Abstract

A new experimental method for observing chromophore relaxation dynamics in nonlinear optical polymer systems is described. The method is similar to dielectric relaxation measurements, which probe the linear susceptibility χ(1), but this new method is chromophore selective and probes the nonlinear susceptibility χ(2) in the frequency domain, monitoring second-harmonic generation during the application of a strong ac electric field. The out-of-phase component of χ(2) exhibits behavior similar to that of the loss component in dielectric relaxation and is shown to be unaffected by electric-field-induced third-order effects. The relation to dielectric relaxation is discussed, and stretched exponential parameters are extracted for a Disperse-Red-1/poly(methyl methacrylate) guest–host system.

© 1998 Optical Society of America

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  32. A. Dhinojwala, G. K. Wong, and J. M. Torkelson, “Relative contribution of the electric-field induced third-order effect to second-harmonic generation in poled, doped, amorphous polymers,” J. Opt. Soc. Am. B 11, 1549 (1994).
    [CrossRef]
  33. For a discussion of some relaxation mechanisms giving rise to the stretched exponential, see J. Klafter and M. F. Shlesinger, “On the relationship of three theories of relaxation in disordered systems,” Proc. Natl. Acad. Sci. USA 83, 848 (1986).
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    [CrossRef]
  37. M. L. Williams, R. F. Landel, and J. P. Ferry, “The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids,” J. Am. Chem. Soc. 77, 3701 (1955).
    [CrossRef]
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    [CrossRef]
  39. H. J. Winkelhahn, H. H. Winter, and D. Neher, “Piezoelectricity and electrostriction of dye-doped polymer electrets,” Appl. Phys. Lett. 64, 1347 (1994).
    [CrossRef]
  40. 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 (1990).
    [CrossRef]
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    [CrossRef]

1997 (1)

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “High-bandwidth polymer modulators,” in Optoelectronic Integrated Circuits, Y. Park and R. V. Ramaswamy, eds., Proc. SPIE 3006, 314 (1997).
[CrossRef]

1996 (3)

P. Kaatz, P. Pretre, U. Meier, U. Stalder, C. Bosshard, P. Gunter, B. Zysset, M. Stahelin, M. Ahlheim, and F. Lehr, “Relaxation processes in nonlinear optical polyimide side-chain polymers,” Macromolecules 29, 1666 (1996).
[CrossRef]

T. Sugihara, H. Haga, and S. Yamamoto, “Electric field response of second order optical nonlinearity in dye doped poled polymer,” Appl. Phys. Lett. 68, 144 (1996).
[CrossRef]

M. Sprave, R. Blum, and M. Eich, “High electric field conduction mechanisms in electrode poling of electro-optic polymers,” Appl. Phys. Lett. 69, 2962 (1996).
[CrossRef]

1995 (2)

W. N. Herman and L. M. Hayden, “Maker fringes revisited: second-harmonic generation from birefringent or absorbing materials,” J. Opt. Soc. Am. B 12, 416 (1995).
[CrossRef]

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, 2895 (1995).
[CrossRef]

1994 (3)

L.-Y. Liu, D. Ramkrishna, and H. S. Lackritz, “Rotational Brownian motion of chromophores and electric field effects in polymer films for second-order nonlinear optics,” Macromolecules 27, 5987 (1994).
[CrossRef]

H. J. Winkelhahn, H. H. Winter, and D. Neher, “Piezoelectricity and electrostriction of dye-doped polymer electrets,” Appl. Phys. Lett. 64, 1347 (1994).
[CrossRef]

A. Dhinojwala, G. K. Wong, and J. M. Torkelson, “Relative contribution of the electric-field induced third-order effect to second-harmonic generation in poled, doped, amorphous polymers,” J. Opt. Soc. Am. B 11, 1549 (1994).
[CrossRef]

1993 (2)

A. Dhinojwala, G. K. Wong, and J. M. Torkelson, “Rotational reorientation dynamics of nonlinear optical chromophores in rubbery and glassy polymers: α-relaxation dynamics probed by second-harmonic generation and dielectric relaxation,” Macromolecules 26, 5943 (1993).
[CrossRef]

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

1991 (6)

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

G. T. Boyd, C. V. Francis, J. E. Trend, and D. A. Ender, “Second-harmonic generation as a probe of rotational mobility in poled polymers,” J. Opt. Soc. Am. B 8, 887 (1991).
[CrossRef]

D. Jungbauer, I. Teraoka, D. Y. Yoon, B. Beck, J. D. Swalen, R. Twieg, and C. G. Willson, “Second-order nonlinear optical properties and relaxation characteristics of poled linear epoxy polymers with tolane chromophores,” J. Appl. Phys. 69, 8011 (1991).
[CrossRef]

W. Kohler, D. R. Robello, C. S. Willand, and D. J. Williams, “Dielectric relaxation study of some novel polymers for nonlinear optics,” Macromolecules 24, 4589 (1991).
[CrossRef]

I. Teraoka, D. Jungbauer, B. Reck, D. Y. Yoon, R. Twieg, and C. G. Willson, “Stability of nonlinear-optical characteristics and dielectric relaxations of poled amorphous polymers with main-chain chromophores,” J. Appl. Phys. 69, 2568 (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 (1991).
[CrossRef]

1990 (4)

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 (1990).
[CrossRef]

W. Kohler, D. R. Robello, P. T. Dao, C. S. Willand, and D. J. Williams, “Second-harmonic generation and thermally stimulated current measurements: a study of some novel polymers for nonlinear optics,” J. Chem. Phys. 93, 9157 (1990).
[CrossRef]

H. L. Hampsch and J. M. Torkelson, “Second harmonic generation in corona-poled, doped polymer films as a function of corona processing,” J. Appl. Phys. 67, 1037 (1990).
[CrossRef]

M. G. Kuzyk, R. C. Moore, and L. A. King, “Second-harmonic-generation measurements of the elastic constant of a molecule in a polymer matrix,” J. Opt. Soc. Am. B 7, 64 (1990).
[CrossRef]

1989 (1)

M. Eich, A. Sen, H. Looser, G. C. Bjorklund, J. D. Swalen, R. Twieg, and D. Y. Yoon, “Corona poling and real-time second-harmonic generation study of a novel covalently functionalized amorphous nonlinear optical polymer,” J. Appl. Phys. 66, 2559 (1989).
[CrossRef]

1987 (2)

1986 (1)

For a discussion of some relaxation mechanisms giving rise to the stretched exponential, see J. Klafter and M. F. Shlesinger, “On the relationship of three theories of relaxation in disordered systems,” Proc. Natl. Acad. Sci. USA 83, 848 (1986).
[CrossRef]

1980 (1)

C. P. Lindsey and G. D. Patterson, “Detailed comparison of the Williams–Watts and Cole–Davidson functions,” J. Chem. Phys. 73, 3348 (1980).
[CrossRef]

1970 (1)

G. Williams and D. C. Watts, “Non-symmetrical dielectric relaxation behavior arising from a simple empirical decay function,” Trans. Faraday Soc. 66, 80 (1970).
[CrossRef]

1962 (1)

D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126, 1977 (1962).
[CrossRef]

1955 (1)

M. L. Williams, R. F. Landel, and J. P. Ferry, “The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids,” J. Am. Chem. Soc. 77, 3701 (1955).
[CrossRef]

Ahlheim, M.

P. Kaatz, P. Pretre, U. Meier, U. Stalder, C. Bosshard, P. Gunter, B. Zysset, M. Stahelin, M. Ahlheim, and F. Lehr, “Relaxation processes in nonlinear optical polyimide side-chain polymers,” Macromolecules 29, 1666 (1996).
[CrossRef]

Beck, B.

D. Jungbauer, I. Teraoka, D. Y. Yoon, B. Beck, J. D. Swalen, R. Twieg, and C. G. Willson, “Second-order nonlinear optical properties and relaxation characteristics of poled linear epoxy polymers with tolane chromophores,” J. Appl. Phys. 69, 8011 (1991).
[CrossRef]

Bjorklund, G. C.

M. Eich, A. Sen, H. Looser, G. C. Bjorklund, J. D. Swalen, R. Twieg, and D. Y. Yoon, “Corona poling and real-time second-harmonic generation study of a novel covalently functionalized amorphous nonlinear optical polymer,” J. Appl. Phys. 66, 2559 (1989).
[CrossRef]

Blum, R.

M. Sprave, R. Blum, and M. Eich, “High electric field conduction mechanisms in electrode poling of electro-optic polymers,” Appl. Phys. Lett. 69, 2962 (1996).
[CrossRef]

Bosshard, C.

P. Kaatz, P. Pretre, U. Meier, U. Stalder, C. Bosshard, P. Gunter, B. Zysset, M. Stahelin, M. Ahlheim, and F. Lehr, “Relaxation processes in nonlinear optical polyimide side-chain polymers,” Macromolecules 29, 1666 (1996).
[CrossRef]

Boyd, G. T.

Brower, S. C.

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

Chen, A.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “High-bandwidth polymer modulators,” in Optoelectronic Integrated Circuits, Y. Park and R. V. Ramaswamy, eds., Proc. SPIE 3006, 314 (1997).
[CrossRef]

Chen, D.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “High-bandwidth polymer modulators,” in Optoelectronic Integrated Circuits, Y. Park and R. V. Ramaswamy, eds., Proc. SPIE 3006, 314 (1997).
[CrossRef]

Dalton, L. R.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “High-bandwidth polymer modulators,” in Optoelectronic Integrated Circuits, Y. Park and R. V. Ramaswamy, eds., Proc. SPIE 3006, 314 (1997).
[CrossRef]

Dao, P. T.

W. Kohler, D. R. Robello, P. T. Dao, C. S. Willand, and D. J. Williams, “Second-harmonic generation and thermally stimulated current measurements: a study of some novel polymers for nonlinear optics,” J. Chem. Phys. 93, 9157 (1990).
[CrossRef]

Dhinojwala, A.

A. Dhinojwala, G. K. Wong, and J. M. Torkelson, “Relative contribution of the electric-field induced third-order effect to second-harmonic generation in poled, doped, amorphous polymers,” J. Opt. Soc. Am. B 11, 1549 (1994).
[CrossRef]

A. Dhinojwala, G. K. Wong, and J. M. Torkelson, “Rotational reorientation dynamics of nonlinear optical chromophores in rubbery and glassy polymers: α-relaxation dynamics probed by second-harmonic generation and dielectric relaxation,” Macromolecules 26, 5943 (1993).
[CrossRef]

Dirk, C. W.

Eich, M.

M. Sprave, R. Blum, and M. Eich, “High electric field conduction mechanisms in electrode poling of electro-optic polymers,” Appl. Phys. Lett. 69, 2962 (1996).
[CrossRef]

M. Eich, A. Sen, H. Looser, G. C. Bjorklund, J. D. Swalen, R. Twieg, and D. Y. Yoon, “Corona poling and real-time second-harmonic generation study of a novel covalently functionalized amorphous nonlinear optical polymer,” J. Appl. Phys. 66, 2559 (1989).
[CrossRef]

Ender, D. A.

Ferry, J. P.

M. L. Williams, R. F. Landel, and J. P. Ferry, “The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids,” J. Am. Chem. Soc. 77, 3701 (1955).
[CrossRef]

Fetterman, H. R.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “High-bandwidth polymer modulators,” in Optoelectronic Integrated Circuits, Y. Park and R. V. Ramaswamy, eds., Proc. SPIE 3006, 314 (1997).
[CrossRef]

Francis, C. V.

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, 2895 (1995).
[CrossRef]

Gunter, P.

P. Kaatz, P. Pretre, U. Meier, U. Stalder, C. Bosshard, P. Gunter, B. Zysset, M. Stahelin, M. Ahlheim, and F. Lehr, “Relaxation processes in nonlinear optical polyimide side-chain polymers,” Macromolecules 29, 1666 (1996).
[CrossRef]

Haga, H.

T. Sugihara, H. Haga, and S. Yamamoto, “Electric field response of second order optical nonlinearity in dye doped poled polymer,” Appl. Phys. Lett. 68, 144 (1996).
[CrossRef]

Hampsch, H. L.

H. L. Hampsch and J. M. Torkelson, “Second harmonic generation in corona-poled, doped polymer films as a function of corona processing,” J. Appl. Phys. 67, 1037 (1990).
[CrossRef]

Hayden, L. M.

W. N. Herman and L. M. Hayden, “Maker fringes revisited: second-harmonic generation from birefringent or absorbing materials,” J. Opt. Soc. Am. B 12, 416 (1995).
[CrossRef]

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

Herman, W. N.

Jungbauer, D.

I. Teraoka, D. Jungbauer, B. Reck, D. Y. Yoon, R. Twieg, and C. G. Willson, “Stability of nonlinear-optical characteristics and dielectric relaxations of poled amorphous polymers with main-chain chromophores,” J. Appl. Phys. 69, 2568 (1991).
[CrossRef]

D. Jungbauer, I. Teraoka, D. Y. Yoon, B. Beck, J. D. Swalen, R. Twieg, and C. G. Willson, “Second-order nonlinear optical properties and relaxation characteristics of poled linear epoxy polymers with tolane chromophores,” J. Appl. Phys. 69, 8011 (1991).
[CrossRef]

Kaatz, P.

P. Kaatz, P. Pretre, U. Meier, U. Stalder, C. Bosshard, P. Gunter, B. Zysset, M. Stahelin, M. Ahlheim, and F. Lehr, “Relaxation processes in nonlinear optical polyimide side-chain polymers,” Macromolecules 29, 1666 (1996).
[CrossRef]

King, L. A.

Klafter, J.

For a discussion of some relaxation mechanisms giving rise to the stretched exponential, see J. Klafter and M. F. Shlesinger, “On the relationship of three theories of relaxation in disordered systems,” Proc. Natl. Acad. Sci. USA 83, 848 (1986).
[CrossRef]

Kleinman, D. A.

D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126, 1977 (1962).
[CrossRef]

Kohler, W.

W. Kohler, D. R. Robello, C. S. Willand, and D. J. Williams, “Dielectric relaxation study of some novel polymers for nonlinear optics,” Macromolecules 24, 4589 (1991).
[CrossRef]

W. Kohler, D. R. Robello, P. T. Dao, C. S. Willand, and D. J. Williams, “Second-harmonic generation and thermally stimulated current measurements: a study of some novel polymers for nonlinear optics,” J. Chem. Phys. 93, 9157 (1990).
[CrossRef]

Kuzyk, M. G.

Lackritz, H. S.

L.-Y. Liu, D. Ramkrishna, and H. S. Lackritz, “Rotational Brownian motion of chromophores and electric field effects in polymer films for second-order nonlinear optics,” Macromolecules 27, 5987 (1994).
[CrossRef]

Landel, R. F.

M. L. Williams, R. F. Landel, and J. P. Ferry, “The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids,” J. Am. Chem. Soc. 77, 3701 (1955).
[CrossRef]

Lehr, F.

P. Kaatz, P. Pretre, U. Meier, U. Stalder, C. Bosshard, P. Gunter, B. Zysset, M. Stahelin, M. Ahlheim, and F. Lehr, “Relaxation processes in nonlinear optical polyimide side-chain polymers,” Macromolecules 29, 1666 (1996).
[CrossRef]

Lei, D.

D. Lei, J. Runt, A. Safari, and R. E. Newnham, “Dielectric properties of azo dye–poly(methyl methacrylate) mixtures,” Macromolecules 20, 1797 (1987).
[CrossRef]

Lindsey, C. P.

C. P. Lindsey and G. D. Patterson, “Detailed comparison of the Williams–Watts and Cole–Davidson functions,” J. Chem. Phys. 73, 3348 (1980).
[CrossRef]

Liu, L.-Y.

L.-Y. Liu, D. Ramkrishna, and H. S. Lackritz, “Rotational Brownian motion of chromophores and electric field effects in polymer films for second-order nonlinear optics,” Macromolecules 27, 5987 (1994).
[CrossRef]

Looser, H.

M. Eich, A. Sen, H. Looser, G. C. Bjorklund, J. D. Swalen, R. Twieg, and D. Y. Yoon, “Corona poling and real-time second-harmonic generation study of a novel covalently functionalized amorphous nonlinear optical polymer,” J. Appl. Phys. 66, 2559 (1989).
[CrossRef]

Meier, U.

P. Kaatz, P. Pretre, U. Meier, U. Stalder, C. Bosshard, P. Gunter, B. Zysset, M. Stahelin, M. Ahlheim, and F. Lehr, “Relaxation processes in nonlinear optical polyimide side-chain polymers,” Macromolecules 29, 1666 (1996).
[CrossRef]

Moore, R. C.

Neher, D.

H. J. Winkelhahn, H. H. Winter, and D. Neher, “Piezoelectricity and electrostriction of dye-doped polymer electrets,” Appl. Phys. Lett. 64, 1347 (1994).
[CrossRef]

Newnham, R. E.

D. Lei, J. Runt, A. Safari, and R. E. Newnham, “Dielectric properties of azo dye–poly(methyl methacrylate) mixtures,” Macromolecules 20, 1797 (1987).
[CrossRef]

Patterson, G. D.

C. P. Lindsey and G. D. Patterson, “Detailed comparison of the Williams–Watts and Cole–Davidson functions,” J. Chem. Phys. 73, 3348 (1980).
[CrossRef]

Pretre, P.

P. Kaatz, P. Pretre, U. Meier, U. Stalder, C. Bosshard, P. Gunter, B. Zysset, M. Stahelin, M. Ahlheim, and F. Lehr, “Relaxation processes in nonlinear optical polyimide side-chain polymers,” Macromolecules 29, 1666 (1996).
[CrossRef]

Ramkrishna, D.

L.-Y. Liu, D. Ramkrishna, and H. S. Lackritz, “Rotational Brownian motion of chromophores and electric field effects in polymer films for second-order nonlinear optics,” Macromolecules 27, 5987 (1994).
[CrossRef]

Reck, B.

I. Teraoka, D. Jungbauer, B. Reck, D. Y. Yoon, R. Twieg, and C. G. Willson, “Stability of nonlinear-optical characteristics and dielectric relaxations of poled amorphous polymers with main-chain chromophores,” J. Appl. Phys. 69, 2568 (1991).
[CrossRef]

Robello, D. R.

W. Kohler, D. R. Robello, C. S. Willand, and D. J. Williams, “Dielectric relaxation study of some novel polymers for nonlinear optics,” Macromolecules 24, 4589 (1991).
[CrossRef]

W. Kohler, D. R. Robello, P. T. Dao, C. S. Willand, and D. J. Williams, “Second-harmonic generation and thermally stimulated current measurements: a study of some novel polymers for nonlinear optics,” J. Chem. Phys. 93, 9157 (1990).
[CrossRef]

Runt, J.

D. Lei, J. Runt, A. Safari, and R. E. Newnham, “Dielectric properties of azo dye–poly(methyl methacrylate) mixtures,” Macromolecules 20, 1797 (1987).
[CrossRef]

Safari, A.

D. Lei, J. Runt, A. Safari, and R. E. Newnham, “Dielectric properties of azo dye–poly(methyl methacrylate) mixtures,” Macromolecules 20, 1797 (1987).
[CrossRef]

Sen, A.

M. Eich, A. Sen, H. Looser, G. C. Bjorklund, J. D. Swalen, R. Twieg, and D. Y. Yoon, “Corona poling and real-time second-harmonic generation study of a novel covalently functionalized amorphous nonlinear optical polymer,” J. Appl. Phys. 66, 2559 (1989).
[CrossRef]

Shi, Y.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “High-bandwidth polymer modulators,” in Optoelectronic Integrated Circuits, Y. Park and R. V. Ramaswamy, eds., Proc. SPIE 3006, 314 (1997).
[CrossRef]

Shlesinger, M. F.

For a discussion of some relaxation mechanisms giving rise to the stretched exponential, see J. Klafter and M. F. Shlesinger, “On the relationship of three theories of relaxation in disordered systems,” Proc. Natl. Acad. Sci. USA 83, 848 (1986).
[CrossRef]

Singer, K. D.

Sohn, J. E.

Sprave, M.

M. Sprave, R. Blum, and M. Eich, “High electric field conduction mechanisms in electrode poling of electro-optic polymers,” Appl. Phys. Lett. 69, 2962 (1996).
[CrossRef]

Stahelin, M.

P. Kaatz, P. Pretre, U. Meier, U. Stalder, C. Bosshard, P. Gunter, B. Zysset, M. Stahelin, M. Ahlheim, and F. Lehr, “Relaxation processes in nonlinear optical polyimide side-chain polymers,” Macromolecules 29, 1666 (1996).
[CrossRef]

Stalder, U.

P. Kaatz, P. Pretre, U. Meier, U. Stalder, C. Bosshard, P. Gunter, B. Zysset, M. Stahelin, M. Ahlheim, and F. Lehr, “Relaxation processes in nonlinear optical polyimide side-chain polymers,” Macromolecules 29, 1666 (1996).
[CrossRef]

Steier, W. H.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “High-bandwidth polymer modulators,” in Optoelectronic Integrated Circuits, Y. Park and R. V. Ramaswamy, eds., Proc. SPIE 3006, 314 (1997).
[CrossRef]

Sugihara, T.

T. Sugihara, H. Haga, and S. Yamamoto, “Electric field response of second order optical nonlinearity in dye doped poled polymer,” Appl. Phys. Lett. 68, 144 (1996).
[CrossRef]

Swalen, J. D.

D. Jungbauer, I. Teraoka, D. Y. Yoon, B. Beck, J. D. Swalen, R. Twieg, and C. G. Willson, “Second-order nonlinear optical properties and relaxation characteristics of poled linear epoxy polymers with tolane chromophores,” J. Appl. Phys. 69, 8011 (1991).
[CrossRef]

M. Eich, A. Sen, H. Looser, G. C. Bjorklund, J. D. Swalen, R. Twieg, and D. Y. Yoon, “Corona poling and real-time second-harmonic generation study of a novel covalently functionalized amorphous nonlinear optical polymer,” J. Appl. Phys. 66, 2559 (1989).
[CrossRef]

Teraoka, I.

D. Jungbauer, I. Teraoka, D. Y. Yoon, B. Beck, J. D. Swalen, R. Twieg, and C. G. Willson, “Second-order nonlinear optical properties and relaxation characteristics of poled linear epoxy polymers with tolane chromophores,” J. Appl. Phys. 69, 8011 (1991).
[CrossRef]

I. Teraoka, D. Jungbauer, B. Reck, D. Y. Yoon, R. Twieg, and C. G. Willson, “Stability of nonlinear-optical characteristics and dielectric relaxations of poled amorphous polymers with main-chain chromophores,” J. Appl. Phys. 69, 2568 (1991).
[CrossRef]

Torkelson, J. M.

A. Dhinojwala, G. K. Wong, and J. M. Torkelson, “Relative contribution of the electric-field induced third-order effect to second-harmonic generation in poled, doped, amorphous polymers,” J. Opt. Soc. Am. B 11, 1549 (1994).
[CrossRef]

A. Dhinojwala, G. K. Wong, and J. M. Torkelson, “Rotational reorientation dynamics of nonlinear optical chromophores in rubbery and glassy polymers: α-relaxation dynamics probed by second-harmonic generation and dielectric relaxation,” Macromolecules 26, 5943 (1993).
[CrossRef]

H. L. Hampsch and J. M. Torkelson, “Second harmonic generation in corona-poled, doped polymer films as a function of corona processing,” J. Appl. Phys. 67, 1037 (1990).
[CrossRef]

Trend, J. E.

Twieg, R.

I. Teraoka, D. Jungbauer, B. Reck, D. Y. Yoon, R. Twieg, and C. G. Willson, “Stability of nonlinear-optical characteristics and dielectric relaxations of poled amorphous polymers with main-chain chromophores,” J. Appl. Phys. 69, 2568 (1991).
[CrossRef]

D. Jungbauer, I. Teraoka, D. Y. Yoon, B. Beck, J. D. Swalen, R. Twieg, and C. G. Willson, “Second-order nonlinear optical properties and relaxation characteristics of poled linear epoxy polymers with tolane chromophores,” J. Appl. Phys. 69, 8011 (1991).
[CrossRef]

M. Eich, A. Sen, H. Looser, G. C. Bjorklund, J. D. Swalen, R. Twieg, and D. Y. Yoon, “Corona poling and real-time second-harmonic generation study of a novel covalently functionalized amorphous nonlinear optical polymer,” J. Appl. Phys. 66, 2559 (1989).
[CrossRef]

Wang, W.

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “High-bandwidth polymer modulators,” in Optoelectronic Integrated Circuits, Y. Park and R. V. Ramaswamy, eds., Proc. SPIE 3006, 314 (1997).
[CrossRef]

Watts, D. C.

G. Williams and D. C. Watts, “Non-symmetrical dielectric relaxation behavior arising from a simple empirical decay function,” Trans. Faraday Soc. 66, 80 (1970).
[CrossRef]

Willand, C. S.

W. Kohler, D. R. Robello, C. S. Willand, and D. J. Williams, “Dielectric relaxation study of some novel polymers for nonlinear optics,” Macromolecules 24, 4589 (1991).
[CrossRef]

W. Kohler, D. R. Robello, P. T. Dao, C. S. Willand, and D. J. Williams, “Second-harmonic generation and thermally stimulated current measurements: a study of some novel polymers for nonlinear optics,” J. Chem. Phys. 93, 9157 (1990).
[CrossRef]

Williams, D. J.

W. Kohler, D. R. Robello, C. S. Willand, and D. J. Williams, “Dielectric relaxation study of some novel polymers for nonlinear optics,” Macromolecules 24, 4589 (1991).
[CrossRef]

W. Kohler, D. R. Robello, P. T. Dao, C. S. Willand, and D. J. Williams, “Second-harmonic generation and thermally stimulated current measurements: a study of some novel polymers for nonlinear optics,” J. Chem. Phys. 93, 9157 (1990).
[CrossRef]

Williams, G.

G. Williams and D. C. Watts, “Non-symmetrical dielectric relaxation behavior arising from a simple empirical decay function,” Trans. Faraday Soc. 66, 80 (1970).
[CrossRef]

Williams, M. L.

M. L. Williams, R. F. Landel, and J. P. Ferry, “The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids,” J. Am. Chem. Soc. 77, 3701 (1955).
[CrossRef]

Willson, C. G.

D. Jungbauer, I. Teraoka, D. Y. Yoon, B. Beck, J. D. Swalen, R. Twieg, and C. G. Willson, “Second-order nonlinear optical properties and relaxation characteristics of poled linear epoxy polymers with tolane chromophores,” J. Appl. Phys. 69, 8011 (1991).
[CrossRef]

I. Teraoka, D. Jungbauer, B. Reck, D. Y. Yoon, R. Twieg, and C. G. Willson, “Stability of nonlinear-optical characteristics and dielectric relaxations of poled amorphous polymers with main-chain chromophores,” J. Appl. Phys. 69, 2568 (1991).
[CrossRef]

Winkelhahn, H. J.

H. J. Winkelhahn, H. H. Winter, and D. Neher, “Piezoelectricity and electrostriction of dye-doped polymer electrets,” Appl. Phys. Lett. 64, 1347 (1994).
[CrossRef]

Winter, H. H.

H. J. Winkelhahn, H. H. Winter, and D. Neher, “Piezoelectricity and electrostriction of dye-doped polymer electrets,” Appl. Phys. Lett. 64, 1347 (1994).
[CrossRef]

Wong, G. K.

A. Dhinojwala, G. K. Wong, and J. M. Torkelson, “Relative contribution of the electric-field induced third-order effect to second-harmonic generation in poled, doped, amorphous polymers,” J. Opt. Soc. Am. B 11, 1549 (1994).
[CrossRef]

A. Dhinojwala, G. K. Wong, and J. M. Torkelson, “Rotational reorientation dynamics of nonlinear optical chromophores in rubbery and glassy polymers: α-relaxation dynamics probed by second-harmonic generation and dielectric relaxation,” Macromolecules 26, 5943 (1993).
[CrossRef]

Wu, J. W.

Yamamoto, S.

T. Sugihara, H. Haga, and S. Yamamoto, “Electric field response of second order optical nonlinearity in dye doped poled polymer,” Appl. Phys. Lett. 68, 144 (1996).
[CrossRef]

Yoon, D. Y.

I. Teraoka, D. Jungbauer, B. Reck, D. Y. Yoon, R. Twieg, and C. G. Willson, “Stability of nonlinear-optical characteristics and dielectric relaxations of poled amorphous polymers with main-chain chromophores,” J. Appl. Phys. 69, 2568 (1991).
[CrossRef]

D. Jungbauer, I. Teraoka, D. Y. Yoon, B. Beck, J. D. Swalen, R. Twieg, and C. G. Willson, “Second-order nonlinear optical properties and relaxation characteristics of poled linear epoxy polymers with tolane chromophores,” J. Appl. Phys. 69, 8011 (1991).
[CrossRef]

M. Eich, A. Sen, H. Looser, G. C. Bjorklund, J. D. Swalen, R. Twieg, and D. Y. Yoon, “Corona poling and real-time second-harmonic generation study of a novel covalently functionalized amorphous nonlinear optical polymer,” J. Appl. Phys. 66, 2559 (1989).
[CrossRef]

Zysset, B.

P. Kaatz, P. Pretre, U. Meier, U. Stalder, C. Bosshard, P. Gunter, B. Zysset, M. Stahelin, M. Ahlheim, and F. Lehr, “Relaxation processes in nonlinear optical polyimide side-chain polymers,” Macromolecules 29, 1666 (1996).
[CrossRef]

Appl. Phys. Lett. (4)

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

T. Sugihara, H. Haga, and S. Yamamoto, “Electric field response of second order optical nonlinearity in dye doped poled polymer,” Appl. Phys. Lett. 68, 144 (1996).
[CrossRef]

M. Sprave, R. Blum, and M. Eich, “High electric field conduction mechanisms in electrode poling of electro-optic polymers,” Appl. Phys. Lett. 69, 2962 (1996).
[CrossRef]

H. J. Winkelhahn, H. H. Winter, and D. Neher, “Piezoelectricity and electrostriction of dye-doped polymer electrets,” Appl. Phys. Lett. 64, 1347 (1994).
[CrossRef]

J. Am. Chem. Soc. (1)

M. L. Williams, R. F. Landel, and J. P. Ferry, “The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids,” J. Am. Chem. Soc. 77, 3701 (1955).
[CrossRef]

J. Appl. Phys. (6)

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, 2895 (1995).
[CrossRef]

I. Teraoka, D. Jungbauer, B. Reck, D. Y. Yoon, R. Twieg, and C. G. Willson, “Stability of nonlinear-optical characteristics and dielectric relaxations of poled amorphous polymers with main-chain chromophores,” J. Appl. Phys. 69, 2568 (1991).
[CrossRef]

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

H. L. Hampsch and J. M. Torkelson, “Second harmonic generation in corona-poled, doped polymer films as a function of corona processing,” J. Appl. Phys. 67, 1037 (1990).
[CrossRef]

M. Eich, A. Sen, H. Looser, G. C. Bjorklund, J. D. Swalen, R. Twieg, and D. Y. Yoon, “Corona poling and real-time second-harmonic generation study of a novel covalently functionalized amorphous nonlinear optical polymer,” J. Appl. Phys. 66, 2559 (1989).
[CrossRef]

D. Jungbauer, I. Teraoka, D. Y. Yoon, B. Beck, J. D. Swalen, R. Twieg, and C. G. Willson, “Second-order nonlinear optical properties and relaxation characteristics of poled linear epoxy polymers with tolane chromophores,” J. Appl. Phys. 69, 8011 (1991).
[CrossRef]

J. Chem. Phys. (2)

W. Kohler, D. R. Robello, P. T. Dao, C. S. Willand, and D. J. Williams, “Second-harmonic generation and thermally stimulated current measurements: a study of some novel polymers for nonlinear optics,” J. Chem. Phys. 93, 9157 (1990).
[CrossRef]

C. P. Lindsey and G. D. Patterson, “Detailed comparison of the Williams–Watts and Cole–Davidson functions,” J. Chem. Phys. 73, 3348 (1980).
[CrossRef]

J. Opt. Soc. Am. B (7)

Macromolecules (5)

D. Lei, J. Runt, A. Safari, and R. E. Newnham, “Dielectric properties of azo dye–poly(methyl methacrylate) mixtures,” Macromolecules 20, 1797 (1987).
[CrossRef]

W. Kohler, D. R. Robello, C. S. Willand, and D. J. Williams, “Dielectric relaxation study of some novel polymers for nonlinear optics,” Macromolecules 24, 4589 (1991).
[CrossRef]

L.-Y. Liu, D. Ramkrishna, and H. S. Lackritz, “Rotational Brownian motion of chromophores and electric field effects in polymer films for second-order nonlinear optics,” Macromolecules 27, 5987 (1994).
[CrossRef]

P. Kaatz, P. Pretre, U. Meier, U. Stalder, C. Bosshard, P. Gunter, B. Zysset, M. Stahelin, M. Ahlheim, and F. Lehr, “Relaxation processes in nonlinear optical polyimide side-chain polymers,” Macromolecules 29, 1666 (1996).
[CrossRef]

A. Dhinojwala, G. K. Wong, and J. M. Torkelson, “Rotational reorientation dynamics of nonlinear optical chromophores in rubbery and glassy polymers: α-relaxation dynamics probed by second-harmonic generation and dielectric relaxation,” Macromolecules 26, 5943 (1993).
[CrossRef]

Phys. Rev. (1)

D. A. Kleinman, “Nonlinear dielectric polarization in optical media,” Phys. Rev. 126, 1977 (1962).
[CrossRef]

Proc. Natl. Acad. Sci. USA (1)

For a discussion of some relaxation mechanisms giving rise to the stretched exponential, see J. Klafter and M. F. Shlesinger, “On the relationship of three theories of relaxation in disordered systems,” Proc. Natl. Acad. Sci. USA 83, 848 (1986).
[CrossRef]

Proc. SPIE (1)

D. Chen, H. R. Fetterman, A. Chen, W. H. Steier, L. R. Dalton, W. Wang, and Y. Shi, “High-bandwidth polymer modulators,” in Optoelectronic Integrated Circuits, Y. Park and R. V. Ramaswamy, eds., Proc. SPIE 3006, 314 (1997).
[CrossRef]

Trans. Faraday Soc. (1)

G. Williams and D. C. Watts, “Non-symmetrical dielectric relaxation behavior arising from a simple empirical decay function,” Trans. Faraday Soc. 66, 80 (1970).
[CrossRef]

Other (12)

R. Kohlrausch, “Theorie des elecktrischen in der Leidner Flashe,” Pogg Ann. Phys. 91, 179 (1854).

N. G. McCrum, B. E. Read, and G. Williams, Anelastic and Dielectric Effects in Polymeric Solids (Wiley, London, 1967).

The negative is used because of the definition of the complex permittivity: ε*=ε−iε.

A. R. Blythe, Electrical Properties of Polymers (Cambridge U. Press, Cambridge, 1979).

D. J. Williams, “Nonlinear optical properties of guest–host polymer structures,” in Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, New York, 1987), Vol. 1, Chap. II-7.

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

D. S. Chemla and J. Zyss, eds., Nonlinear Optical Properties of Organic Molecules and Crystals (Academic, Orlando, Fla., 1987), Vols. 1 and 2.

G. A. Lindsay and K. D. Singer, eds., Polymers for Second-Order Nonlinear Optics, ACS Symp. Ser. 601, (1995).

F. Ghebremichael and H. S. Lackritz, “Electro-optic and second harmonic generation studies of dye-doped polymers,” in Organic Thin Films for Photonic Applications, Vol. 21 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 458.

J. A. Cline and W. N. Herman, “Chielectric relaxation: frequency domain chromophore dynamics in nonlinear optical polymers,” in Organic Thin Films for Photonic Applications, Vol. 21 of 1995 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1995), p. 206.

W. N. Herman and J. A. Cline, “Chielectric relaxation and electrically-induced strain effects,” presented at the National Science Foundation/Office of Naval Research Third International Conference on Organic Nonlinear Optics, Marco Island, Fla., December 16–20, 1996.

R. D. Dureiko, D. E. Schuele, and K. D. Singer, “Modeling relaxation processes in poled polymer films,” presented at the National Science Foundation/Office of Naval Research Third International Conference on Organic Nonlinear Optics, Marco Island, Fla., December 16–20, 1996. See also the same authors, “Modeling relaxation processes in poled electro-optic polymer films,” J. Opt. Soc. Am. B 15, 338 (1998).
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Second-harmonic response to a sinusoidal electric field at frequencies of 0.125, 2, and 64 Hz. The data from 16, 16, and 164 cycles, respectively, have been folded onto two cycles of the applied field.

Fig. 2
Fig. 2

Frequency response of the in-phase component of χ(2) at temperatures from 24 to 117 °C.

Fig. 3
Fig. 3

Frequency response of the out-of-phase component of χ(2) at temperatures from 24 to 117 °C. The solid curves are data fits based on the Kohlrausch–Williams–Watts30,31 (KWW) distribution.

Fig. 4
Fig. 4

Replot of Fig. 3 for the out-of-phase component of χ(2) with the response curves normalized by the maximum value at each temperature and the frequency normalized to the location, fmax, of the maximum.

Fig. 5
Fig. 5

Arrhenius-type plot of average decay time 〈τ〉 relative to the average decay time, τg, at the glass transition temperature.

Fig. 6
Fig. 6

Temperature dependence of the out-of-phase component of χ(2) taken at a frequency of 4 Hz.

Fig. 7
Fig. 7

Temperature dependence of the in-phase component of χ(2) taken at a frequency of 4 Hz.

Tables (1)

Tables Icon

Table 1 KWW Fit Parameters for DR1/PMMA

Equations (34)

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

Pi=ε0[χij(1)Ej+χijk(2)EjEk+χijkl(3)EjEkEl+],
χ(2)=χ0(2) sin(Ωt-δϕ)=χin(2) sin Ωt-χout(2) cos Ωt,
χin(2)χ0(2) cos δϕ,χout(2)=χ0(2) sin δϕ.
d33χ333(2)/2cos3 θ,
d31χ311(2)/2cos θ-cos3 θ.
χ(2)=2d=Nf2ωfω2(βcos3 θ+γEAcos4 θ),
EA=EΩ sin Ωt,
cos3 θEΩ sin(Ωt-δϕA),cos4 θ1.
d=A+B(2)EΩ sin(Ωt-δϕA)+B(3)EΩ sin(Ωt),
d=din sin(Ωt)-dout cos(Ωt),
din=A+[B(2) cos(δϕA)+B(3)]EΩ,
dout=B(2) sin(δϕA)EΩ.
d=A+B sin(Ωt-δϕ)EΩ,
B cos δϕ=B(2) cos(δϕA)+B(3),
B sin δϕ=B(2) sin(δϕA).
P2ω=A+B sin(Ωt-δϕ) V0l2,
φ(t)=exp-tτβ.
ε*(Ω)-ε=(ε0-ε)Φ(Ω),
Φ(Ω)=0 exp(-iΩt)-dφ(t)dtdt.
-Φim(Ω)=Ω0 cos(Ωt)φ(t)dt,
-Φim(Ω)=n=1(-1)n-1(Ωτ)-nβ Γ(nβ+1)Γ(n+1) sinβ nπ2,
τ=τβ Γ1β.
Asign(m1)(u-u2-m12)1/2,
B2(m0-A2),
δϕ12 cos-14 (2m2-A2)B2-2,
u2m2-m02,
m01NP j=1NPSHj,m11NP j=1NPV(tj)SHj,
m21NP j=1NP[V(tj)]2SHj,
Shift(s)j=1N[V(tj-s)]2SHj,
δϕ=2πfsmax.
P2ωl2d2 exp(-2ξ) (sin2 ψ+sinh2 ξ)(ψ2+ξ2),
ψ=2πlλ (n1c1-n2c2),ξ=2πlλ n2κ2c2.
P2ωd2(thickabsorbingfilm).
P2ωl2d2,(thinfilm),

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