, M. W. Kim, S. G. Grubb, “Observation of molecular reorientation at a two-dimensional-liquid phase transition,” Phys. Rev. Lett. 55, 2903 (1985); Th. Rasing, G. Berkovic, Y. R. Shen, S. G. Grubb, M. W. Kim, “A novel method for measurements of second-order non-linearities of organic molecules,” Chem. Phys. Lett. 130, 1 (1986).
[CrossRef] [PubMed]

Kim, Mahn Won

Th. Rasing, Y. R. Shen, Mahn Won Kim, P. Vaint, J. Block, “Orientation of surfactant molecules at a liquid-air interface measured by optical second-harmonic generation,” Phys. Rev. A 31, 537 (1985).
[CrossRef] [PubMed]

Kolinsky, P. V.

Kuzyk, M. G.

Marowski, G.

B. Dick, A. Gierulski, G. Marowski, G. A. Reider, “Determination of the nonlinear optical susceptibility χ(2) of surface layers by sum and difference frequency generation in reflection and transmission,” Appl. Phys. B 38, 107 (1985).
[CrossRef]

Marowsky, G.

G. Marowsky, L. F. Chi, D. Mobius, R. Steinhoff, Y. R. Shen, D. Dorsch, B. Rieger, “Nonlinear optical properties of hemicyanine monolayers and the protonation effect,” Chem. Phys. Lett. 147, 420 (1988).
[CrossRef]

Mishina, E. D.

O. A. Aktsipetrov, N. N. Akhmediev, I. M. Baranova, E. D. Mishina, V. R. Novak, “Structure of Langmuir films by second harmonic reflection,” Sov. Phys. JETP 62, 524 (1985).

O. A. Aktsipetrov, N. N. Akhmediev, E. D. Mishina, V. R. Novak, “Second harmonic generation on reflection from a monomolecular Langmuir layer,” JETP Lett. 37, 207 (1983).

Mizrahi, V.

Mobius, D.

G. Marowsky, L. F. Chi, D. Mobius, R. Steinhoff, Y. R. Shen, D. Dorsch, B. Rieger, “Nonlinear optical properties of hemicyanine monolayers and the protonation effect,” Chem. Phys. Lett. 147, 420 (1988).
[CrossRef]

Neal, D. B.

Novak, V. R.

O. A. Aktsipetrov, N. N. Akhmediev, I. M. Baranova, E. D. Mishina, V. R. Novak, “Structure of Langmuir films by second harmonic reflection,” Sov. Phys. JETP 62, 524 (1985).

O. A. Aktsipetrov, N. N. Akhmediev, E. D. Mishina, V. R. Novak, “Second harmonic generation on reflection from a monomolecular Langmuir layer,” JETP Lett. 37, 207 (1983).

Pershan, P. S.

N. Bloembergen, P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 138, 606 (1962).
[CrossRef]

Peterson, I. R.

Petty, M. C.

Rasing, Th.

Th. Rasing, Y. R. Shen, Mahn Won Kim, P. Vaint, J. Block, “Orientation of surfactant molecules at a liquid-air interface measured by optical second-harmonic generation,” Phys. Rev. A 31, 537 (1985).
[CrossRef] [PubMed]

Th. Rasing, Y. R. Shen, M. W. Kim, S. G. Grubb, “Observation of molecular reorientation at a two-dimensional-liquid phase transition,” Phys. Rev. Lett. 55, 2903 (1985); Th. Rasing, G. Berkovic, Y. R. Shen, S. G. Grubb, M. W. Kim, “A novel method for measurements of second-order non-linearities of organic molecules,” Chem. Phys. Lett. 130, 1 (1986).
[CrossRef] [PubMed]

Reider, G. A.

B. Dick, A. Gierulski, G. Marowski, G. A. Reider, “Determination of the nonlinear optical susceptibility χ(2) of surface layers by sum and difference frequency generation in reflection and transmission,” Appl. Phys. B 38, 107 (1985).
[CrossRef]

Rieger, B.

G. Marowsky, L. F. Chi, D. Mobius, R. Steinhoff, Y. R. Shen, D. Dorsch, B. Rieger, “Nonlinear optical properties of hemicyanine monolayers and the protonation effect,” Chem. Phys. Lett. 147, 420 (1988).
[CrossRef]

Roberts, G. G.

Shen, Y. R.

G. Marowsky, L. F. Chi, D. Mobius, R. Steinhoff, Y. R. Shen, D. Dorsch, B. Rieger, “Nonlinear optical properties of hemicyanine monolayers and the protonation effect,” Chem. Phys. Lett. 147, 420 (1988).
[CrossRef]

P. Guyot-Sionnest, Y. R. Shen, T. F. Heinz, “Comments on “Determination of the nonlinear optical susceptibility χ(2)of surface layers by Dick et al.,” Appl. Phys. B 42, 237 (1987).
[CrossRef]

P. Guyot-Sionnest, H. Hsiung, Y. R. Shen, “Surface polar ordering in a liquid crystal observed by optical-harmonic generation,” Phys. Rev. Lett. 57, 2963 (1986).
[CrossRef] [PubMed]

Th. Rasing, Y. R. Shen, M. W. Kim, S. G. Grubb, “Observation of molecular reorientation at a two-dimensional-liquid phase transition,” Phys. Rev. Lett. 55, 2903 (1985); Th. Rasing, G. Berkovic, Y. R. Shen, S. G. Grubb, M. W. Kim, “A novel method for measurements of second-order non-linearities of organic molecules,” Chem. Phys. Lett. 130, 1 (1986).
[CrossRef] [PubMed]

Th. Rasing, Y. R. Shen, Mahn Won Kim, P. Vaint, J. Block, “Orientation of surfactant molecules at a liquid-air interface measured by optical second-harmonic generation,” Phys. Rev. A 31, 537 (1985).
[CrossRef] [PubMed]

T. F. Heinz, H. W. K. Tom, Y. R. Shen, “Determination of molecular orientation of monolayer adsorbates by optical second-harmonic generation,” Phys. Rev. A 28, 1883 (1983).
[CrossRef]

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

Singer, K. D.

Sipe, J. E.

Sohn, J. E.

Steinhoff, R.

G. Marowsky, L. F. Chi, D. Mobius, R. Steinhoff, Y. R. Shen, D. Dorsch, B. Rieger, “Nonlinear optical properties of hemicyanine monolayers and the protonation effect,” Chem. Phys. Lett. 147, 420 (1988).
[CrossRef]

Tom, H. W. K.

T. F. Heinz, H. W. K. Tom, Y. R. Shen, “Determination of molecular orientation of monolayer adsorbates by optical second-harmonic generation,” Phys. Rev. A 28, 1883 (1983).
[CrossRef]

Vaint, P.

Th. Rasing, Y. R. Shen, Mahn Won Kim, P. Vaint, J. Block, “Orientation of surfactant molecules at a liquid-air interface measured by optical second-harmonic generation,” Phys. Rev. A 31, 537 (1985).
[CrossRef] [PubMed]

Wang, W. C.

Z. Chen, W. Chen, J. B. Zheng, W. C. Wang, Z. M. Zhang, “Surface enhanced SHG study on Langmuir–Blodgett, monomolecular layers,” Opt. Commun. 54, 305 (1985).
[CrossRef]

Zhang, Z. M.

Z. Chen, W. Chen, J. B. Zheng, W. C. Wang, Z. M. Zhang, “Surface enhanced SHG study on Langmuir–Blodgett, monomolecular layers,” Opt. Commun. 54, 305 (1985).
[CrossRef]

Zheng, J. B.

Z. Chen, W. Chen, J. B. Zheng, W. C. Wang, Z. M. Zhang, “Surface enhanced SHG study on Langmuir–Blodgett, monomolecular layers,” Opt. Commun. 54, 305 (1985).
[CrossRef]

Appl. Phys. B (2)

P. Guyot-Sionnest, Y. R. Shen, T. F. Heinz, “Comments on “Determination of the nonlinear optical susceptibility χ(2)of surface layers by Dick et al.,” Appl. Phys. B 42, 237 (1987).
[CrossRef]

B. Dick, A. Gierulski, G. Marowski, G. A. Reider, “Determination of the nonlinear optical susceptibility χ(2) of surface layers by sum and difference frequency generation in reflection and transmission,” Appl. Phys. B 38, 107 (1985).
[CrossRef]

Chem. Phys. Lett. (1)

G. Marowsky, L. F. Chi, D. Mobius, R. Steinhoff, Y. R. Shen, D. Dorsch, B. Rieger, “Nonlinear optical properties of hemicyanine monolayers and the protonation effect,” Chem. Phys. Lett. 147, 420 (1988).
[CrossRef]

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

JETP Lett. (1)

O. A. Aktsipetrov, N. N. Akhmediev, E. D. Mishina, V. R. Novak, “Second harmonic generation on reflection from a monomolecular Langmuir layer,” JETP Lett. 37, 207 (1983).

Opt. Commun. (1)

Z. Chen, W. Chen, J. B. Zheng, W. C. Wang, Z. M. Zhang, “Surface enhanced SHG study on Langmuir–Blodgett, monomolecular layers,” Opt. Commun. 54, 305 (1985).
[CrossRef]

Phys. Rev. (1)

N. Bloembergen, P. S. Pershan, “Light waves at the boundary of nonlinear media,” Phys. Rev. 138, 606 (1962).
[CrossRef]

Phys. Rev. A (2)

T. F. Heinz, H. W. K. Tom, Y. R. Shen, “Determination of molecular orientation of monolayer adsorbates by optical second-harmonic generation,” Phys. Rev. A 28, 1883 (1983).
[CrossRef]

Th. Rasing, Y. R. Shen, Mahn Won Kim, P. Vaint, J. Block, “Orientation of surfactant molecules at a liquid-air interface measured by optical second-harmonic generation,” Phys. Rev. A 31, 537 (1985).
[CrossRef] [PubMed]

Phys. Rev. B (1)

L. M. Hayden, “Local-field effects in Langmuir-Blodgett films of hemicyanine and behenic acid mixtures,” Phys. Rev. B 38, 3718 (1988).
[CrossRef]

Phys. Rev. Lett. (2)

Th. Rasing, Y. R. Shen, M. W. Kim, S. G. Grubb, “Observation of molecular reorientation at a two-dimensional-liquid phase transition,” Phys. Rev. Lett. 55, 2903 (1985); Th. Rasing, G. Berkovic, Y. R. Shen, S. G. Grubb, M. W. Kim, “A novel method for measurements of second-order non-linearities of organic molecules,” Chem. Phys. Lett. 130, 1 (1986).
[CrossRef] [PubMed]

P. Guyot-Sionnest, H. Hsiung, Y. R. Shen, “Surface polar ordering in a liquid crystal observed by optical-harmonic generation,” Phys. Rev. Lett. 57, 2963 (1986).
[CrossRef] [PubMed]

Sov. Phys. JETP (1)

O. A. Aktsipetrov, N. N. Akhmediev, I. M. Baranova, E. D. Mishina, V. R. Novak, “Structure of Langmuir films by second harmonic reflection,” Sov. Phys. JETP 62, 524 (1985).

Other (3)

D. J. Williams, ed., Nonlinear Optical Properties of Organic and Polymeric Materialse, ACS Symp. Ser.233 (1983).
[CrossRef]

J. Messier, F. Kajzar, P. N. Prasad, D. R. Ulrich, eds., Nonlinear Optical Effects in Organic Polymers, NATO ASI Series E, Vol. 162 (Kluwer, Dordrecht, The Netherlands, 1989).
[CrossRef]

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

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Figures (7)

Fig. 1
Fig. 1

Three-layer structure consisting of two semi-infinite linear media, r and t, bounded by a thin nonlinear layer m of thickness d. The various angles are defined in the text.

Fig. 2
Fig. 2

Theoretical p-polarized SHG intensity curves for three positive values of A/B plotted as a function of the polarization angle (α) of the fundamental field.

Fig. 3
Fig. 3

Theoretical p-polarized SHG intensity curves for three negative values of A/B plotted as a function of the polarization angle (α) of the fundamental field.

Fig. 4
Fig. 4

Chemical structure of the amphiphilic hemicyanine dye molecule that was used to form the Langmuir films for reflection SHG measurements.

Fig. 5
Fig. 5

Experimental p-polarized SHG intensity data and a theoretical fit for a hemicyanine Langmuir film compressed to 20 dyn/cm.

Fig. 6
Fig. 6

Experimental s-polarized SHG intensity data and a theoretical fit for a hemicyanine Langmuir film compressed to 20 dyn/cm.

Fig. 7
Fig. 7

Experimental p-polarized SHG intensity data and a theoretical fit for a hemicyanine Langmuir film compressed to 40 dyn/cm.

Equations (13)

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E p r = 4 π i ( ω d c 1 ) ( 1 ) ( ε t 2 1 / 2 / ε m 2 1 / 2 ) sin θ m 2 P z nl + cos θ t 2 P x nl ( ε t 2 1 / 2 cos θ r 2 + ε r 2 1 / 2 cos θ t 2 ) , E s r = 4 π i ( ω d c 1 ) P y nl ( ε t 2 1 / 2 cos θ t 2 + ε r 2 1 / 2 cos θ r 2 ) ,
ε r 1 1 / 2 sin θ i = ε r 2 1 / 2 sin θ r 2 = ε m 2 1 / 2 sin θ m 2 = ε t 2 1 / 2 sin θ t 2 .
P i = | E x , E y , E z | | χ i x x χ i y x χ i z x χ i x y χ i y y χ i z y χ i x z χ i y z χ i z z | | E x E y E z | ,
| E x E y E z | = | a cos α c sin α b cos α | E ,
a = 2 ε r 1 1 / 2 cos θ r 1 cos θ t 1 ( ε t 1 1 / 2 cos θ r 1 + ε r 1 1 / 2 cos θ t 1 ) , b = 2 ε r 1 1 / 2 cos θ r 1 ε t 1 1 / 2 sin θ m 1 ε m 1 1 / 2 ( ε t 1 1 / 2 cos θ r 1 + ε r 1 1 / 2 cos θ t 1 ) , c = 2 ε r 1 1 / 2 cos θ r 1 ( ε t 1 1 / 2 cos θ t 1 + ε r 1 1 / 2 cos θ r 1 ) ,
ε r 1 1 / 2 sin θ i = ε r 1 1 / 2 sin θ r 1 = ε m 1 1 / 2 sin θ m 1 = ε t 1 1 / 2 sin θ t 1 .
E p r = ( A cos 2 α + B sin 2 α + C sin 2 α ) E 2 , E s r = ( F cos 2 α + G sin 2 α + H sin 2 α ) E 2 ,
A = 4 π i ( ω d c 1 ) ( ε g ε 2 ) 4 cos 2 θ sin θ [ ε g cos θ + ( ε g sin θ ) 1 / 2 ] 3 × [ ( ε g sin 2 θ ) ( 1 2 ε 2 ε 1 ) χ z y y + sin 2 θ ( ε g ε 1 ) 2 χ z z z ] , B = 4 π i ( ω d c 1 ) ( ε g ε 2 ) × 4 cos 2 θ sin θ χ z y y [ ε g cos θ + ( ε g sin 2 θ ) 1 / 2 ] [ cos θ + ( ε g sin 2 θ ) 1 / 2 ] 2 , H = 4 π i ( ω d c 1 ) ( ε g ε 2 ) × 4 cos 2 θ sin θ χ z y y [ ε g cos θ + ( ε g sin 2 θ ) 1 / 2 ] [ cos θ + ( ε g sin 2 θ ) 1 / 2 ] 2 ,
I SHG α p I 2 = ( A cos 2 α + B sin 2 α ) 2 , I SHG α s I 2 = ( H sin 2 α ) 2 ,
A / B = ( 2 ε 2 ε 1 tan α tan β + tan 2 α ) ,
I SHG 45 ° s I SHG s p = H 2 B 2 = ε 2 2 ε 1 2 .
I SHG 45 ° s I SHG s p = H 2 B 2 = ε 2 2 ε 1 2 χ y z y 2 χ z y y 2 ,
χ z z z = N cos 3 ψ β ξ ξ ξ , χ z y y = 1 2 N sin 2 ψ cos ψ β ξ ξ ξ ,

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