Abstract

We present a generalized model for the electro-optic response of chromophores in a viscoelastic polymer matrix to a combined dc and ac applied poling field. The model includes a local molecular field of random orientation at each chromophore site to take into account the influence of the polymer matrix on the chromophore reorientation. Hence the model relies on a physically intuitive picture of chromophore dynamics in a viscoelastic polymer matrix. The dynamics is described by the rotational diffusion equation, where the local molecular field is inferred and a solution is presented with a variational approach. We obtain an analytical expression for the electro-optic response both at the modulating frequency and at two times the modulating frequency, having explicit frequency and molecular-field dependence. The model is successfully compared with frequency-resolved ellipsometric measurements in an azo-dye containing polymer guest–host system that is poled in a combined dc and ac electric field. The experimental setup is a modified Teng–Man ellipsometer in a balanced detection scheme, and, as a model system for investigating the electro-optic response, we use the chromophore Disperse Red 1 in a polymer matrix of poly(methyl methacrylate). Finally, the model is compared with independent experiments on a 2,5-dimethyl-4-(p-nitrophenylazo)-anisole containing photorefractive polymer composite, and good qualitative agreement is found.

© 2003 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  23. F. Ghebremichael and M. G. Kuzyk, “Optical second-harmonic generation as a probe of the temperature dependence of the distribution of sites in a poly(methyl methacrylate) polymer doped with disperse red 1 azo dye,” J. Appl. Phys. 77, 2896–2901 (1995).
    [CrossRef]
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    [CrossRef]
  25. A. W. Harper, S. Sun, L. R. Dalton, S. M. Garner, A. Chen, S. Kalluri, W. H. Steier, and B. H. Robinson, “Translating microscopic optical nonlinearity into macroscopic optical nonlinearity: the role of chromophore-chromophore electrostatic interactions,” J. Opt. Soc. Am. B 15, 329–337 (1998).
    [CrossRef]
  26. B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
    [CrossRef]

2002

1999

F. Michelotti, G. Nicolao, F. Tesi, and M. Bertolotti, “On the measurement of the electro-optic properties of poled side-chain copolymer films with a modified Teng–Man technique,” Chem. Phys. 245, 311–326 (1999).
[CrossRef]

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

1998

1997

B. Kippelen, F. Meyers, N. Peyghambarian, and S. R. Marder, “Chromophore design for photorefractive applications,” J. Am. Chem. Soc. 119, 4559–4560 (1997).
[CrossRef]

1996

B. Kippelen, Sandalphon, K. Meerholz, and N. Peyghambarian, “Birefringence, Pockels, and Kerr effects in photorefractive polymers,” Appl. Phys. Lett. 68, 1748–1750 (1996).
[CrossRef]

T. Verbiest, D. M. Burland, and C. A. Walsh, “Use of the lognormal distribution function to describe orientational relaxation in optically nonlinear polymers,” Macromolecules 29, 6310–6316 (1996).
[CrossRef]

Sandalphon, B. Kippelen, K. Meerholz, and N. Peyghambarian, “Ellipsometric measurements of poling birefringence, the Pockels effect, and the Kerr effect in high-performance photorefractive polymer composites,” Appl. Opt. 35, 2346–2354 (1996).
[CrossRef]

1995

F. Ghebremichael and M. G. Kuzyk, “Optical second-harmonic generation as a probe of the temperature dependence of the distribution of sites in a poly(methyl methacrylate) polymer doped with disperse red 1 azo dye,” J. Appl. Phys. 77, 2896–2901 (1995).
[CrossRef]

1994

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–500 (1994).
[CrossRef]

A. Dhinojwala, G. K. Wong, and J. M. Torkelson, “Rotational reorientation dynamics of disperse red 1 in polystyrene: α-relaxation dynamics probed by second harmonic generation and dielectric relaxation,” J. Chem. Phys. 100, 6046–6054 (1994).
[CrossRef]

W. E. Moerner, S. M. Silence, F. Hache, and G. C. Bjorklund, “Orientationally enhanced photorefractive effect in polymers,” J. Opt. Soc. Am. B 11, 320–330 (1994).
[CrossRef]

1993

S. C. Brower and L. M. Hayden, “Activation volume associated with the relaxation and the second order nonlinear optical susceptibility in a guest-host polymer,” Appl. Phys. Lett. 63, 2059–2061 (1993).
[CrossRef]

1991

L. T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
[CrossRef]

K. D. Singer and L. A. King, “Relaxation phenomena in polymer nonlinear optical materials,” J. Appl. Phys. 70, 3251–3255 (1991).
[CrossRef]

J. W. Wu, “Birefringent and electro-optic effects in poled polymer films: steady-state and transient properties,” J. Opt. Soc. Am. B 8, 142–152 (1991).
[CrossRef]

1990

1989

L. A. Dissardo and R. M. Hill, “The fractal nature of the cluster model dielectric response functions,” J. Appl. Phys. 66, 2511–2524 (1989).
[CrossRef]

Aniszfeld, R.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

Bertolotti, M.

F. Michelotti, G. Nicolao, F. Tesi, and M. Bertolotti, “On the measurement of the electro-optic properties of poled side-chain copolymer films with a modified Teng–Man technique,” Chem. Phys. 245, 311–326 (1999).
[CrossRef]

Bjorklund, G. C.

Brower, S. C.

S. C. Brower and L. M. Hayden, “Activation volume associated with the relaxation and the second order nonlinear optical susceptibility in a guest-host polymer,” Appl. Phys. Lett. 63, 2059–2061 (1993).
[CrossRef]

Burland, D. M.

T. Verbiest, D. M. Burland, and C. A. Walsh, “Use of the lognormal distribution function to describe orientational relaxation in optically nonlinear polymers,” Macromolecules 29, 6310–6316 (1996).
[CrossRef]

Chang, C.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

Chen, A.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

A. W. Harper, S. Sun, L. R. Dalton, S. M. Garner, A. Chen, S. Kalluri, W. H. Steier, and B. H. Robinson, “Translating microscopic optical nonlinearity into macroscopic optical nonlinearity: the role of chromophore-chromophore electrostatic interactions,” J. Opt. Soc. Am. B 15, 329–337 (1998).
[CrossRef]

Cheng, L. T.

L. T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
[CrossRef]

Cline, J. A.

Dalton, L. R.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

A. W. Harper, S. Sun, L. R. Dalton, S. M. Garner, A. Chen, S. Kalluri, W. H. Steier, and B. H. Robinson, “Translating microscopic optical nonlinearity into macroscopic optical nonlinearity: the role of chromophore-chromophore electrostatic interactions,” J. Opt. Soc. Am. B 15, 329–337 (1998).
[CrossRef]

Dhinojwala, A.

A. Dhinojwala, G. K. Wong, and J. M. Torkelson, “Rotational reorientation dynamics of disperse red 1 in polystyrene: α-relaxation dynamics probed by second harmonic generation and dielectric relaxation,” J. Chem. Phys. 100, 6046–6054 (1994).
[CrossRef]

Dirk, C. W.

Dissardo, L. A.

L. A. Dissardo and R. M. Hill, “The fractal nature of the cluster model dielectric response functions,” J. Appl. Phys. 66, 2511–2524 (1989).
[CrossRef]

Dureiko, R. D.

Garner, S.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

Garner, S. M.

Ghebremichael, F.

F. Ghebremichael and M. G. Kuzyk, “Optical second-harmonic generation as a probe of the temperature dependence of the distribution of sites in a poly(methyl methacrylate) polymer doped with disperse red 1 azo dye,” J. Appl. Phys. 77, 2896–2901 (1995).
[CrossRef]

Hache, F.

Harper, A. W.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

A. W. Harper, S. Sun, L. R. Dalton, S. M. Garner, A. Chen, S. Kalluri, W. H. Steier, and B. H. Robinson, “Translating microscopic optical nonlinearity into macroscopic optical nonlinearity: the role of chromophore-chromophore electrostatic interactions,” J. Opt. Soc. Am. B 15, 329–337 (1998).
[CrossRef]

Hayden, L. M.

S. J. Strutz and L. M. Hayden, “Effect of pressure and temperature on chromophore reorientation in a side-chain nonlinear optical polymer,” J. Polym. Sci. Part B Polym. Phys. 36, 2793–2803 (1998).
[CrossRef]

S. C. Brower and L. M. Hayden, “Activation volume associated with the relaxation and the second order nonlinear optical susceptibility in a guest-host polymer,” Appl. Phys. Lett. 63, 2059–2061 (1993).
[CrossRef]

Herman, W. N.

Hill, R. M.

L. A. Dissardo and R. M. Hill, “The fractal nature of the cluster model dielectric response functions,” J. Appl. Phys. 66, 2511–2524 (1989).
[CrossRef]

Houbrecht, S.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

Jen, A. K. Y.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

Jespersen, K.

Johansen, P. M.

Kalluri, S.

King, L. A.

K. D. Singer and L. A. King, “Relaxation phenomena in polymer nonlinear optical materials,” J. Appl. Phys. 70, 3251–3255 (1991).
[CrossRef]

Kippelen, B.

B. Kippelen, F. Meyers, N. Peyghambarian, and S. R. Marder, “Chromophore design for photorefractive applications,” J. Am. Chem. Soc. 119, 4559–4560 (1997).
[CrossRef]

B. Kippelen, Sandalphon, K. Meerholz, and N. Peyghambarian, “Birefringence, Pockels, and Kerr effects in photorefractive polymers,” Appl. Phys. Lett. 68, 1748–1750 (1996).
[CrossRef]

Sandalphon, B. Kippelen, K. Meerholz, and N. Peyghambarian, “Ellipsometric measurements of poling birefringence, the Pockels effect, and the Kerr effect in high-performance photorefractive polymer composites,” Appl. Opt. 35, 2346–2354 (1996).
[CrossRef]

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–500 (1994).
[CrossRef]

Kuzyk, M. G.

F. Ghebremichael and M. G. Kuzyk, “Optical second-harmonic generation as a probe of the temperature dependence of the distribution of sites in a poly(methyl methacrylate) polymer doped with disperse red 1 azo dye,” J. Appl. Phys. 77, 2896–2901 (1995).
[CrossRef]

M. G. Kuzyk, J. E. Sohn, and C. W. Dirk, “Mechanisms of quadratic electro-optic modulation of dye-doped polymer systems,” J. Opt. Soc. Am. B 7, 842–858 (1990).
[CrossRef]

Ledoux, I.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

Lee, M.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

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]

Marder, S. R.

B. Kippelen, F. Meyers, N. Peyghambarian, and S. R. Marder, “Chromophore design for photorefractive applications,” J. Am. Chem. Soc. 119, 4559–4560 (1997).
[CrossRef]

L. T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
[CrossRef]

Meerholz, K.

Sandalphon, B. Kippelen, K. Meerholz, and N. Peyghambarian, “Ellipsometric measurements of poling birefringence, the Pockels effect, and the Kerr effect in high-performance photorefractive polymer composites,” Appl. Opt. 35, 2346–2354 (1996).
[CrossRef]

B. Kippelen, Sandalphon, K. Meerholz, and N. Peyghambarian, “Birefringence, Pockels, and Kerr effects in photorefractive polymers,” Appl. Phys. Lett. 68, 1748–1750 (1996).
[CrossRef]

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–500 (1994).
[CrossRef]

Meredith, G. R.

L. T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
[CrossRef]

Meyers, F.

B. Kippelen, F. Meyers, N. Peyghambarian, and S. R. Marder, “Chromophore design for photorefractive applications,” J. Am. Chem. Soc. 119, 4559–4560 (1997).
[CrossRef]

Michelotti, F.

F. Michelotti, G. Nicolao, F. Tesi, and M. Bertolotti, “On the measurement of the electro-optic properties of poled side-chain copolymer films with a modified Teng–Man technique,” Chem. Phys. 245, 311–326 (1999).
[CrossRef]

Moerner, W. E.

Nicolao, G.

F. Michelotti, G. Nicolao, F. Tesi, and M. Bertolotti, “On the measurement of the electro-optic properties of poled side-chain copolymer films with a modified Teng–Man technique,” Chem. Phys. 245, 311–326 (1999).
[CrossRef]

Pedersen, T. G.

Persoons, A.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

Peyghambarian, N.

B. Kippelen, F. Meyers, N. Peyghambarian, and S. R. Marder, “Chromophore design for photorefractive applications,” J. Am. Chem. Soc. 119, 4559–4560 (1997).
[CrossRef]

B. Kippelen, Sandalphon, K. Meerholz, and N. Peyghambarian, “Birefringence, Pockels, and Kerr effects in photorefractive polymers,” Appl. Phys. Lett. 68, 1748–1750 (1996).
[CrossRef]

Sandalphon, B. Kippelen, K. Meerholz, and N. Peyghambarian, “Ellipsometric measurements of poling birefringence, the Pockels effect, and the Kerr effect in high-performance photorefractive polymer composites,” Appl. Opt. 35, 2346–2354 (1996).
[CrossRef]

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–500 (1994).
[CrossRef]

Ren, A.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

Rikken, G.

L. T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
[CrossRef]

Robinson, B. H.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

A. W. Harper, S. Sun, L. R. Dalton, S. M. Garner, A. Chen, S. Kalluri, W. H. Steier, and B. H. Robinson, “Translating microscopic optical nonlinearity into macroscopic optical nonlinearity: the role of chromophore-chromophore electrostatic interactions,” J. Opt. Soc. Am. B 15, 329–337 (1998).
[CrossRef]

Sandalphon,

Sandalphon, B. Kippelen, K. Meerholz, and N. Peyghambarian, “Ellipsometric measurements of poling birefringence, the Pockels effect, and the Kerr effect in high-performance photorefractive polymer composites,” Appl. Opt. 35, 2346–2354 (1996).
[CrossRef]

B. Kippelen, Sandalphon, K. Meerholz, and N. Peyghambarian, “Birefringence, Pockels, and Kerr effects in photorefractive polymers,” Appl. Phys. Lett. 68, 1748–1750 (1996).
[CrossRef]

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–500 (1994).
[CrossRef]

Schildkraut, J. S.

Schuele, D. E.

Silence, S. M.

Singer, K. D.

R. D. Dureiko, D. E. Schuele, and K. D. Singer, “Modeling relaxation processes in poled electro-optic polymer films,” J. Opt. Soc. Am. B 15, 338–350 (1998).
[CrossRef]

K. D. Singer and L. A. King, “Relaxation phenomena in polymer nonlinear optical materials,” J. Appl. Phys. 70, 3251–3255 (1991).
[CrossRef]

Sohn, J. E.

Steier, W. H.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

A. W. Harper, S. Sun, L. R. Dalton, S. M. Garner, A. Chen, S. Kalluri, W. H. Steier, and B. H. Robinson, “Translating microscopic optical nonlinearity into macroscopic optical nonlinearity: the role of chromophore-chromophore electrostatic interactions,” J. Opt. Soc. Am. B 15, 329–337 (1998).
[CrossRef]

Stevenson, S. H.

L. T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
[CrossRef]

Strutz, S. J.

S. J. Strutz and L. M. Hayden, “Effect of pressure and temperature on chromophore reorientation in a side-chain nonlinear optical polymer,” J. Polym. Sci. Part B Polym. Phys. 36, 2793–2803 (1998).
[CrossRef]

Sun, S.

Tam, W.

L. T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
[CrossRef]

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]

Tesi, F.

F. Michelotti, G. Nicolao, F. Tesi, and M. Bertolotti, “On the measurement of the electro-optic properties of poled side-chain copolymer films with a modified Teng–Man technique,” Chem. Phys. 245, 311–326 (1999).
[CrossRef]

Todorova, G.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

Torkelson, J. M.

A. Dhinojwala, G. K. Wong, and J. M. Torkelson, “Rotational reorientation dynamics of disperse red 1 in polystyrene: α-relaxation dynamics probed by second harmonic generation and dielectric relaxation,” J. Chem. Phys. 100, 6046–6054 (1994).
[CrossRef]

Verbiest, T.

T. Verbiest, D. M. Burland, and C. A. Walsh, “Use of the lognormal distribution function to describe orientational relaxation in optically nonlinear polymers,” Macromolecules 29, 6310–6316 (1996).
[CrossRef]

Volodin, B. L.

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–500 (1994).
[CrossRef]

Walsh, C. A.

T. Verbiest, D. M. Burland, and C. A. Walsh, “Use of the lognormal distribution function to describe orientational relaxation in optically nonlinear polymers,” Macromolecules 29, 6310–6316 (1996).
[CrossRef]

Wang, F.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

Wong, G. K.

A. Dhinojwala, G. K. Wong, and J. M. Torkelson, “Rotational reorientation dynamics of disperse red 1 in polystyrene: α-relaxation dynamics probed by second harmonic generation and dielectric relaxation,” J. Chem. Phys. 100, 6046–6054 (1994).
[CrossRef]

Wu, J. W.

Wyller, J.

Zyss, J.

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

S. C. Brower and L. M. Hayden, “Activation volume associated with the relaxation and the second order nonlinear optical susceptibility in a guest-host polymer,” Appl. Phys. Lett. 63, 2059–2061 (1993).
[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]

B. Kippelen, Sandalphon, K. Meerholz, and N. Peyghambarian, “Birefringence, Pockels, and Kerr effects in photorefractive polymers,” Appl. Phys. Lett. 68, 1748–1750 (1996).
[CrossRef]

Chem. Phys.

F. Michelotti, G. Nicolao, F. Tesi, and M. Bertolotti, “On the measurement of the electro-optic properties of poled side-chain copolymer films with a modified Teng–Man technique,” Chem. Phys. 245, 311–326 (1999).
[CrossRef]

B. H. Robinson, L. R. Dalton, A. W. Harper, A. Ren, F. Wang, C. Chang, G. Todorova, M. Lee, R. Aniszfeld, S. Garner, A. Chen, W. H. Steier, S. Houbrecht, A. Persoons, I. Ledoux, J. Zyss, and A. K. Y. Jen, “The molecular and supramolecular engineering of polymeric electro-optic materials,” Chem. Phys. 245, 35–50 (1999).
[CrossRef]

J. Am. Chem. Soc.

B. Kippelen, F. Meyers, N. Peyghambarian, and S. R. Marder, “Chromophore design for photorefractive applications,” J. Am. Chem. Soc. 119, 4559–4560 (1997).
[CrossRef]

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F. Ghebremichael and M. G. Kuzyk, “Optical second-harmonic generation as a probe of the temperature dependence of the distribution of sites in a poly(methyl methacrylate) polymer doped with disperse red 1 azo dye,” J. Appl. Phys. 77, 2896–2901 (1995).
[CrossRef]

K. D. Singer and L. A. King, “Relaxation phenomena in polymer nonlinear optical materials,” J. Appl. Phys. 70, 3251–3255 (1991).
[CrossRef]

L. A. Dissardo and R. M. Hill, “The fractal nature of the cluster model dielectric response functions,” J. Appl. Phys. 66, 2511–2524 (1989).
[CrossRef]

J. Chem. Phys.

A. Dhinojwala, G. K. Wong, and J. M. Torkelson, “Rotational reorientation dynamics of disperse red 1 in polystyrene: α-relaxation dynamics probed by second harmonic generation and dielectric relaxation,” J. Chem. Phys. 100, 6046–6054 (1994).
[CrossRef]

J. Opt. Soc. Am. B

J. Phys. Chem.

L. T. Cheng, W. Tam, S. H. Stevenson, G. R. Meredith, G. Rikken, and S. R. Marder, “Experimental investigations of organic molecular nonlinear optical polarizabilities. 1. Methods and results on benzene and stilbene derivatives,” J. Phys. Chem. 95, 10631–10643 (1991).
[CrossRef]

J. Polym. Sci. Part B Polym. Phys.

S. J. Strutz and L. M. Hayden, “Effect of pressure and temperature on chromophore reorientation in a side-chain nonlinear optical polymer,” J. Polym. Sci. Part B Polym. Phys. 36, 2793–2803 (1998).
[CrossRef]

Macromolecules

T. Verbiest, D. M. Burland, and C. A. Walsh, “Use of the lognormal distribution function to describe orientational relaxation in optically nonlinear polymers,” Macromolecules 29, 6310–6316 (1996).
[CrossRef]

Nature

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, and N. Peyghambarian, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–500 (1994).
[CrossRef]

Other

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Figures (8)

Fig. 1
Fig. 1

Transmission ellipsometer featuring a balanced-detection scheme and lock-in amplification. The components are a polarizer, P, the optical polymer sample, S, a quarter-wave plate, QWP, a Wollaston prism, A, and photodiodes, D1 and D2. The two output ray intensities are subtracted and lock-in amplified. The external poling field is supplied by 1:1000 amplification of a wave-generator output. The mount for the optical polymer under study is temperature controlled.

Fig. 2
Fig. 2

Schematic diagram of the four optical components of the setup. Polarizer, P, sample, S, quarter-wave plate, QWP, and analyzer, A. The input polarization is 45°, and the orientation of the quarter-wave plate and the analyzer are defined by θ+ζ and φ+ζ, respectively. The tilt angle ζ is introduced to obtain 50:50 transmission in the presence of transmission inhomogeneities. The balanced-detection scheme enables us to measure at the points A and B simultaneously on the ellipsometer response curve. The ellipsometer response curve is the transmitted intensity, I, as a function of phase retardation, Γ.

Fig. 3
Fig. 3

Coordinate system visualizing the directors of the dipole moment, μ, the applied field, E, and the local molecular field, EM.

Fig. 4
Fig. 4

Comparisons of the electro-optic responses at the modulating frequency, ω, and at twice the modulating frequency, 2ω. The solid curve represents the results from the present extended model, whereas the dashed curve shows those from the original oriented-gas model. The simulations are based on typical parameters given in Table 3. The local molecular field is clearly seen to reduce the electro-optic response.

Fig. 5
Fig. 5

Simulations of the normalized ω response (solid curve) and 2ω response (dashed curve) for various values of the dc component of the poling field, α0. The parameter α0 takes on the values 0.005, 0.01, 0.02, 0.04, 0.08, and 0.16, in the order of increasing amplitude in the curves. Increasing the dc component enhances the ω response drastically, while the 2ω response is influenced only very little.

Fig. 6
Fig. 6

Stretched exponential KWW relaxation in DR1 containing PMMA at T=88 °C (Tg). The polymer is poled for 2 h at 30 V/μm before turn-off. The parameters are estimated to be β=0.33±0.01 and τ˜=25.3±2.4 s.

Fig. 7
Fig. 7

In-phase spectrum of the electro-optic response of DR1 containing PMMA. The upper and lower curves are the electro-optic response at the modulating frequency, ω, and at twice the modulating frequency, 2ω, respectively. The dots represent the experimental data, and the full curves represent the curve fit to the present model with the ratio CBR/CEO given by the electro-optic properties for DR1 in Ref. 14, and with the parameters β and τ˜ of the KWW model at Tg.

Fig. 8
Fig. 8

Successful curve fit from the extended model to DMNPAA data at 690 nm reproduced from Ref. 12. The material is the photorefractive composite DMNPAA:PVK:ESZ:TNF. In the curve fit, realistic values for the parameters β and τ˜ from a relevant KWW relaxation experiment have been inserted, and we have taken the presented values for the electro-optic properties as fixed parameters. Dashed curves represent results with the original oriented-gas model.

Tables (3)

Tables Icon

Table 1 Jones Matrices

Tables Icon

Table 2 Iij(ε) and the Angle-Dependent Help Functions

Tables Icon

Table 3 Calculation Parameters

Equations (27)

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FOM=29kT μ2Δα+μβ,
idI02 [1±cos(2ζ)sin(δψsp)].
ΔidI0cos(2ζ)δψsp.
ΔnBR(t)=NΔα2nε0 a2(t),
ΔnEO(t)Nβ333(ω; ω, 0)5nε0 a1(t)E(t),
an=124π0πPn(cos θ)f(θ, φ, u)sin ududΩ,
dΩ=sin θdθdφ.
τ ft=2f+(fU),
=θˆ θ+1sin θ φˆ φ
U=-α0cos θ-α1cos θ cos ωt-ε cos δ,
f=Z-1exp(α0cos θ+ηα1cos θ+ε cos δ),
Z-114πi0(ε)1+(α0+ηα1)23i12(ε)i02(ε)-12-(α0+ηα1) i1(ε)i0(ε)cos u+(α0+ηα1)232i12(ε)i02(ε)-i2(ε)i0(ε)P2(cos u),
η(t)=12 [W(ε, ω)exp(-iωt)+W*(ε, ω)exp(iωt)].
in(ε)=12-11exp(εx)Pn(x)dx.
S=02π/ω0π4πτ ft-2f-(fU)2dΩ sin ududt.
W(ε, ω)
=[I22(ε)+α02I33(ε)]+iωτ[I12(ε)+α02I34(ε)][I22(ε)+α02I33(ε)]+(ωτ)2[I11(ε)+α02I44(ε)],
a1(t)=α0+η(t)α13 r1(ε),
a2(t)=[α0+η(t)α1]215 r2(ε).
r1(ε)=1-i12(ε)i02(ε),
r2(ε)=1-2 i12(ε)i02(ε)+2 i12(ε)i2(ε)i03(ε)-i22(ε)i02(ε).
Δnω=α0α1215 CBRr2(ε)|W|cos(θ)+13 CEOkTμ r1(ε)[1+|W|cos(θ)],
Δn2ω=α12130 CBRr2(ε)|W|2cos(2θ)+16 CEOkTμ r1(ε)|W|cos(θ),
ΔnωLFΔnωHF=2+Δαβr2(ε)r1(ε)μkT.
CBRCEO=52Δαβ333.
E(t)=Edc+12 Eac[exp(-iωt)+c.c.],
Δno,e=2πn (Bo,eEp2+2Co,eEpET+3Do,eET2),

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