Abstract

The physical properties of a hologram written in a photorefractive polymer composite are predicted from a macroscopic model based on ellipsometry. An electric poling field increases the birefringence of the composite. The way that the bulk birefringence changes with the electric field is used to predict the holographic index contrast, and, by comparison with experiment, accurate deductions of the holographic space-charge field are made. A photorefractive polymer composite was used that contained 47.5 wt. % 1-(2-Ethylhexyloxy)2,5-dimethyl-4-(4 nitrophenylazo)benzene electro-optic dye. When sinusoidal modulation in optical intensity is used with high contrast, the higher spatial harmonics of the modulation of the holographic space-charge field become important. The amplitude of the first-order modulation in the space-charge field is accordingly reduced by 13% relative to the predictions of the standard model of photorefractivity in the case of a high-saturation field.

© 2000 Optical Society of America

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References

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  1. F. H. Mok, G. W. Burr, and D. Psaltis, “System metric for holographic memory systems,” Opt. Lett. 21, 896–898 (1996).
    [CrossRef] [PubMed]
  2. 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]
  3. Many studies, including Ref. 2, the more recent publication of J. A. Herlocker et al. [J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Geunther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999)] and references therein, maintain arbitrary units for birefringence and holographic index contrast.
    [CrossRef]
  4. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  5. G. G. Malliaras, V. V. Krasnikov, H. J. Bolink, and G. Hadziioannou, “Control of charge trapping in a photorefractive polymer,” Appl. Phys. Lett. 66, 1038–1040 (1995); see also D. D. Nolte, “Photorefractive transport and multi-wave mixing,” in Photorefractive Effects and Materials, D. D. Nolte, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1995), Chap. 1, pp. 12–17.
    [CrossRef]
  6. A. M. Cox, R. D. Blackburn, D. P. West, T. A. King, F. A. Wade, and D. A. Leigh, “Crystallization-resistant photorefractive polymer composite with high diffraction efficiency and reproducibility,” Appl. Phys. Lett. 68, 2801–2803 (1996).
    [CrossRef]
  7. J. D. Shakos, A. M. Cox, D. P. West, K. S. West, F. A. Wade, T. A. King, and R. D. Blackburn, “Processes limiting the rate of response in photorefractive composites,” Opt. Commun. 150, 230–234 (1998).
    [CrossRef]
  8. K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
    [CrossRef]
  9. M. D. Rahn, D. P. West, K. Khand, J. D. Shakos, R. M. Shelby, “High optical quality and fast response speed holographic data storage in a photorefractive polymer,” submitted to J. Appl. Phys.
  10. S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, “Observation of the photorefractive effect in a polymer,” Phys. Rev. Lett. 66, 1846–1849 (1991).
    [CrossRef] [PubMed]
  11. W. E. Moerner, A. Grunnet-Jepsen, and C. L. Thompson, “Photorefractive polymers,” Annu. Rev. Mater. Sci. 27, 585–623 (1997).
    [CrossRef]
  12. Z. Sekkat and W. Knoll, “Stationary state and dynamics of birefringence and nonlinear optical properties induced by electric field poling in polymeric films,” Ber. Bunsenges. Phys. Chem. 98, 1231–1242 (1994).
    [CrossRef]
  13. M. G. Kuzyk and C. Poga, “Quadratic electro-optics of guest-host polymers,” in Molecular Nonlinear Optics, J. Zyss, ed. (Academic, San Diego, Calif., 1994), p. 327.
  14. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]

1999 (1)

Many studies, including Ref. 2, the more recent publication of J. A. Herlocker et al. [J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Geunther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999)] and references therein, maintain arbitrary units for birefringence and holographic index contrast.
[CrossRef]

1998 (2)

J. D. Shakos, A. M. Cox, D. P. West, K. S. West, F. A. Wade, T. A. King, and R. D. Blackburn, “Processes limiting the rate of response in photorefractive composites,” Opt. Commun. 150, 230–234 (1998).
[CrossRef]

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

1997 (1)

W. E. Moerner, A. Grunnet-Jepsen, and C. L. Thompson, “Photorefractive polymers,” Annu. Rev. Mater. Sci. 27, 585–623 (1997).
[CrossRef]

1996 (2)

A. M. Cox, R. D. Blackburn, D. P. West, T. A. King, F. A. Wade, and D. A. Leigh, “Crystallization-resistant photorefractive polymer composite with high diffraction efficiency and reproducibility,” Appl. Phys. Lett. 68, 2801–2803 (1996).
[CrossRef]

F. H. Mok, G. W. Burr, and D. Psaltis, “System metric for holographic memory systems,” Opt. Lett. 21, 896–898 (1996).
[CrossRef] [PubMed]

1994 (2)

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]

Z. Sekkat and W. Knoll, “Stationary state and dynamics of birefringence and nonlinear optical properties induced by electric field poling in polymeric films,” Ber. Bunsenges. Phys. Chem. 98, 1231–1242 (1994).
[CrossRef]

1991 (1)

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, “Observation of the photorefractive effect in a polymer,” Phys. Rev. Lett. 66, 1846–1849 (1991).
[CrossRef] [PubMed]

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Bjorklund, G. C.

Blackburn, R. D.

J. D. Shakos, A. M. Cox, D. P. West, K. S. West, F. A. Wade, T. A. King, and R. D. Blackburn, “Processes limiting the rate of response in photorefractive composites,” Opt. Commun. 150, 230–234 (1998).
[CrossRef]

A. M. Cox, R. D. Blackburn, D. P. West, T. A. King, F. A. Wade, and D. A. Leigh, “Crystallization-resistant photorefractive polymer composite with high diffraction efficiency and reproducibility,” Appl. Phys. Lett. 68, 2801–2803 (1996).
[CrossRef]

Burr, G. W.

Cox, A. M.

J. D. Shakos, A. M. Cox, D. P. West, K. S. West, F. A. Wade, T. A. King, and R. D. Blackburn, “Processes limiting the rate of response in photorefractive composites,” Opt. Commun. 150, 230–234 (1998).
[CrossRef]

A. M. Cox, R. D. Blackburn, D. P. West, T. A. King, F. A. Wade, and D. A. Leigh, “Crystallization-resistant photorefractive polymer composite with high diffraction efficiency and reproducibility,” Appl. Phys. Lett. 68, 2801–2803 (1996).
[CrossRef]

Ducharme, S.

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, “Observation of the photorefractive effect in a polymer,” Phys. Rev. Lett. 66, 1846–1849 (1991).
[CrossRef] [PubMed]

Ferrio, K. B.

Many studies, including Ref. 2, the more recent publication of J. A. Herlocker et al. [J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Geunther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999)] and references therein, maintain arbitrary units for birefringence and holographic index contrast.
[CrossRef]

Geunther, B. D.

Many studies, including Ref. 2, the more recent publication of J. A. Herlocker et al. [J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Geunther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999)] and references therein, maintain arbitrary units for birefringence and holographic index contrast.
[CrossRef]

Grunnet-Jepsen, A.

W. E. Moerner, A. Grunnet-Jepsen, and C. L. Thompson, “Photorefractive polymers,” Annu. Rev. Mater. Sci. 27, 585–623 (1997).
[CrossRef]

Hache, F.

Hendrickx, E.

Many studies, including Ref. 2, the more recent publication of J. A. Herlocker et al. [J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Geunther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999)] and references therein, maintain arbitrary units for birefringence and holographic index contrast.
[CrossRef]

Herlocker, J. A.

Many studies, including Ref. 2, the more recent publication of J. A. Herlocker et al. [J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Geunther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999)] and references therein, maintain arbitrary units for birefringence and holographic index contrast.
[CrossRef]

Khand, K.

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

King, T. A.

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

J. D. Shakos, A. M. Cox, D. P. West, K. S. West, F. A. Wade, T. A. King, and R. D. Blackburn, “Processes limiting the rate of response in photorefractive composites,” Opt. Commun. 150, 230–234 (1998).
[CrossRef]

A. M. Cox, R. D. Blackburn, D. P. West, T. A. King, F. A. Wade, and D. A. Leigh, “Crystallization-resistant photorefractive polymer composite with high diffraction efficiency and reproducibility,” Appl. Phys. Lett. 68, 2801–2803 (1996).
[CrossRef]

Kippelen, B.

Many studies, including Ref. 2, the more recent publication of J. A. Herlocker et al. [J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Geunther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999)] and references therein, maintain arbitrary units for birefringence and holographic index contrast.
[CrossRef]

Knoll, W.

Z. Sekkat and W. Knoll, “Stationary state and dynamics of birefringence and nonlinear optical properties induced by electric field poling in polymeric films,” Ber. Bunsenges. Phys. Chem. 98, 1231–1242 (1994).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Leigh, D. A.

A. M. Cox, R. D. Blackburn, D. P. West, T. A. King, F. A. Wade, and D. A. Leigh, “Crystallization-resistant photorefractive polymer composite with high diffraction efficiency and reproducibility,” Appl. Phys. Lett. 68, 2801–2803 (1996).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Mery, S.

Many studies, including Ref. 2, the more recent publication of J. A. Herlocker et al. [J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Geunther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999)] and references therein, maintain arbitrary units for birefringence and holographic index contrast.
[CrossRef]

Moerner, W. E.

W. E. Moerner, A. Grunnet-Jepsen, and C. L. Thompson, “Photorefractive polymers,” Annu. Rev. Mater. Sci. 27, 585–623 (1997).
[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]

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, “Observation of the photorefractive effect in a polymer,” Phys. Rev. Lett. 66, 1846–1849 (1991).
[CrossRef] [PubMed]

Mok, F. H.

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Peyghambarian, N.

Many studies, including Ref. 2, the more recent publication of J. A. Herlocker et al. [J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Geunther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999)] and references therein, maintain arbitrary units for birefringence and holographic index contrast.
[CrossRef]

Psaltis, D.

Rahn, M. D.

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

Scott, J. C.

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, “Observation of the photorefractive effect in a polymer,” Phys. Rev. Lett. 66, 1846–1849 (1991).
[CrossRef] [PubMed]

Sekkat, Z.

Z. Sekkat and W. Knoll, “Stationary state and dynamics of birefringence and nonlinear optical properties induced by electric field poling in polymeric films,” Ber. Bunsenges. Phys. Chem. 98, 1231–1242 (1994).
[CrossRef]

Shakos, J. D.

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

J. D. Shakos, A. M. Cox, D. P. West, K. S. West, F. A. Wade, T. A. King, and R. D. Blackburn, “Processes limiting the rate of response in photorefractive composites,” Opt. Commun. 150, 230–234 (1998).
[CrossRef]

Silence, S. M.

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Thompson, C. L.

W. E. Moerner, A. Grunnet-Jepsen, and C. L. Thompson, “Photorefractive polymers,” Annu. Rev. Mater. Sci. 27, 585–623 (1997).
[CrossRef]

Twieg, R. J.

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, “Observation of the photorefractive effect in a polymer,” Phys. Rev. Lett. 66, 1846–1849 (1991).
[CrossRef] [PubMed]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Wade, F. A.

J. D. Shakos, A. M. Cox, D. P. West, K. S. West, F. A. Wade, T. A. King, and R. D. Blackburn, “Processes limiting the rate of response in photorefractive composites,” Opt. Commun. 150, 230–234 (1998).
[CrossRef]

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

A. M. Cox, R. D. Blackburn, D. P. West, T. A. King, F. A. Wade, and D. A. Leigh, “Crystallization-resistant photorefractive polymer composite with high diffraction efficiency and reproducibility,” Appl. Phys. Lett. 68, 2801–2803 (1996).
[CrossRef]

West, D. P.

J. D. Shakos, A. M. Cox, D. P. West, K. S. West, F. A. Wade, T. A. King, and R. D. Blackburn, “Processes limiting the rate of response in photorefractive composites,” Opt. Commun. 150, 230–234 (1998).
[CrossRef]

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

A. M. Cox, R. D. Blackburn, D. P. West, T. A. King, F. A. Wade, and D. A. Leigh, “Crystallization-resistant photorefractive polymer composite with high diffraction efficiency and reproducibility,” Appl. Phys. Lett. 68, 2801–2803 (1996).
[CrossRef]

West, K. S.

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

J. D. Shakos, A. M. Cox, D. P. West, K. S. West, F. A. Wade, T. A. King, and R. D. Blackburn, “Processes limiting the rate of response in photorefractive composites,” Opt. Commun. 150, 230–234 (1998).
[CrossRef]

Annu. Rev. Mater. Sci. (1)

W. E. Moerner, A. Grunnet-Jepsen, and C. L. Thompson, “Photorefractive polymers,” Annu. Rev. Mater. Sci. 27, 585–623 (1997).
[CrossRef]

Appl. Phys. Lett. (2)

Many studies, including Ref. 2, the more recent publication of J. A. Herlocker et al. [J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Geunther, S. Mery, B. Kippelen, and N. Peyghambarian, “Direct observation of orientation limit in a fast photorefractive polymer composite,” Appl. Phys. Lett. 74, 2253–2255 (1999)] and references therein, maintain arbitrary units for birefringence and holographic index contrast.
[CrossRef]

A. M. Cox, R. D. Blackburn, D. P. West, T. A. King, F. A. Wade, and D. A. Leigh, “Crystallization-resistant photorefractive polymer composite with high diffraction efficiency and reproducibility,” Appl. Phys. Lett. 68, 2801–2803 (1996).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Ber. Bunsenges. Phys. Chem. (1)

Z. Sekkat and W. Knoll, “Stationary state and dynamics of birefringence and nonlinear optical properties induced by electric field poling in polymeric films,” Ber. Bunsenges. Phys. Chem. 98, 1231–1242 (1994).
[CrossRef]

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. I. Steady-state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

J. Appl. Phys. (1)

K. S. West, D. P. West, M. D. Rahn, J. D. Shakos, F. A. Wade, K. Khand, and T. A. King, “Photorefractive polymer composite trapping properties and a link with chromophore structure,” J. Appl. Phys. 84, 5893–5899 (1998).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

J. D. Shakos, A. M. Cox, D. P. West, K. S. West, F. A. Wade, T. A. King, and R. D. Blackburn, “Processes limiting the rate of response in photorefractive composites,” Opt. Commun. 150, 230–234 (1998).
[CrossRef]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

S. Ducharme, J. C. Scott, R. J. Twieg, and W. E. Moerner, “Observation of the photorefractive effect in a polymer,” Phys. Rev. Lett. 66, 1846–1849 (1991).
[CrossRef] [PubMed]

Other (3)

G. G. Malliaras, V. V. Krasnikov, H. J. Bolink, and G. Hadziioannou, “Control of charge trapping in a photorefractive polymer,” Appl. Phys. Lett. 66, 1038–1040 (1995); see also D. D. Nolte, “Photorefractive transport and multi-wave mixing,” in Photorefractive Effects and Materials, D. D. Nolte, ed. (Kluwer Academic, Dordrecht, The Netherlands, 1995), Chap. 1, pp. 12–17.
[CrossRef]

M. D. Rahn, D. P. West, K. Khand, J. D. Shakos, R. M. Shelby, “High optical quality and fast response speed holographic data storage in a photorefractive polymer,” submitted to J. Appl. Phys.

M. G. Kuzyk and C. Poga, “Quadratic electro-optics of guest-host polymers,” in Molecular Nonlinear Optics, J. Zyss, ed. (Academic, San Diego, Calif., 1994), p. 327.

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Figures (8)

Fig. 1
Fig. 1

The photorefractive polymer composite consists of three components: (a) poly(N-vinylcarbazole), (b) TNF, and (c) a nonlinear dopant dye EHDNPB added at a high concentration (47.5%) to form a crystallization-resistant reorientational photorefractive polymer composite.

Fig. 2
Fig. 2

Photorefractive polymer composite device placed between two crossed Glan–Taylor polarizers. The transmission through the ellipsometer was measured as the total transmitted intensity detected relative to the intensity incident upon the sample. Transmission data as a function of poling field strength (applied along the sample normal) were taken, allowing 10 s for chromophore alignment to occur and a steady-state signal to be achieved. The time allowed for chromophore relaxation between measurements was 5 min.

Fig. 3
Fig. 3

Assuming uniaxial symmetry for the poled polymer, the refractive-index anisotropy may be described by an ellipse with principal axes ne and no. ns and np represent the refractive index seen by the s- and p-eigenpolarizations of the light entering the sample in the ellipsometer. ψ denotes the angle of the refracted light path relative to the sample normal.

Fig. 4
Fig. 4

Hologram-recording geometry: (a) Two p-polarized writing beams from a 632.8-nm He–Ne laser source interact at the polymer surface; (b) the diffraction grating vector within the polymer is tilted 58.3° from the direction of the sample normal and the poling field. The electric field vector of the probe beam is directed along bˆ. The resultant electric field in the polymer is Eres=Epol+Esc, where Esc is directed along the grating vector kˆ.ψ and β are the angles of bˆ and Eres, respectively, relative to the optic axis. The space-charge field creating the hologram has the effect of modulating not only the magnitude but also the orientation of the resultant electric field within the polymer. The two extremes of refractive index represented by Emax, the maximum resultant field, and Emin, the minimum resultant field, lead to the holographic index contrast.

Fig. 5
Fig. 5

Birefringence (ne-no) versus the applied electric poling field, E (volts per micrometer) of a photorefractive polymer device containing 47.5 wt. % EHDNPB and 1 wt. % TNF. The field transmission factors for s- and p-polarized beams As and Ap, respectively (see Appendix A), were 0.64526 and 0.76913, which are values optimized such that the linear term in the birefringence dependence on the field is minimized. These values are within the uncertainty of the experimentally determined values of As=0.645±0.02 and Ap=0.762±0.02. The fit to the data points is a quadratic, where ne-no=(4.96×10-7)E2+5.12×10-4.

Fig. 6
Fig. 6

Refractive index, predicted by Eq. (13), seen by the probe beam as a function of position as the beam propagates through the photorefractive polymer sample containing 47.5 wt. % EHDNPB and 1 wt. % TNF. The applied field was 50 Vµm-1, and the first-order modulation of the space-charge field amplitude was 87% of the value predicted by Eq. (9) in accordance with the ellipsometric results plotted in Fig. 7. The refractive-index profile is nearly sinusoidal, and the ratio of the first- and the second-harmonic amplitudes is approximately 4.6:1 when calculated by numerical methods. The amplitudes of higher-harmonic components are small and are therefore ignored.

Fig. 7
Fig. 7

Amplitude of the first Fourier component of the holographic refractive-index modulation amplitude versus the applied electric field (volts per micrometer) from a photorefractive polymer device containing 47.5 wt. % EHDNPB and 1 wt. % TNF. The dashed curve indicates the prediction based on the analysis presented in the text and the quadratic expression for the birefringence (Fig. 5) when the space-charge field is assigned according to Eq. (9). The calculation assumes that Δno=-3/10(ne-no), m=0.95. The solid curve is the corresponding prediction for use of 87% of the first-order space-charge field modulation predicted by Eq. (9). Both predictions assume a high saturation field, Eq. Inset, first-order diffracted-beam detector signal versus time after the start of the experiment for an applied field of 33 V µm-1. The shutter is closed after 70 s, which is when the detector begins to collect data; the first data point is taken as the steady-state diffracted signal. With the same power detector, the reference beam signal incident upon the sample and transmitted through the sample resulted in detector readings of 176 and 99 V, respectively. The internal and external diffraction efficiencies are therefore 5.2% and 2.9%, respectively, at this applied field. At 58 V µm-1 they are 24.4% and 13.7%, respectively, which is typical for the relatively low chromophore concentration used. The diffracted signal was allowed to decay to background levels before subsequent data were taken.

Fig. 8
Fig. 8

Diagram of the experimental arrangement used for holographic index-contrast measurements. Two plane-wave p-polarized beams, an object beam and a probe beam, intersect inside the photorefractive polymer and form a refractive-index grating by means of the reorientationally enhanced photorefractive effect. The wave plates are used to make the intensity in each beam equal to 165 mW cm-2 and hence to make m>0.95. The diameter of the object beam was 2.7 mm, and an aperture restricted the probe-beam diameter to 0.9 mm. During grating recording, a poling field is applied to the device along its normal vector, and the shutter is opened for 70 s to allow the object beam to fall onto the sample and record a grating. By this time Δnh reaches a steady-state value at all poling field strengths used. The shutter is then closed, and the decay of the diffracted beam is monitored.

Equations (34)

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1np(ψ)2=sin2 ψne2+cos2 ψno2
ne-no=sin2 ψ1Δna+ns2-cos2 ψno21/2-no,
ne-no=Δnacos2 ψ.
D=E=01+χE,
n2(ψ)|E0=1+χ(ψ)+Δχ(ψ, E),
n2(ψ)|E0=n2(ψ)|E=0+Δχ(ψ, E),
1n2(ψ)E0=1n2(ψ)E=0+Δ1n2(ψ)E=1n2(ψ)E=0-2n3Δn(ψ, E),
Eres=Epol+Esc.
Esc=σpσp+σdmEpol cos θk[1+(Epol/Eq)2]-1/2,
n(ψ)n+(ne-no)E=0 cos2 ψ,
Δn(ψ)=(ne-no)E0 cos2(ψ-β),
n(ψ)=1[n+(ne-no)E=0 cos2 ψ]2-2n3[(ne-no)E0 cos2(ψ-β)]-1/2.
n(ψ)=1[n+(ne-no)E=0 cos2 ψ]2-2n3[(ne-no)E0 cos2(ψ-β)+Δno]-1/2,
Δno=3kBTβ333-μgΔα6kBTβ333+3μgΔα(ne-no)E0
η=exp(-αL)sin2πΔnhLλeˆ1·eˆ2,
00-1.
-sin α cos ϕsin ϕ-cos ϕ cos α=nˆ.
s=nˆ  zˆ=sin φcos φ sin α0.
p=-sin α cos ϕsin ϕ0,
ψ1=90-cos-1(nˆ·pˆ)
1-cos2 ψ2=1n22(1-cos2 ψ1),
Ein=ExEy0,
Eˆin=cos asin a0,
Es=Eˆin·sˆ,
Ep=Eˆin·pˆ.
Δna=np(ψ)-ns.
Es=As exp-iπLΔnaλ(Es)sˆ,
Ep=Ap expiπLΔnaλ(Ep)pˆ,
Aˆ=cos bsin b0,
EsT=Es·Aˆ,
EpT=Ep·Aˆ.
E=EsT+EpT=As exp-iπLΔnaλ(Es)(sˆ·Aˆ)+Ap expiπLΔnaλ(Ep)(pˆ·Aˆ),
I=[As(Es)(sˆ·Aˆ)]2+[Ap(Ep)(pˆ·Aˆ)]2+2As(Es)(sˆ·Aˆ)Ap(Ep)(pˆ·Aˆ)cos2πLΔnaλ.
Δna=λ2πLcos-1I-Ts2-Tp22TsTp.

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