Abstract

We present measurements of the optical second-harmonic generation in self assembled multilayer films of PAZO/PAH polymers with the aim to investigate molecular order in the layer-by-layer architecture. The experiments are performed in transmission, using a femtosecond Ti:Sa pulsed laser, which allows a more accurate determination of the amplitude of the second harmonic signal, without interference fringes usually present in nanosecond experiments. We found that the first bilayer, in contact with the substrate, presents a broad distribution of the orientation of the molecules, while the addition of successive bilayers (up to 12) produces ordering of the molecules with a small tilt angle respect to the surface normal. This result, together with the monotonic increment of the second harmonic signal with the number of layers indicates that the molecules grow orderly assembled in these films.

©2009 Optical Society of America

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References

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  1. G. Decher and J. B. Schlenoff, Multilayer Thin Films: Sequentially Assembly of Nanocomposite Materials (Wiley-VCH, 2002).
  2. A. Garg, R. M. Davis, C. Durak, J. R. Heflin, and H. W. Gibson, “Polar orientation of a pendant anionic chromophore in thick layer-by-layer self-assembled polymeric films,” J. App. Phys.  104, 053116 1–8 (2008).
    [Crossref]
  3. S. S. Shiratori and M. F. Rubner, “pH-Dependent Thickness Behavior of Sequentially Adsorbed Layers of Weak Polyelectrolytes,” Macromol.  33, 4213–4219 (2000).
    [Crossref]
  4. Soo-Hyoung Lee, S. Balasubramanian, D. Y. Kim, N. K. Viswanathan, S. Bian, J. Kumar, and S. K. Tripathy, “Azo Polymer Multilayer Films by Electrostatic Self-Assembly and Layer-by-Layer Post Azo Functionalization,” Macromol.  33, 6534–6540 (2000).
    [Crossref]
  5. Y. R. Shen, “Optical Second Harmonic Generation at Interfaces,” Annu. Rev. Phys. Chem.  40, 327–350 (1989).
    [Crossref]
  6. G. J. Simpson and K. L. Rowlen, “Measurement of Orientation in Organic Thin Films,” Acc. Chem. Res.  33, 781–789 (2000).
    [Crossref] [PubMed]
  7. J. R. Heflin, C. Figura, D. Marciu, Y Liu, and R. O. Claus, “Thickness dependence of second-harmonic generation in thin films fabricated from ionically self-assembled monolayers,” Appl. Phys. Lett.  74, 495–497 (1999).
    [Crossref]
  8. E. Kang, T. Bu, P. Jin, J. Sun, Y. Yang, and J. Shen, “Layer-by-Layer Deposited Organic/Inorganic Hybrid Multilayer Films Containing Noncentrosymmetrically Orientated Azobenzene Chromophores,” Langmuir,  23, 7594–7601 (2007).
    [Crossref] [PubMed]
  9. Y. Lvov, S. Yamada, and T. Kunitake, “Non-linear optical effects in layer-by-layer alternate films of polycations and an azobenzene-containing polyanion,” Thin Solid Films  300, 107–112 (1996)
    [Crossref]
  10. F. Kajzar, J. Messier, J. Zyss, and I. Ledoux, “Nonlinear Interferometry in Langmuir-Blodgett multilayers of polydiacetylene,” Opt. Commun.  45, 133–137 (1983).
    [Crossref]
  11. P.D Maker, R.W Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett.  8, 21–22 (1962).
  12. B. Dick, “Irreducible tensor analysis of sum- and difference- frequency generation in partially oriented samples,” Chem. Phys.  96, 199–215 (1985).
    [Crossref]
  13. B. Dick, A. Gierulski, and G. Marowsky, “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, 107–116 (1985).
    [Crossref]
  14. P. Guyot-Sionnest and Y. R. Shen, “Comments on “Determination of the Nonlinear Optical Susceptibility χ(2 of Surface Layers by Sum and Difference Frequency Generation in Reflection and Transmission,” Appl. Phys. B  42, 237–238 (1987).
    [Crossref]

2008 (1)

A. Garg, R. M. Davis, C. Durak, J. R. Heflin, and H. W. Gibson, “Polar orientation of a pendant anionic chromophore in thick layer-by-layer self-assembled polymeric films,” J. App. Phys.  104, 053116 1–8 (2008).
[Crossref]

2007 (1)

E. Kang, T. Bu, P. Jin, J. Sun, Y. Yang, and J. Shen, “Layer-by-Layer Deposited Organic/Inorganic Hybrid Multilayer Films Containing Noncentrosymmetrically Orientated Azobenzene Chromophores,” Langmuir,  23, 7594–7601 (2007).
[Crossref] [PubMed]

2000 (3)

G. J. Simpson and K. L. Rowlen, “Measurement of Orientation in Organic Thin Films,” Acc. Chem. Res.  33, 781–789 (2000).
[Crossref] [PubMed]

S. S. Shiratori and M. F. Rubner, “pH-Dependent Thickness Behavior of Sequentially Adsorbed Layers of Weak Polyelectrolytes,” Macromol.  33, 4213–4219 (2000).
[Crossref]

Soo-Hyoung Lee, S. Balasubramanian, D. Y. Kim, N. K. Viswanathan, S. Bian, J. Kumar, and S. K. Tripathy, “Azo Polymer Multilayer Films by Electrostatic Self-Assembly and Layer-by-Layer Post Azo Functionalization,” Macromol.  33, 6534–6540 (2000).
[Crossref]

1999 (1)

J. R. Heflin, C. Figura, D. Marciu, Y Liu, and R. O. Claus, “Thickness dependence of second-harmonic generation in thin films fabricated from ionically self-assembled monolayers,” Appl. Phys. Lett.  74, 495–497 (1999).
[Crossref]

1996 (1)

Y. Lvov, S. Yamada, and T. Kunitake, “Non-linear optical effects in layer-by-layer alternate films of polycations and an azobenzene-containing polyanion,” Thin Solid Films  300, 107–112 (1996)
[Crossref]

1989 (1)

Y. R. Shen, “Optical Second Harmonic Generation at Interfaces,” Annu. Rev. Phys. Chem.  40, 327–350 (1989).
[Crossref]

1987 (1)

P. Guyot-Sionnest and Y. R. Shen, “Comments on “Determination of the Nonlinear Optical Susceptibility χ(2 of Surface Layers by Sum and Difference Frequency Generation in Reflection and Transmission,” Appl. Phys. B  42, 237–238 (1987).
[Crossref]

1985 (2)

B. Dick, “Irreducible tensor analysis of sum- and difference- frequency generation in partially oriented samples,” Chem. Phys.  96, 199–215 (1985).
[Crossref]

B. Dick, A. Gierulski, and G. Marowsky, “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, 107–116 (1985).
[Crossref]

1983 (1)

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

Balasubramanian, S.

Soo-Hyoung Lee, S. Balasubramanian, D. Y. Kim, N. K. Viswanathan, S. Bian, J. Kumar, and S. K. Tripathy, “Azo Polymer Multilayer Films by Electrostatic Self-Assembly and Layer-by-Layer Post Azo Functionalization,” Macromol.  33, 6534–6540 (2000).
[Crossref]

Bian, S.

Soo-Hyoung Lee, S. Balasubramanian, D. Y. Kim, N. K. Viswanathan, S. Bian, J. Kumar, and S. K. Tripathy, “Azo Polymer Multilayer Films by Electrostatic Self-Assembly and Layer-by-Layer Post Azo Functionalization,” Macromol.  33, 6534–6540 (2000).
[Crossref]

Bu, T.

E. Kang, T. Bu, P. Jin, J. Sun, Y. Yang, and J. Shen, “Layer-by-Layer Deposited Organic/Inorganic Hybrid Multilayer Films Containing Noncentrosymmetrically Orientated Azobenzene Chromophores,” Langmuir,  23, 7594–7601 (2007).
[Crossref] [PubMed]

Claus, R. O.

J. R. Heflin, C. Figura, D. Marciu, Y Liu, and R. O. Claus, “Thickness dependence of second-harmonic generation in thin films fabricated from ionically self-assembled monolayers,” Appl. Phys. Lett.  74, 495–497 (1999).
[Crossref]

Davis, R. M.

A. Garg, R. M. Davis, C. Durak, J. R. Heflin, and H. W. Gibson, “Polar orientation of a pendant anionic chromophore in thick layer-by-layer self-assembled polymeric films,” J. App. Phys.  104, 053116 1–8 (2008).
[Crossref]

Decher, G.

G. Decher and J. B. Schlenoff, Multilayer Thin Films: Sequentially Assembly of Nanocomposite Materials (Wiley-VCH, 2002).

Dick, B.

B. Dick, “Irreducible tensor analysis of sum- and difference- frequency generation in partially oriented samples,” Chem. Phys.  96, 199–215 (1985).
[Crossref]

B. Dick, A. Gierulski, and G. Marowsky, “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, 107–116 (1985).
[Crossref]

Durak, C.

A. Garg, R. M. Davis, C. Durak, J. R. Heflin, and H. W. Gibson, “Polar orientation of a pendant anionic chromophore in thick layer-by-layer self-assembled polymeric films,” J. App. Phys.  104, 053116 1–8 (2008).
[Crossref]

Figura, C.

J. R. Heflin, C. Figura, D. Marciu, Y Liu, and R. O. Claus, “Thickness dependence of second-harmonic generation in thin films fabricated from ionically self-assembled monolayers,” Appl. Phys. Lett.  74, 495–497 (1999).
[Crossref]

Garg, A.

A. Garg, R. M. Davis, C. Durak, J. R. Heflin, and H. W. Gibson, “Polar orientation of a pendant anionic chromophore in thick layer-by-layer self-assembled polymeric films,” J. App. Phys.  104, 053116 1–8 (2008).
[Crossref]

Gibson, H. W.

A. Garg, R. M. Davis, C. Durak, J. R. Heflin, and H. W. Gibson, “Polar orientation of a pendant anionic chromophore in thick layer-by-layer self-assembled polymeric films,” J. App. Phys.  104, 053116 1–8 (2008).
[Crossref]

Gierulski, A.

B. Dick, A. Gierulski, and G. Marowsky, “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, 107–116 (1985).
[Crossref]

Guyot-Sionnest, P.

P. Guyot-Sionnest and Y. R. Shen, “Comments on “Determination of the Nonlinear Optical Susceptibility χ(2 of Surface Layers by Sum and Difference Frequency Generation in Reflection and Transmission,” Appl. Phys. B  42, 237–238 (1987).
[Crossref]

Heflin, J. R.

A. Garg, R. M. Davis, C. Durak, J. R. Heflin, and H. W. Gibson, “Polar orientation of a pendant anionic chromophore in thick layer-by-layer self-assembled polymeric films,” J. App. Phys.  104, 053116 1–8 (2008).
[Crossref]

J. R. Heflin, C. Figura, D. Marciu, Y Liu, and R. O. Claus, “Thickness dependence of second-harmonic generation in thin films fabricated from ionically self-assembled monolayers,” Appl. Phys. Lett.  74, 495–497 (1999).
[Crossref]

Jin, P.

E. Kang, T. Bu, P. Jin, J. Sun, Y. Yang, and J. Shen, “Layer-by-Layer Deposited Organic/Inorganic Hybrid Multilayer Films Containing Noncentrosymmetrically Orientated Azobenzene Chromophores,” Langmuir,  23, 7594–7601 (2007).
[Crossref] [PubMed]

Kajzar, F.

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

Kang, E.

E. Kang, T. Bu, P. Jin, J. Sun, Y. Yang, and J. Shen, “Layer-by-Layer Deposited Organic/Inorganic Hybrid Multilayer Films Containing Noncentrosymmetrically Orientated Azobenzene Chromophores,” Langmuir,  23, 7594–7601 (2007).
[Crossref] [PubMed]

Kim, D. Y.

Soo-Hyoung Lee, S. Balasubramanian, D. Y. Kim, N. K. Viswanathan, S. Bian, J. Kumar, and S. K. Tripathy, “Azo Polymer Multilayer Films by Electrostatic Self-Assembly and Layer-by-Layer Post Azo Functionalization,” Macromol.  33, 6534–6540 (2000).
[Crossref]

Kumar, J.

Soo-Hyoung Lee, S. Balasubramanian, D. Y. Kim, N. K. Viswanathan, S. Bian, J. Kumar, and S. K. Tripathy, “Azo Polymer Multilayer Films by Electrostatic Self-Assembly and Layer-by-Layer Post Azo Functionalization,” Macromol.  33, 6534–6540 (2000).
[Crossref]

Kunitake, T.

Y. Lvov, S. Yamada, and T. Kunitake, “Non-linear optical effects in layer-by-layer alternate films of polycations and an azobenzene-containing polyanion,” Thin Solid Films  300, 107–112 (1996)
[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]

Lvov, Y.

Y. Lvov, S. Yamada, and T. Kunitake, “Non-linear optical effects in layer-by-layer alternate films of polycations and an azobenzene-containing polyanion,” Thin Solid Films  300, 107–112 (1996)
[Crossref]

Maker, P.D

P.D Maker, R.W Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett.  8, 21–22 (1962).

Marciu, D.

J. R. Heflin, C. Figura, D. Marciu, Y Liu, and R. O. Claus, “Thickness dependence of second-harmonic generation in thin films fabricated from ionically self-assembled monolayers,” Appl. Phys. Lett.  74, 495–497 (1999).
[Crossref]

Marowsky, G.

B. Dick, A. Gierulski, and G. Marowsky, “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, 107–116 (1985).
[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]

Nisenoff, M.

P.D Maker, R.W Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett.  8, 21–22 (1962).

Rowlen, K. L.

G. J. Simpson and K. L. Rowlen, “Measurement of Orientation in Organic Thin Films,” Acc. Chem. Res.  33, 781–789 (2000).
[Crossref] [PubMed]

Rubner, M. F.

S. S. Shiratori and M. F. Rubner, “pH-Dependent Thickness Behavior of Sequentially Adsorbed Layers of Weak Polyelectrolytes,” Macromol.  33, 4213–4219 (2000).
[Crossref]

Savage, C. M.

P.D Maker, R.W Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett.  8, 21–22 (1962).

Schlenoff, J. B.

G. Decher and J. B. Schlenoff, Multilayer Thin Films: Sequentially Assembly of Nanocomposite Materials (Wiley-VCH, 2002).

Shen, J.

E. Kang, T. Bu, P. Jin, J. Sun, Y. Yang, and J. Shen, “Layer-by-Layer Deposited Organic/Inorganic Hybrid Multilayer Films Containing Noncentrosymmetrically Orientated Azobenzene Chromophores,” Langmuir,  23, 7594–7601 (2007).
[Crossref] [PubMed]

Shen, Y. R.

Y. R. Shen, “Optical Second Harmonic Generation at Interfaces,” Annu. Rev. Phys. Chem.  40, 327–350 (1989).
[Crossref]

P. Guyot-Sionnest and Y. R. Shen, “Comments on “Determination of the Nonlinear Optical Susceptibility χ(2 of Surface Layers by Sum and Difference Frequency Generation in Reflection and Transmission,” Appl. Phys. B  42, 237–238 (1987).
[Crossref]

Shiratori, S. S.

S. S. Shiratori and M. F. Rubner, “pH-Dependent Thickness Behavior of Sequentially Adsorbed Layers of Weak Polyelectrolytes,” Macromol.  33, 4213–4219 (2000).
[Crossref]

Simpson, G. J.

G. J. Simpson and K. L. Rowlen, “Measurement of Orientation in Organic Thin Films,” Acc. Chem. Res.  33, 781–789 (2000).
[Crossref] [PubMed]

Soo-Hyoung Lee,

Soo-Hyoung Lee, S. Balasubramanian, D. Y. Kim, N. K. Viswanathan, S. Bian, J. Kumar, and S. K. Tripathy, “Azo Polymer Multilayer Films by Electrostatic Self-Assembly and Layer-by-Layer Post Azo Functionalization,” Macromol.  33, 6534–6540 (2000).
[Crossref]

Sun, J.

E. Kang, T. Bu, P. Jin, J. Sun, Y. Yang, and J. Shen, “Layer-by-Layer Deposited Organic/Inorganic Hybrid Multilayer Films Containing Noncentrosymmetrically Orientated Azobenzene Chromophores,” Langmuir,  23, 7594–7601 (2007).
[Crossref] [PubMed]

Terhune, R.W

P.D Maker, R.W Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett.  8, 21–22 (1962).

Tripathy, S. K.

Soo-Hyoung Lee, S. Balasubramanian, D. Y. Kim, N. K. Viswanathan, S. Bian, J. Kumar, and S. K. Tripathy, “Azo Polymer Multilayer Films by Electrostatic Self-Assembly and Layer-by-Layer Post Azo Functionalization,” Macromol.  33, 6534–6540 (2000).
[Crossref]

Viswanathan, N. K.

Soo-Hyoung Lee, S. Balasubramanian, D. Y. Kim, N. K. Viswanathan, S. Bian, J. Kumar, and S. K. Tripathy, “Azo Polymer Multilayer Films by Electrostatic Self-Assembly and Layer-by-Layer Post Azo Functionalization,” Macromol.  33, 6534–6540 (2000).
[Crossref]

Y Liu,

J. R. Heflin, C. Figura, D. Marciu, Y Liu, and R. O. Claus, “Thickness dependence of second-harmonic generation in thin films fabricated from ionically self-assembled monolayers,” Appl. Phys. Lett.  74, 495–497 (1999).
[Crossref]

Yamada, S.

Y. Lvov, S. Yamada, and T. Kunitake, “Non-linear optical effects in layer-by-layer alternate films of polycations and an azobenzene-containing polyanion,” Thin Solid Films  300, 107–112 (1996)
[Crossref]

Yang, Y.

E. Kang, T. Bu, P. Jin, J. Sun, Y. Yang, and J. Shen, “Layer-by-Layer Deposited Organic/Inorganic Hybrid Multilayer Films Containing Noncentrosymmetrically Orientated Azobenzene Chromophores,” Langmuir,  23, 7594–7601 (2007).
[Crossref] [PubMed]

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]

Acc. Chem. Res. (1)

G. J. Simpson and K. L. Rowlen, “Measurement of Orientation in Organic Thin Films,” Acc. Chem. Res.  33, 781–789 (2000).
[Crossref] [PubMed]

Annu. Rev. Phys. Chem. (1)

Y. R. Shen, “Optical Second Harmonic Generation at Interfaces,” Annu. Rev. Phys. Chem.  40, 327–350 (1989).
[Crossref]

Appl. Phys. B (2)

B. Dick, A. Gierulski, and G. Marowsky, “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, 107–116 (1985).
[Crossref]

P. Guyot-Sionnest and Y. R. Shen, “Comments on “Determination of the Nonlinear Optical Susceptibility χ(2 of Surface Layers by Sum and Difference Frequency Generation in Reflection and Transmission,” Appl. Phys. B  42, 237–238 (1987).
[Crossref]

Appl. Phys. Lett. (1)

J. R. Heflin, C. Figura, D. Marciu, Y Liu, and R. O. Claus, “Thickness dependence of second-harmonic generation in thin films fabricated from ionically self-assembled monolayers,” Appl. Phys. Lett.  74, 495–497 (1999).
[Crossref]

Chem. Phys. (1)

B. Dick, “Irreducible tensor analysis of sum- and difference- frequency generation in partially oriented samples,” Chem. Phys.  96, 199–215 (1985).
[Crossref]

J. App. Phys. (1)

A. Garg, R. M. Davis, C. Durak, J. R. Heflin, and H. W. Gibson, “Polar orientation of a pendant anionic chromophore in thick layer-by-layer self-assembled polymeric films,” J. App. Phys.  104, 053116 1–8 (2008).
[Crossref]

Langmuir (1)

E. Kang, T. Bu, P. Jin, J. Sun, Y. Yang, and J. Shen, “Layer-by-Layer Deposited Organic/Inorganic Hybrid Multilayer Films Containing Noncentrosymmetrically Orientated Azobenzene Chromophores,” Langmuir,  23, 7594–7601 (2007).
[Crossref] [PubMed]

Macromol. (2)

S. S. Shiratori and M. F. Rubner, “pH-Dependent Thickness Behavior of Sequentially Adsorbed Layers of Weak Polyelectrolytes,” Macromol.  33, 4213–4219 (2000).
[Crossref]

Soo-Hyoung Lee, S. Balasubramanian, D. Y. Kim, N. K. Viswanathan, S. Bian, J. Kumar, and S. K. Tripathy, “Azo Polymer Multilayer Films by Electrostatic Self-Assembly and Layer-by-Layer Post Azo Functionalization,” Macromol.  33, 6534–6540 (2000).
[Crossref]

Opt. Commun. (1)

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

Phys. Rev. Lett. (1)

P.D Maker, R.W Terhune, M. Nisenoff, and C. M. Savage, “Effects of dispersion and focusing on the production of optical harmonics,” Phys. Rev. Lett.  8, 21–22 (1962).

Thin Solid Films (1)

Y. Lvov, S. Yamada, and T. Kunitake, “Non-linear optical effects in layer-by-layer alternate films of polycations and an azobenzene-containing polyanion,” Thin Solid Films  300, 107–112 (1996)
[Crossref]

Other (1)

G. Decher and J. B. Schlenoff, Multilayer Thin Films: Sequentially Assembly of Nanocomposite Materials (Wiley-VCH, 2002).

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Figures (3)

Fig. 1.
Fig. 1.

(a) UV/Vis spectra of the (PAH/PAZO) n assemblies. Curves, from down to top, correspond to n=1, 4, 6, and 12. (b) Absorbance at the maximum (black squares) and ellipsometric thickness (open circles) as a function of n, solid lines are linear fits. The thickness increases about 1 nm per bilayer.

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Fig. 2.
Fig. 2.

(a) Spectral response of (PAH/PAZO) 12 film proves that the observed signal is SH. (b) Excitation power dependence of the SH signal at λ2ω =398nm, following a quadratic law.

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Fig. 3.
Fig. 3.

(a) s’- and (b) p’-polarized SH response (rotated 15 degrees from the s- or p- polarized signals) of (PAH/PAZO)6 as a function of the polarization angle of the fundamental beam (90° corresponds to s- polarized incident beam). (c) is the total signal. Full lines are fittings following Eq (5). (d) Square root of second-harmonic intensity of PAH/PAZO films as a function of the number of deposited bilayers. Squares correspond to the maximum total signal measured, triangles correspond to the same quantity obtained from the fitting function. Dotted line is a guide to the eye.

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Equations (6)

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

P=χ(1)E+χ(2)E·E+χ(3)E·E·E+…
pi=μi+αij(1)Ej+βijk(2)EjEk+…
D=〈cos3θZ′Z〉〈cosθZ′Z〉 ,
D=χZZZ(2)χZZZ(2)+2χZXX(2) .
Is2ω(γ)=C d2 ∣s1sin(2γ)χXXZ∣2 (Iω)2 ,
Ip2ω(γ)=C d2 ∣cos2(γ)[s2χXXZ+s3χZXX+s4χZZZ]+s4χZXX∣2 (Iω)2 ,

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