Abstract

The derivation of the analytical form for index-contrast growth during hologram formation in a photorefractive-polymer composite is presented. The transfer function for chromophore rotation in an amorphous medium is found initially, and this is then convolved with an exponentially growing space-charge field to determine the index-contrast transient. This analysis reveals that index-contrast growth is fully characterized by just two parameters: the rise time of the space-charge field and the rotational diffusion constant. Good agreement between theory and measurement is found for a range of materials and experimental conditions.

© 2002 Optical Society of America

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  1. R. Bittner, C. Bräuchle, and K. Meerholz, “Influence of the glass-transition temperature and the chromophore content on the grating buildup dynamics of poly(N-vinylcarbazole)-based photorefractive polymers,” Appl. Opt. 37, 2843–2851 (1998).
    [CrossRef]
  2. J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, 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).
    [CrossRef]
  3. M. A. Diaz-Garcia, D. Wright, J. D. Casperson, B. Smith, E. Glazer, W. E. Moerner, L. I. Sukhomlinova, and R. J. Tweig, “Photorefractive properties of poly(N-vinyl carbazole)-based composites for high-speed applications,” Chem. Mater. 11, 1784–1791 (1999).
    [CrossRef]
  4. D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, M. E. Moerner, and R. J. Tweig, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
    [CrossRef]
  5. D. J. Binks and D. P. West, “Analytical form for holographic contrast growth in photorefractive polymers,” Appl. Phys. B 74, 279–282 (2002).
    [CrossRef]
  6. Z. Sekkat and W. Knoll, “Stationary state and dynamics of birefringence and nonlinear optical properties induced by electric field in polymeric films,” Ber. Bunsenges. Phys. Chem. 98, 1231–1242 (1994).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. N. V. Kukhatarev, V. B. Markov, M. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1979).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2002 (1)

D. J. Binks and D. P. West, “Analytical form for holographic contrast growth in photorefractive polymers,” Appl. Phys. B 74, 279–282 (2002).
[CrossRef]

2001 (2)

D. J. Binks, K. Khand, and D. P. West, “Poling and relaxation of dipoles in dispersive media,” J. Appl. Phys. 89, 231–236 (2001).
[CrossRef]

K. Khand, D. J. Binks, D. P. West, and M. D. Rahn, “Photorefractive trapping and the correlation between recording and erasure dynamics in a polymer composite,” J. Mod. Opt. 48, 93–101 (2001).
[CrossRef]

2000 (2)

1999 (2)

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, 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).
[CrossRef]

M. A. Diaz-Garcia, D. Wright, J. D. Casperson, B. Smith, E. Glazer, W. E. Moerner, L. I. Sukhomlinova, and R. J. Tweig, “Photorefractive properties of poly(N-vinyl carbazole)-based composites for high-speed applications,” Chem. Mater. 11, 1784–1791 (1999).
[CrossRef]

1998 (3)

D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, M. E. Moerner, and R. J. Tweig, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
[CrossRef]

R. Bittner, C. Bräuchle, and K. Meerholz, “Influence of the glass-transition temperature and the chromophore content on the grating buildup dynamics of poly(N-vinylcarbazole)-based photorefractive polymers,” Appl. Opt. 37, 2843–2851 (1998).
[CrossRef]

A. Grunnet-Jepsen, D. Wright, B. Smith, M. S. Bratcher, M. S. DeClue, J. S. Siegel, and W. E. Moerner, “Spectroscopic determination of trap density in C60-sensitized photorefractive polymers,” Chem. Phys. Lett. 291, 553–561 (1998).
[CrossRef]

1994 (2)

W. E. Moerner and S. M. Silence, “Polymeric photorefractive materials,” Chem. Rev. 94, 127–155 (1994).
[CrossRef]

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

1979 (2)

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

N. V. Kukhatarev, V. B. Markov, M. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

1969 (1)

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

Binks, D. J.

D. J. Binks and D. P. West, “Analytical form for holographic contrast growth in photorefractive polymers,” Appl. Phys. B 74, 279–282 (2002).
[CrossRef]

K. Khand, D. J. Binks, D. P. West, and M. D. Rahn, “Photorefractive trapping and the correlation between recording and erasure dynamics in a polymer composite,” J. Mod. Opt. 48, 93–101 (2001).
[CrossRef]

D. J. Binks, K. Khand, and D. P. West, “Poling and relaxation of dipoles in dispersive media,” J. Appl. Phys. 89, 231–236 (2001).
[CrossRef]

D. J. Binks and D. P. West, “Dispersive rotation of dipoles in amorphous media,” Appl. Phys. Lett. 77, 1108–1110 (2000).
[CrossRef]

Bittner, R.

Bratcher, M. S.

A. Grunnet-Jepsen, D. Wright, B. Smith, M. S. Bratcher, M. S. DeClue, J. S. Siegel, and W. E. Moerner, “Spectroscopic determination of trap density in C60-sensitized photorefractive polymers,” Chem. Phys. Lett. 291, 553–561 (1998).
[CrossRef]

Bräuchle, C.

Casperson, J. D.

M. A. Diaz-Garcia, D. Wright, J. D. Casperson, B. Smith, E. Glazer, W. E. Moerner, L. I. Sukhomlinova, and R. J. Tweig, “Photorefractive properties of poly(N-vinyl carbazole)-based composites for high-speed applications,” Chem. Mater. 11, 1784–1791 (1999).
[CrossRef]

D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, M. E. Moerner, and R. J. Tweig, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
[CrossRef]

DeClue, M.

D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, M. E. Moerner, and R. J. Tweig, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
[CrossRef]

DeClue, M. S.

A. Grunnet-Jepsen, D. Wright, B. Smith, M. S. Bratcher, M. S. DeClue, J. S. Siegel, and W. E. Moerner, “Spectroscopic determination of trap density in C60-sensitized photorefractive polymers,” Chem. Phys. Lett. 291, 553–561 (1998).
[CrossRef]

Diaz-Garcia, M. A.

M. A. Diaz-Garcia, D. Wright, J. D. Casperson, B. Smith, E. Glazer, W. E. Moerner, L. I. Sukhomlinova, and R. J. Tweig, “Photorefractive properties of poly(N-vinyl carbazole)-based composites for high-speed applications,” Chem. Mater. 11, 1784–1791 (1999).
[CrossRef]

D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, M. E. Moerner, and R. J. Tweig, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
[CrossRef]

Ferrio, K. B.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, 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).
[CrossRef]

Glazer, E.

M. A. Diaz-Garcia, D. Wright, J. D. Casperson, B. Smith, E. Glazer, W. E. Moerner, L. I. Sukhomlinova, and R. J. Tweig, “Photorefractive properties of poly(N-vinyl carbazole)-based composites for high-speed applications,” Chem. Mater. 11, 1784–1791 (1999).
[CrossRef]

Grunnet-Jepsen, A.

A. Grunnet-Jepsen, D. Wright, B. Smith, M. S. Bratcher, M. S. DeClue, J. S. Siegel, and W. E. Moerner, “Spectroscopic determination of trap density in C60-sensitized photorefractive polymers,” Chem. Phys. Lett. 291, 553–561 (1998).
[CrossRef]

Guenther, B. D.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, 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).
[CrossRef]

Hendrickx, E.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, 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).
[CrossRef]

Herlocker, J. A.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, 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).
[CrossRef]

Khand, K.

D. J. Binks, K. Khand, and D. P. West, “Poling and relaxation of dipoles in dispersive media,” J. Appl. Phys. 89, 231–236 (2001).
[CrossRef]

K. Khand, D. J. Binks, D. P. West, and M. D. Rahn, “Photorefractive trapping and the correlation between recording and erasure dynamics in a polymer composite,” J. Mod. Opt. 48, 93–101 (2001).
[CrossRef]

J. D. Shakos, M. D. Rahn, D. P. West, and K. Khand, “Holographic index-contrast prediction in a photorefractive polymer composite based on electric-field-induced birefringence,” J. Opt. Soc. Am. B 17, 373–380 (2000).
[CrossRef]

Kippelen, B.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, 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).
[CrossRef]

Knoll, W.

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

Kogelnik, H.

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

Kukhatarev, N. V.

N. V. Kukhatarev, V. B. Markov, M. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Kukhaterev, N. V.

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

Markov, V. B.

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

N. V. Kukhatarev, V. B. Markov, M. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Meerholz, K.

Mery, S.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, 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).
[CrossRef]

Moerner, M. E.

D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, M. E. Moerner, and R. J. Tweig, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
[CrossRef]

Moerner, W. E.

M. A. Diaz-Garcia, D. Wright, J. D. Casperson, B. Smith, E. Glazer, W. E. Moerner, L. I. Sukhomlinova, and R. J. Tweig, “Photorefractive properties of poly(N-vinyl carbazole)-based composites for high-speed applications,” Chem. Mater. 11, 1784–1791 (1999).
[CrossRef]

A. Grunnet-Jepsen, D. Wright, B. Smith, M. S. Bratcher, M. S. DeClue, J. S. Siegel, and W. E. Moerner, “Spectroscopic determination of trap density in C60-sensitized photorefractive polymers,” Chem. Phys. Lett. 291, 553–561 (1998).
[CrossRef]

W. E. Moerner and S. M. Silence, “Polymeric photorefractive materials,” Chem. Rev. 94, 127–155 (1994).
[CrossRef]

Peyghambarian, N.

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, 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).
[CrossRef]

Rahn, M. D.

K. Khand, D. J. Binks, D. P. West, and M. D. Rahn, “Photorefractive trapping and the correlation between recording and erasure dynamics in a polymer composite,” J. Mod. Opt. 48, 93–101 (2001).
[CrossRef]

J. D. Shakos, M. D. Rahn, D. P. West, and K. Khand, “Holographic index-contrast prediction in a photorefractive polymer composite based on electric-field-induced birefringence,” J. Opt. Soc. Am. B 17, 373–380 (2000).
[CrossRef]

Sekkat, Z.

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

Shakos, J. D.

Siegel, J. S.

A. Grunnet-Jepsen, D. Wright, B. Smith, M. S. Bratcher, M. S. DeClue, J. S. Siegel, and W. E. Moerner, “Spectroscopic determination of trap density in C60-sensitized photorefractive polymers,” Chem. Phys. Lett. 291, 553–561 (1998).
[CrossRef]

Silence, S. M.

W. E. Moerner and S. M. Silence, “Polymeric photorefractive materials,” Chem. Rev. 94, 127–155 (1994).
[CrossRef]

Smith, B.

M. A. Diaz-Garcia, D. Wright, J. D. Casperson, B. Smith, E. Glazer, W. E. Moerner, L. I. Sukhomlinova, and R. J. Tweig, “Photorefractive properties of poly(N-vinyl carbazole)-based composites for high-speed applications,” Chem. Mater. 11, 1784–1791 (1999).
[CrossRef]

A. Grunnet-Jepsen, D. Wright, B. Smith, M. S. Bratcher, M. S. DeClue, J. S. Siegel, and W. E. Moerner, “Spectroscopic determination of trap density in C60-sensitized photorefractive polymers,” Chem. Phys. Lett. 291, 553–561 (1998).
[CrossRef]

Soskin, M.

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

N. V. Kukhatarev, V. B. Markov, M. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Sukhomlinova, L. I.

M. A. Diaz-Garcia, D. Wright, J. D. Casperson, B. Smith, E. Glazer, W. E. Moerner, L. I. Sukhomlinova, and R. J. Tweig, “Photorefractive properties of poly(N-vinyl carbazole)-based composites for high-speed applications,” Chem. Mater. 11, 1784–1791 (1999).
[CrossRef]

Tweig, R. J.

M. A. Diaz-Garcia, D. Wright, J. D. Casperson, B. Smith, E. Glazer, W. E. Moerner, L. I. Sukhomlinova, and R. J. Tweig, “Photorefractive properties of poly(N-vinyl carbazole)-based composites for high-speed applications,” Chem. Mater. 11, 1784–1791 (1999).
[CrossRef]

D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, M. E. Moerner, and R. J. Tweig, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhatarev, V. B. Markov, M. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

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

West, D. P.

D. J. Binks and D. P. West, “Analytical form for holographic contrast growth in photorefractive polymers,” Appl. Phys. B 74, 279–282 (2002).
[CrossRef]

K. Khand, D. J. Binks, D. P. West, and M. D. Rahn, “Photorefractive trapping and the correlation between recording and erasure dynamics in a polymer composite,” J. Mod. Opt. 48, 93–101 (2001).
[CrossRef]

D. J. Binks, K. Khand, and D. P. West, “Poling and relaxation of dipoles in dispersive media,” J. Appl. Phys. 89, 231–236 (2001).
[CrossRef]

J. D. Shakos, M. D. Rahn, D. P. West, and K. Khand, “Holographic index-contrast prediction in a photorefractive polymer composite based on electric-field-induced birefringence,” J. Opt. Soc. Am. B 17, 373–380 (2000).
[CrossRef]

D. J. Binks and D. P. West, “Dispersive rotation of dipoles in amorphous media,” Appl. Phys. Lett. 77, 1108–1110 (2000).
[CrossRef]

Wright, D.

M. A. Diaz-Garcia, D. Wright, J. D. Casperson, B. Smith, E. Glazer, W. E. Moerner, L. I. Sukhomlinova, and R. J. Tweig, “Photorefractive properties of poly(N-vinyl carbazole)-based composites for high-speed applications,” Chem. Mater. 11, 1784–1791 (1999).
[CrossRef]

A. Grunnet-Jepsen, D. Wright, B. Smith, M. S. Bratcher, M. S. DeClue, J. S. Siegel, and W. E. Moerner, “Spectroscopic determination of trap density in C60-sensitized photorefractive polymers,” Chem. Phys. Lett. 291, 553–561 (1998).
[CrossRef]

D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, M. E. Moerner, and R. J. Tweig, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. B (1)

D. J. Binks and D. P. West, “Analytical form for holographic contrast growth in photorefractive polymers,” Appl. Phys. B 74, 279–282 (2002).
[CrossRef]

Appl. Phys. Lett. (3)

J. A. Herlocker, K. B. Ferrio, E. Hendrickx, B. D. Guenther, 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).
[CrossRef]

D. Wright, M. A. Diaz-Garcia, J. D. Casperson, M. DeClue, M. E. Moerner, and R. J. Tweig, “High-speed photorefractive polymer composites,” Appl. Phys. Lett. 73, 1490–1492 (1998).
[CrossRef]

D. J. Binks and D. P. West, “Dispersive rotation of dipoles in amorphous media,” Appl. Phys. Lett. 77, 1108–1110 (2000).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick holographic media,” 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 in polymeric films,” Ber. Bunsenges. Phys. Chem. 98, 1231–1242 (1994).
[CrossRef]

Chem. Mater. (1)

M. A. Diaz-Garcia, D. Wright, J. D. Casperson, B. Smith, E. Glazer, W. E. Moerner, L. I. Sukhomlinova, and R. J. Tweig, “Photorefractive properties of poly(N-vinyl carbazole)-based composites for high-speed applications,” Chem. Mater. 11, 1784–1791 (1999).
[CrossRef]

Chem. Phys. Lett. (1)

A. Grunnet-Jepsen, D. Wright, B. Smith, M. S. Bratcher, M. S. DeClue, J. S. Siegel, and W. E. Moerner, “Spectroscopic determination of trap density in C60-sensitized photorefractive polymers,” Chem. Phys. Lett. 291, 553–561 (1998).
[CrossRef]

Chem. Rev. (1)

W. E. Moerner and S. M. Silence, “Polymeric photorefractive materials,” Chem. Rev. 94, 127–155 (1994).
[CrossRef]

Ferroelectrics (2)

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

N. V. Kukhatarev, V. B. Markov, M. Soskin, and V. L. Vinetskii, “Holographic storage in electro-optic crystals. II. Beam coupling–light amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

J. Appl. Phys. (1)

D. J. Binks, K. Khand, and D. P. West, “Poling and relaxation of dipoles in dispersive media,” J. Appl. Phys. 89, 231–236 (2001).
[CrossRef]

J. Mod. Opt. (1)

K. Khand, D. J. Binks, D. P. West, and M. D. Rahn, “Photorefractive trapping and the correlation between recording and erasure dynamics in a polymer composite,” J. Mod. Opt. 48, 93–101 (2001).
[CrossRef]

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Other (10)

M. R. Spiegel, Theory and Problems of Laplace Transforms, 1st ed. (McGraw-Hill, New York, 1965), App. B, p. 245.

M. R. Spiegel, Theory and Problems of Laplace Transforms, 1st ed. (McGraw-Hill, New York, 1965), Chap. 7, p. 202.

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products, 5th ed., A. Jeffrey, ed. (Academic, London, 1994), Vol. 1, Chap. 3, p. 366.

M. R. Spiegel, Mathematical Handbook of Formulas and Tables, 1st ed. (McGraw-Hill, New York, 1968), Vol. 1, Chap. 16, p. 101.

I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series and Products, 5th ed., A. Jeffrey, ed. (Academic, London, 1994), Vol. 1, Chap. 8, p. 951.

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in C, 1st ed. (Cambridge University, Cambridge, 1986), Vol. 1, Chap. 6, p. 171.

I. S. Gradshteyn and I. M. Ryzhik, in Tables of Integrals, Series and Products, 5th ed., A. Jeffrey, ed. (Academic, London, UK, 1994), Vol. 1, Chap. 8, p. 950.

I. S. Gradshteyn and I. M. Ryzhik, in Tables of Integrals, Series and Products, 5th ed., A. Jeffrey, ed. (Academic, London, 1994), Vol. 1, Chap. 8, p. 951.

L. Solymar, D. J. Webb, and A. Grunnet-Jepsen, The Physics and Applications of Photorefractive Materials (Oxford University, Oxford, UK, 1996).

D. J. Williams, Nonlinear Optical Properties of Organic Molecules and Crystals, D. S. Chemla and J. Zyss, eds. (Academic, New York, 1987).

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Figures (10)

Fig. 1
Fig. 1

Second-order parameter transient for various values of space-charge field rise time, τsc. The calculations utilized a diffusion constant of D0=0.059 (millisecond time scale) and an effective applied field of 26 V/µm.

Fig. 2
Fig. 2

Second-order parameter transient for various values of diffusion constant, D0 (millisecond time scale). The calculations utilized a space-charge field rise time of τsc=1 s and an effective applied field of 26 V/µm.

Fig. 3
Fig. 3

Second-order parameter transient for various values of applied field, E. The calculations utilized a space-charge field rise time of τsc=1 s and a diffusion constant of D0=0.059 (millisecond time scale).

Fig. 4
Fig. 4

Transmission-ellipsometry experiment. The sample is placed between crossed polarizers and is positioned such that its normal forms a 45° angle, in both the horizontal and vertical planes, with the path of the probe beam. This beam originates from a 5-mW helium–neon laser operating at a wavelength of 633 nm.

Fig. 5
Fig. 5

Transmission-ellipsometry transients for the materials studied.

Fig. 6
Fig. 6

Degenerate four-wave mixing experiment. The write beams and the probe used in the experiment are split off from the output of a ∼50-mW helium–neon laser operating at a wavelength of 633 nm. The zeroth- and first-order diffracted probe beams are detected by two calibrated, wide-area photodiodes.

Fig. 7
Fig. 7

Index-contrast transients for a range of total write-beam intensities. The write-beam intensities are measured external to the sample. The material used in this case is a composite of PVK:EHDNPB:C60 in the ratio, by weight, of 52:47.5:0.5. The sample was 67 µm thick, and a field of 65 V/µm was applied across it. One writing beam formed an external angle of 25° with the sample normal, and the other formed an angle of 65°. The transient was sampled at 1 kHz, but for clarity only one data point per second is plotted. The lines plotted through each data set correspond to the fit to Eq. (14).

Fig. 8
Fig. 8

Index-contrast transients for photorefractive-polymer composites containing different sensitizer species. One writing beam formed an external angle of 20° with the sample normal, and the other formed an angle of 70°. The applied field was 50 V/µm, and the total write-beam intensity was 165 mW/cm2, in each case. The transient was sampled every 100 ms, but, for clarity, only every 20th point is shown. The fit to Eq. (14) is shown as a curve through the corresponding data points.

Fig. 9
Fig. 9

Index-contrast transients for a range of applied fields. The two writing beams formed angles of 20° and 70° with the sample normal and had a total intensity of 165 mW/cm2. For clarity, only every 20th point is shown, and the fit to Eq. (14) is shown as a solid curve.

Fig. 10
Fig. 10

Path of the contour integration in the complex plane. The (×) represents the location of the pole at p=-g.

Equations (39)

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An=Pn(cos θ),
1D Ant=-n(n+1)An+u n(n+1)2n+1[An-1(t)-An+1(t)],
u=μEakT,
A2(t)=A21+τ1τ2-τ1ts1-τ2τ2-τ1ts2,
s1,2=-1τ1,2=-2D0(21-u2/5)-2D0(21),
A2=u215+u2u215.
A2(p)=A21p+τ1τ2-τ1 Γ(s1+1)ps1+1-τ2τ2-τ1 Γ(s2+1)ps2+1,
T2(p)=A2(p)Ea(p)=u15 μkT 1+τ1τ2-τ1 Γ(s1+1)ps1-τ2τ2-τ1 Γ(s2+1)ps2.
ΔnA2Eres2=[Ea+Esc cos(Kz)]2=Ea2+2Ea·Esc cos(Kz)+Esc2 cos2(Kz),
Δn1|Ea|×|Esc(t)|.
|Esc(t)|=Esc()[1-exp(-t/τsc)],
|Esc(p)|=Esc()1p-1p+τsc-1,
A2PR(p)=|Esc(p)|×T2(p)=EaEsc()15 μkT21p+k1ps1+1-k2ps2+1-1p+τsc-1+k1ps1(p+τsc-1)-k2ps2(p+τsc-1),
ki=τiτ2-τ1×Γ(si+1),i=1, 2.
A2PR(t)=EaEsc()15 μkT21+τ1τ2-τ1ts1-τ2τ2-τ1ts2-exp-tτsc×1+γ(s1+1,-t/τsc)(τ1-τ2)(-τsc)s1-γ(s2+1,-t/τsc)(τ1-τ2)(-τsc)s2,
γ(α+1, x)=0x exp(-z)×zαdz.
Δn=λLπ cos(θ1)cos(θ2)×sin-1(η),
f(p)=pm(p+g),
f(t)=12πi c-ic+i pm(p+g) exp(pt)dp.
 pm(p+g) exp(pt)dp=2πi×(residues).
f(r, θ)×exp(pt)=rm exp(imθ)r exp(iθ)+g exp[r exp(iθ)t],
rm exp(imθ)r exp(iθ)+g<Mrk asr,
CD pm(p+g) exp(pt)dp
=-0 xm(x-g) exp(-xt)exp(imπ)dx
asε0, R.
EF pm(p+g) exp(pt)dp
=0 xm(x-g) exp(-xt)exp(-imπ)dx
asε0,R.
f(t)=12πi ABf(p)exp(pt)dp=(residues)-12πi EFf(p)exp(pt)dp+CDf(p)exp(pt)dp=(-g)m exp(-gt)+sin(mπ)π 0 xm(x-g) exp(-xt)dx.
0 xm(x-g) exp(-xt)dx
=(-g)m exp(-gt)×Γ(m+1)×Γ(-m,-gt)=(-τsc)si exp(-t/τsc)×Γ(1-si)×Γ(si,-gt),
i=1, 2,
Γ(α+1, x)=x exp(-z)×zαdz.
f(t)=(-τsc)si×exp(-t/τsc)×1-sin(siπ)π×Γ(1-si)×Γ(si,-t/τsc),i=1, 2.
Γ(si+1)=siΓ(si),Γ(si)×Γ(1-si)=πsin(siπ),
γ(si,-t/τsc)=Γ(si)-Γ(si,-t/τsc).
γ(si+1,-t/τsc)=0-t/τsc exp(-z)×zsidz,
γ(si+1)=n=06 (-1)nn!(si+1+n)(-t/τsc)si+1+n,
γ(si+1)=Γ(si+1)-(-t/τsc)si×exp(-t/τsc)×n=06 (-1)n(-t/τsc)n×Γ(n-si)Γ(-si).

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