Abstract

We incorporate a mixture of polystyrene (PS) and the highly conductive N, N′-diphenyl-N, N′-bis(3-methylphenyl)-[1, 1′-biphenyl]-4, 4′-diamine (TPD) as charge transporting agent into a photorefractive composite, wherein the liquid crystal 4-cyano-4-n-pentylbiphenyl (5CB) is the electro-optical unit and the perylene bisimide dimer DiPBI acts as sensitizing component. Investigation of the photocurrent reveals a strong enhancement of the photoconductivity. Compared to composites, wherein poly-n-vinylcarbazole (PVK) is the charge transporting agent, the internal photocurrent efficiency is enhanced 11 times. This dramatic improvement is attributed to an increase of charge generation and transport and it allows for a reduction of the applied electric field to get a photoconductivity that is comparable to PVK comprising composites.

© 2012 OSA

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  14. K. Ditte, W. Jiang, T. Schemme, C. Denz, and Z. Wang, “Innovative Sensitizer DiPBI Outperforms PCBM,” Adv. Mater.24, 2104–2108 (2012).
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  21. A. Grunnet-Jepsen, D. Wright, B. Smith, M. Bratcher, M. DeClue, J. Siegel, and W. Moerner, “Spectroscopic determination of trap density in C-60-sensitized photorefractive polymers,” Chem. Phys. Lett.291, 553–561 (1998).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  28. P. Yeh, “Two-Wave Mixing in Nonlinear Media,” IEEE J. Quantum. Electron.25, 97–132 (1989).
    [CrossRef]

2012

K. Ditte, W. Jiang, T. Schemme, C. Denz, and Z. Wang, “Innovative Sensitizer DiPBI Outperforms PCBM,” Adv. Mater.24, 2104–2108 (2012).
[CrossRef] [PubMed]

2011

S. Köber, M. Salvador, and K. Meerholz, “Organic Photorefractive Materials and Applications,” Adv. Mater.23, 4725–4763 (2011).
[CrossRef]

2010

P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
[CrossRef] [PubMed]

2009

2007

J. Morgado, L. Alccer, M. Esteves, N. Pires, and B. Gigante, “New stylbene-based arylamines with dehydroabietic acid methyl ester moieties for organic light-emitting diodes,” Thin Solid Films515, 7697–7700 (2007).
[CrossRef]

H. Qian, Z. Wang, W. Yue, and D. Zhu, “Exceptional Coupling of Tetrachloroperylene Bisimide: Combination of Ullmann Reaction and C–H Transformation,” J. Am. Chem. Soc.129, 10664–10665 (2007).
[CrossRef] [PubMed]

2006

S. R. Mohan and M. Joshi, “Field dependence of hole mobility in TPD-doped polystyrene,” Solid State Commun.139, 181–185 (2006).
[CrossRef]

2004

G. B. Jung, M. Yoshida, T. Mutai, R. Fujimura, S. Ashihara, T. Shimura, K. Araki, and K. Kuroda, “High-speed TPD-based Photorefractive Polymer Composites,” Sen’i Gakkaishi60, 193–197 (2004).
[CrossRef] [PubMed]

F. Khan, A.-M. Hor, and P. R. Sundararajan, “Morphological reasoning for the enhanced charge carrier mobility of a hole transport molecule in polystyrene,” Pure Appl. Chem.76, 1509–1520 (2004).
[CrossRef]

O. Ostroverkhova and W. Moerner, “Organic photorefractives: Mechanisms, materials, and applications,” Chem. Rev.104, 3267–3314 (2004).
[CrossRef] [PubMed]

2003

M.-M. Shi, H.-Z. Chen, J.-Z. Sun, J. Ye, and M. Wang, “Excellent ambipolar photoconductivity of PVK film doped with fluoroperylene diimide,” Chem. Phys. Lett.381, 666–671 (2003).
[CrossRef]

2002

O. Ostroverkhova and K. Singer, “Space-charge dynamics in photorefractive polymers,” J. Appl. Phys.92, 1727–1743 (2002).
[CrossRef]

2001

D. V. Steenwinckel, E. Hendrickx, and A. Persoons, “Dynamics and steady-state properties of photorefractive poly(N-vinylcarbazole)-based composites sensitized with (2,4,7-trinitro-9-fluorenylidene)malononitrile in a 0–3 wt % range,” J. Chem. Phys.114, 9557–9564 (2001).
[CrossRef]

2000

E. Hendrickx, B. Kippelen, S. Thayumanavan, S. R. Marder, A. Persoons, and N. Peyghambarian, “High photogeneration efficiency of charge-transfer complexes formed between low ionization potential arylamines and C60,” J. Chem. Phys.112, 9557–9561 (2000).
[CrossRef]

T. K. Däubler, R. Bittner, K. Meerholz, V. Cimrová, and D. Neher, “Charge carrier photogeneration, trapping, and space-charge field formation in PVK-based photorefractive materials,” Phys. Rev. B61, 13515–13527 (2000).
[CrossRef]

1998

H. J. Bolink, V. V. Krasnikov, P. H. J. Kouwer, and G. Hadziioannou, “A Novel Polyaryl Ether Based Photorefractive Composite,” Chem. Mater.10, 3951–3957 (1998).
[CrossRef]

A. Grunnet-Jepsen, D. Wright, B. Smith, M. Bratcher, M. DeClue, J. Siegel, and W. Moerner, “Spectroscopic determination of trap density in C-60-sensitized photorefractive polymers,” Chem. Phys. Lett.291, 553–561 (1998).
[CrossRef]

J. Zhang and K. Singer, “Homogeneous photorefractive polymer/nematogen composite,” Appl. Phys. Lett.72, 2948–2950 (1998).
[CrossRef]

C. Denz, K.-O. Müller, T. Heimann, and T. Tschudi, “Volume holographic storage demonstrator based on phase-coded multiplexing,” IEEE J. Sel. Top. Quantum Electron.4, 832–839 (1998).
[CrossRef]

1997

K. Buse, “Light-induced charge transport processes in photorefractive crystals II: Materials,” Appl. Phys. B: Lasers Opt.64, 391–407 (1997).
[CrossRef]

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

K. Ogino, T. Nomura, T. Shichi, S.-H. Park, H. Sato, T. Aoyama, and T. Wada, “Synthesis of Polymers Having Tetraphenyldiaminobiphenyl Units for a Host Polymer of Photorefractive Composite,” Chem. Mater.9, 2768–2775 (1997).
[CrossRef]

1994

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

1989

P. Yeh, “Two-Wave Mixing in Nonlinear Media,” IEEE J. Quantum. Electron.25, 97–132 (1989).
[CrossRef]

1962

D. F. Swinehart, “The Beer-Lambert Law,” J. Chem. Educ.39, 333–335 (1962).
[CrossRef]

Alccer, L.

J. Morgado, L. Alccer, M. Esteves, N. Pires, and B. Gigante, “New stylbene-based arylamines with dehydroabietic acid methyl ester moieties for organic light-emitting diodes,” Thin Solid Films515, 7697–7700 (2007).
[CrossRef]

Aoyama, T.

K. Ogino, T. Nomura, T. Shichi, S.-H. Park, H. Sato, T. Aoyama, and T. Wada, “Synthesis of Polymers Having Tetraphenyldiaminobiphenyl Units for a Host Polymer of Photorefractive Composite,” Chem. Mater.9, 2768–2775 (1997).
[CrossRef]

Araki, K.

G. B. Jung, M. Yoshida, T. Mutai, R. Fujimura, S. Ashihara, T. Shimura, K. Araki, and K. Kuroda, “High-speed TPD-based Photorefractive Polymer Composites,” Sen’i Gakkaishi60, 193–197 (2004).
[CrossRef] [PubMed]

Ashihara, S.

G. B. Jung, M. Yoshida, T. Mutai, R. Fujimura, S. Ashihara, T. Shimura, K. Araki, and K. Kuroda, “High-speed TPD-based Photorefractive Polymer Composites,” Sen’i Gakkaishi60, 193–197 (2004).
[CrossRef] [PubMed]

Bablumian, A.

P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
[CrossRef] [PubMed]

Bittner, R.

T. K. Däubler, R. Bittner, K. Meerholz, V. Cimrová, and D. Neher, “Charge carrier photogeneration, trapping, and space-charge field formation in PVK-based photorefractive materials,” Phys. Rev. B61, 13515–13527 (2000).
[CrossRef]

Blanche, P.-A.

P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
[CrossRef] [PubMed]

Bolink, H. J.

H. J. Bolink, V. V. Krasnikov, P. H. J. Kouwer, and G. Hadziioannou, “A Novel Polyaryl Ether Based Photorefractive Composite,” Chem. Mater.10, 3951–3957 (1998).
[CrossRef]

Bratcher, M.

A. Grunnet-Jepsen, D. Wright, B. Smith, M. Bratcher, M. DeClue, J. Siegel, and W. Moerner, “Spectroscopic determination of trap density in C-60-sensitized photorefractive polymers,” Chem. Phys. Lett.291, 553–561 (1998).
[CrossRef]

Buse, K.

K. Buse, “Light-induced charge transport processes in photorefractive crystals II: Materials,” Appl. Phys. B: Lasers Opt.64, 391–407 (1997).
[CrossRef]

Chen, H.-Z.

M.-M. Shi, H.-Z. Chen, J.-Z. Sun, J. Ye, and M. Wang, “Excellent ambipolar photoconductivity of PVK film doped with fluoroperylene diimide,” Chem. Phys. Lett.381, 666–671 (2003).
[CrossRef]

Christenson, C.

P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
[CrossRef] [PubMed]

Cimrová, V.

T. K. Däubler, R. Bittner, K. Meerholz, V. Cimrová, and D. Neher, “Charge carrier photogeneration, trapping, and space-charge field formation in PVK-based photorefractive materials,” Phys. Rev. B61, 13515–13527 (2000).
[CrossRef]

Däubler, T. K.

T. K. Däubler, R. Bittner, K. Meerholz, V. Cimrová, and D. Neher, “Charge carrier photogeneration, trapping, and space-charge field formation in PVK-based photorefractive materials,” Phys. Rev. B61, 13515–13527 (2000).
[CrossRef]

DeClue, M.

A. Grunnet-Jepsen, D. Wright, B. Smith, M. Bratcher, M. DeClue, J. Siegel, and W. Moerner, “Spectroscopic determination of trap density in C-60-sensitized photorefractive polymers,” Chem. Phys. Lett.291, 553–561 (1998).
[CrossRef]

Denz, C.

K. Ditte, W. Jiang, T. Schemme, C. Denz, and Z. Wang, “Innovative Sensitizer DiPBI Outperforms PCBM,” Adv. Mater.24, 2104–2108 (2012).
[CrossRef] [PubMed]

C. Denz, K.-O. Müller, T. Heimann, and T. Tschudi, “Volume holographic storage demonstrator based on phase-coded multiplexing,” IEEE J. Sel. Top. Quantum Electron.4, 832–839 (1998).
[CrossRef]

Ditte, K.

K. Ditte, W. Jiang, T. Schemme, C. Denz, and Z. Wang, “Innovative Sensitizer DiPBI Outperforms PCBM,” Adv. Mater.24, 2104–2108 (2012).
[CrossRef] [PubMed]

Dong, H.

A. Lv, S. R. Puniredd, J. Zhang, Z. Li, H. Zhu, W. Jiang, H. Dong, Y. He, L. Jiang, Y. Li, W. Pisula, Q. Meng, W. Hu, and Z. Wang, “High Mobility Air Stable Organic Single Crystal Transistors of a n-Type Diperylene Bisimide,” Adv. Mater. (to be published).
[PubMed]

Esteves, M.

J. Morgado, L. Alccer, M. Esteves, N. Pires, and B. Gigante, “New stylbene-based arylamines with dehydroabietic acid methyl ester moieties for organic light-emitting diodes,” Thin Solid Films515, 7697–7700 (2007).
[CrossRef]

Flores, D.

P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
[CrossRef] [PubMed]

Fujimura, R.

G. B. Jung, M. Yoshida, T. Mutai, R. Fujimura, S. Ashihara, T. Shimura, K. Araki, and K. Kuroda, “High-speed TPD-based Photorefractive Polymer Composites,” Sen’i Gakkaishi60, 193–197 (2004).
[CrossRef] [PubMed]

Gigante, B.

J. Morgado, L. Alccer, M. Esteves, N. Pires, and B. Gigante, “New stylbene-based arylamines with dehydroabietic acid methyl ester moieties for organic light-emitting diodes,” Thin Solid Films515, 7697–7700 (2007).
[CrossRef]

Grunnet-Jepsen, A.

A. Grunnet-Jepsen, D. Wright, B. Smith, M. Bratcher, M. DeClue, J. Siegel, and W. Moerner, “Spectroscopic determination of trap density in C-60-sensitized photorefractive polymers,” Chem. Phys. Lett.291, 553–561 (1998).
[CrossRef]

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

Gu, T.

P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
[CrossRef] [PubMed]

Günter, P.

P. Günter and J.-P. Huignard, Photorefractive Materials and their Applications 1: Basic Effects (Springer, 2006).
[CrossRef]

Hadziioannou, G.

H. J. Bolink, V. V. Krasnikov, P. H. J. Kouwer, and G. Hadziioannou, “A Novel Polyaryl Ether Based Photorefractive Composite,” Chem. Mater.10, 3951–3957 (1998).
[CrossRef]

He, Y.

A. Lv, S. R. Puniredd, J. Zhang, Z. Li, H. Zhu, W. Jiang, H. Dong, Y. He, L. Jiang, Y. Li, W. Pisula, Q. Meng, W. Hu, and Z. Wang, “High Mobility Air Stable Organic Single Crystal Transistors of a n-Type Diperylene Bisimide,” Adv. Mater. (to be published).
[PubMed]

Heimann, T.

C. Denz, K.-O. Müller, T. Heimann, and T. Tschudi, “Volume holographic storage demonstrator based on phase-coded multiplexing,” IEEE J. Sel. Top. Quantum Electron.4, 832–839 (1998).
[CrossRef]

Hendrickx, E.

D. V. Steenwinckel, E. Hendrickx, and A. Persoons, “Dynamics and steady-state properties of photorefractive poly(N-vinylcarbazole)-based composites sensitized with (2,4,7-trinitro-9-fluorenylidene)malononitrile in a 0–3 wt % range,” J. Chem. Phys.114, 9557–9564 (2001).
[CrossRef]

E. Hendrickx, B. Kippelen, S. Thayumanavan, S. R. Marder, A. Persoons, and N. Peyghambarian, “High photogeneration efficiency of charge-transfer complexes formed between low ionization potential arylamines and C60,” J. Chem. Phys.112, 9557–9561 (2000).
[CrossRef]

Hor, A.-M.

F. Khan, A.-M. Hor, and P. R. Sundararajan, “Morphological reasoning for the enhanced charge carrier mobility of a hole transport molecule in polystyrene,” Pure Appl. Chem.76, 1509–1520 (2004).
[CrossRef]

Hsieh, W.-Y.

P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
[CrossRef] [PubMed]

Hu, W.

A. Lv, S. R. Puniredd, J. Zhang, Z. Li, H. Zhu, W. Jiang, H. Dong, Y. He, L. Jiang, Y. Li, W. Pisula, Q. Meng, W. Hu, and Z. Wang, “High Mobility Air Stable Organic Single Crystal Transistors of a n-Type Diperylene Bisimide,” Adv. Mater. (to be published).
[PubMed]

Huignard, J.-P.

P. Günter and J.-P. Huignard, Photorefractive Materials and their Applications 1: Basic Effects (Springer, 2006).
[CrossRef]

Jeong, K.

Jiang, L.

A. Lv, S. R. Puniredd, J. Zhang, Z. Li, H. Zhu, W. Jiang, H. Dong, Y. He, L. Jiang, Y. Li, W. Pisula, Q. Meng, W. Hu, and Z. Wang, “High Mobility Air Stable Organic Single Crystal Transistors of a n-Type Diperylene Bisimide,” Adv. Mater. (to be published).
[PubMed]

Jiang, W.

K. Ditte, W. Jiang, T. Schemme, C. Denz, and Z. Wang, “Innovative Sensitizer DiPBI Outperforms PCBM,” Adv. Mater.24, 2104–2108 (2012).
[CrossRef] [PubMed]

A. Lv, S. R. Puniredd, J. Zhang, Z. Li, H. Zhu, W. Jiang, H. Dong, Y. He, L. Jiang, Y. Li, W. Pisula, Q. Meng, W. Hu, and Z. Wang, “High Mobility Air Stable Organic Single Crystal Transistors of a n-Type Diperylene Bisimide,” Adv. Mater. (to be published).
[PubMed]

Joshi, M.

S. R. Mohan and M. Joshi, “Field dependence of hole mobility in TPD-doped polystyrene,” Solid State Commun.139, 181–185 (2006).
[CrossRef]

Jung, G. B.

G. B. Jung, M. Yoshida, T. Mutai, R. Fujimura, S. Ashihara, T. Shimura, K. Araki, and K. Kuroda, “High-speed TPD-based Photorefractive Polymer Composites,” Sen’i Gakkaishi60, 193–197 (2004).
[CrossRef] [PubMed]

Kathaperumal, M.

P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
[CrossRef] [PubMed]

Khan, F.

F. Khan, A.-M. Hor, and P. R. Sundararajan, “Morphological reasoning for the enhanced charge carrier mobility of a hole transport molecule in polystyrene,” Pure Appl. Chem.76, 1509–1520 (2004).
[CrossRef]

Kippelen, B.

E. Hendrickx, B. Kippelen, S. Thayumanavan, S. R. Marder, A. Persoons, and N. Peyghambarian, “High photogeneration efficiency of charge-transfer complexes formed between low ionization potential arylamines and C60,” J. Chem. Phys.112, 9557–9561 (2000).
[CrossRef]

Köber, S.

Kouwer, P. H. J.

H. J. Bolink, V. V. Krasnikov, P. H. J. Kouwer, and G. Hadziioannou, “A Novel Polyaryl Ether Based Photorefractive Composite,” Chem. Mater.10, 3951–3957 (1998).
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G. B. Jung, M. Yoshida, T. Mutai, R. Fujimura, S. Ashihara, T. Shimura, K. Araki, and K. Kuroda, “High-speed TPD-based Photorefractive Polymer Composites,” Sen’i Gakkaishi60, 193–197 (2004).
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A. Lv, S. R. Puniredd, J. Zhang, Z. Li, H. Zhu, W. Jiang, H. Dong, Y. He, L. Jiang, Y. Li, W. Pisula, Q. Meng, W. Hu, and Z. Wang, “High Mobility Air Stable Organic Single Crystal Transistors of a n-Type Diperylene Bisimide,” Adv. Mater. (to be published).
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A. Lv, S. R. Puniredd, J. Zhang, Z. Li, H. Zhu, W. Jiang, H. Dong, Y. He, L. Jiang, Y. Li, W. Pisula, Q. Meng, W. Hu, and Z. Wang, “High Mobility Air Stable Organic Single Crystal Transistors of a n-Type Diperylene Bisimide,” Adv. Mater. (to be published).
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P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
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A. Lv, S. R. Puniredd, J. Zhang, Z. Li, H. Zhu, W. Jiang, H. Dong, Y. He, L. Jiang, Y. Li, W. Pisula, Q. Meng, W. Hu, and Z. Wang, “High Mobility Air Stable Organic Single Crystal Transistors of a n-Type Diperylene Bisimide,” Adv. Mater. (to be published).
[PubMed]

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E. Hendrickx, B. Kippelen, S. Thayumanavan, S. R. Marder, A. Persoons, and N. Peyghambarian, “High photogeneration efficiency of charge-transfer complexes formed between low ionization potential arylamines and C60,” J. Chem. Phys.112, 9557–9561 (2000).
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M. Salvador, J. Prauzner, S. Köber, K. Meerholz, J. J. Turek, K. Jeong, and D. D. Nolte, “Three-dimensional holographic imaging of living tissue using a highly sensitive photorefractive polymer device,” Opt. Express17, 11834–11849 (2009).
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A. Lv, S. R. Puniredd, J. Zhang, Z. Li, H. Zhu, W. Jiang, H. Dong, Y. He, L. Jiang, Y. Li, W. Pisula, Q. Meng, W. Hu, and Z. Wang, “High Mobility Air Stable Organic Single Crystal Transistors of a n-Type Diperylene Bisimide,” Adv. Mater. (to be published).
[PubMed]

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O. Ostroverkhova and W. Moerner, “Organic photorefractives: Mechanisms, materials, and applications,” Chem. Rev.104, 3267–3314 (2004).
[CrossRef] [PubMed]

A. Grunnet-Jepsen, D. Wright, B. Smith, M. Bratcher, M. DeClue, J. Siegel, and W. Moerner, “Spectroscopic determination of trap density in C-60-sensitized photorefractive polymers,” Chem. Phys. Lett.291, 553–561 (1998).
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W. Moerner, A. Grunnet-Jepsen, and C. Thompson, “Photorefractive Polymers,” Annu. Rev. Mater. Sci.27, 585–623 (1997).
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Moerner, W. E.

W. E. Moerner and S. M. Silence, “Polymeric photorefractive materials,” Chem. Rev.94, 127–155 (1994).
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S. R. Mohan and M. Joshi, “Field dependence of hole mobility in TPD-doped polystyrene,” Solid State Commun.139, 181–185 (2006).
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J. Morgado, L. Alccer, M. Esteves, N. Pires, and B. Gigante, “New stylbene-based arylamines with dehydroabietic acid methyl ester moieties for organic light-emitting diodes,” Thin Solid Films515, 7697–7700 (2007).
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C. Denz, K.-O. Müller, T. Heimann, and T. Tschudi, “Volume holographic storage demonstrator based on phase-coded multiplexing,” IEEE J. Sel. Top. Quantum Electron.4, 832–839 (1998).
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G. B. Jung, M. Yoshida, T. Mutai, R. Fujimura, S. Ashihara, T. Shimura, K. Araki, and K. Kuroda, “High-speed TPD-based Photorefractive Polymer Composites,” Sen’i Gakkaishi60, 193–197 (2004).
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T. K. Däubler, R. Bittner, K. Meerholz, V. Cimrová, and D. Neher, “Charge carrier photogeneration, trapping, and space-charge field formation in PVK-based photorefractive materials,” Phys. Rev. B61, 13515–13527 (2000).
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Nomura, T.

K. Ogino, T. Nomura, T. Shichi, S.-H. Park, H. Sato, T. Aoyama, and T. Wada, “Synthesis of Polymers Having Tetraphenyldiaminobiphenyl Units for a Host Polymer of Photorefractive Composite,” Chem. Mater.9, 2768–2775 (1997).
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P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
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J. Thomas, R. A. Norwood, and N. Peyghambarian, “Non-linear optical polymers for photorefractive applications,” J. Mater. Chem.19, 7476–7489 (2009).
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K. Ogino, T. Nomura, T. Shichi, S.-H. Park, H. Sato, T. Aoyama, and T. Wada, “Synthesis of Polymers Having Tetraphenyldiaminobiphenyl Units for a Host Polymer of Photorefractive Composite,” Chem. Mater.9, 2768–2775 (1997).
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O. Ostroverkhova and W. Moerner, “Organic photorefractives: Mechanisms, materials, and applications,” Chem. Rev.104, 3267–3314 (2004).
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O. Ostroverkhova and K. Singer, “Space-charge dynamics in photorefractive polymers,” J. Appl. Phys.92, 1727–1743 (2002).
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K. Ogino, T. Nomura, T. Shichi, S.-H. Park, H. Sato, T. Aoyama, and T. Wada, “Synthesis of Polymers Having Tetraphenyldiaminobiphenyl Units for a Host Polymer of Photorefractive Composite,” Chem. Mater.9, 2768–2775 (1997).
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D. V. Steenwinckel, E. Hendrickx, and A. Persoons, “Dynamics and steady-state properties of photorefractive poly(N-vinylcarbazole)-based composites sensitized with (2,4,7-trinitro-9-fluorenylidene)malononitrile in a 0–3 wt % range,” J. Chem. Phys.114, 9557–9564 (2001).
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E. Hendrickx, B. Kippelen, S. Thayumanavan, S. R. Marder, A. Persoons, and N. Peyghambarian, “High photogeneration efficiency of charge-transfer complexes formed between low ionization potential arylamines and C60,” J. Chem. Phys.112, 9557–9561 (2000).
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P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
[CrossRef] [PubMed]

J. Thomas, R. A. Norwood, and N. Peyghambarian, “Non-linear optical polymers for photorefractive applications,” J. Mater. Chem.19, 7476–7489 (2009).
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E. Hendrickx, B. Kippelen, S. Thayumanavan, S. R. Marder, A. Persoons, and N. Peyghambarian, “High photogeneration efficiency of charge-transfer complexes formed between low ionization potential arylamines and C60,” J. Chem. Phys.112, 9557–9561 (2000).
[CrossRef]

Pires, N.

J. Morgado, L. Alccer, M. Esteves, N. Pires, and B. Gigante, “New stylbene-based arylamines with dehydroabietic acid methyl ester moieties for organic light-emitting diodes,” Thin Solid Films515, 7697–7700 (2007).
[CrossRef]

Pisula, W.

A. Lv, S. R. Puniredd, J. Zhang, Z. Li, H. Zhu, W. Jiang, H. Dong, Y. He, L. Jiang, Y. Li, W. Pisula, Q. Meng, W. Hu, and Z. Wang, “High Mobility Air Stable Organic Single Crystal Transistors of a n-Type Diperylene Bisimide,” Adv. Mater. (to be published).
[PubMed]

Prauzner, J.

Puniredd, S. R.

A. Lv, S. R. Puniredd, J. Zhang, Z. Li, H. Zhu, W. Jiang, H. Dong, Y. He, L. Jiang, Y. Li, W. Pisula, Q. Meng, W. Hu, and Z. Wang, “High Mobility Air Stable Organic Single Crystal Transistors of a n-Type Diperylene Bisimide,” Adv. Mater. (to be published).
[PubMed]

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H. Qian, Z. Wang, W. Yue, and D. Zhu, “Exceptional Coupling of Tetrachloroperylene Bisimide: Combination of Ullmann Reaction and C–H Transformation,” J. Am. Chem. Soc.129, 10664–10665 (2007).
[CrossRef] [PubMed]

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P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
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Sato, H.

K. Ogino, T. Nomura, T. Shichi, S.-H. Park, H. Sato, T. Aoyama, and T. Wada, “Synthesis of Polymers Having Tetraphenyldiaminobiphenyl Units for a Host Polymer of Photorefractive Composite,” Chem. Mater.9, 2768–2775 (1997).
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K. Ditte, W. Jiang, T. Schemme, C. Denz, and Z. Wang, “Innovative Sensitizer DiPBI Outperforms PCBM,” Adv. Mater.24, 2104–2108 (2012).
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M.-M. Shi, H.-Z. Chen, J.-Z. Sun, J. Ye, and M. Wang, “Excellent ambipolar photoconductivity of PVK film doped with fluoroperylene diimide,” Chem. Phys. Lett.381, 666–671 (2003).
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K. Ogino, T. Nomura, T. Shichi, S.-H. Park, H. Sato, T. Aoyama, and T. Wada, “Synthesis of Polymers Having Tetraphenyldiaminobiphenyl Units for a Host Polymer of Photorefractive Composite,” Chem. Mater.9, 2768–2775 (1997).
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G. B. Jung, M. Yoshida, T. Mutai, R. Fujimura, S. Ashihara, T. Shimura, K. Araki, and K. Kuroda, “High-speed TPD-based Photorefractive Polymer Composites,” Sen’i Gakkaishi60, 193–197 (2004).
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Siddiqui, O.

P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
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A. Grunnet-Jepsen, D. Wright, B. Smith, M. Bratcher, M. DeClue, J. Siegel, and W. Moerner, “Spectroscopic determination of trap density in C-60-sensitized photorefractive polymers,” Chem. Phys. Lett.291, 553–561 (1998).
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W. E. Moerner and S. M. Silence, “Polymeric photorefractive materials,” Chem. Rev.94, 127–155 (1994).
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O. Ostroverkhova and K. Singer, “Space-charge dynamics in photorefractive polymers,” J. Appl. Phys.92, 1727–1743 (2002).
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J. Zhang and K. Singer, “Homogeneous photorefractive polymer/nematogen composite,” Appl. Phys. Lett.72, 2948–2950 (1998).
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Smith, B.

A. Grunnet-Jepsen, D. Wright, B. Smith, M. Bratcher, M. DeClue, J. Siegel, and W. Moerner, “Spectroscopic determination of trap density in C-60-sensitized photorefractive polymers,” Chem. Phys. Lett.291, 553–561 (1998).
[CrossRef]

Steenwinckel, D. V.

D. V. Steenwinckel, E. Hendrickx, and A. Persoons, “Dynamics and steady-state properties of photorefractive poly(N-vinylcarbazole)-based composites sensitized with (2,4,7-trinitro-9-fluorenylidene)malononitrile in a 0–3 wt % range,” J. Chem. Phys.114, 9557–9564 (2001).
[CrossRef]

Sun, J.-Z.

M.-M. Shi, H.-Z. Chen, J.-Z. Sun, J. Ye, and M. Wang, “Excellent ambipolar photoconductivity of PVK film doped with fluoroperylene diimide,” Chem. Phys. Lett.381, 666–671 (2003).
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E. Hendrickx, B. Kippelen, S. Thayumanavan, S. R. Marder, A. Persoons, and N. Peyghambarian, “High photogeneration efficiency of charge-transfer complexes formed between low ionization potential arylamines and C60,” J. Chem. Phys.112, 9557–9561 (2000).
[CrossRef]

Thomas, J.

P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
[CrossRef] [PubMed]

J. Thomas, R. A. Norwood, and N. Peyghambarian, “Non-linear optical polymers for photorefractive applications,” J. Mater. Chem.19, 7476–7489 (2009).
[CrossRef]

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W. Moerner, A. Grunnet-Jepsen, and C. Thompson, “Photorefractive Polymers,” Annu. Rev. Mater. Sci.27, 585–623 (1997).
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C. Denz, K.-O. Müller, T. Heimann, and T. Tschudi, “Volume holographic storage demonstrator based on phase-coded multiplexing,” IEEE J. Sel. Top. Quantum Electron.4, 832–839 (1998).
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Voorakaranam, R.

P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
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K. Ogino, T. Nomura, T. Shichi, S.-H. Park, H. Sato, T. Aoyama, and T. Wada, “Synthesis of Polymers Having Tetraphenyldiaminobiphenyl Units for a Host Polymer of Photorefractive Composite,” Chem. Mater.9, 2768–2775 (1997).
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Wang, M.

M.-M. Shi, H.-Z. Chen, J.-Z. Sun, J. Ye, and M. Wang, “Excellent ambipolar photoconductivity of PVK film doped with fluoroperylene diimide,” Chem. Phys. Lett.381, 666–671 (2003).
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P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
[CrossRef] [PubMed]

Wang, Z.

K. Ditte, W. Jiang, T. Schemme, C. Denz, and Z. Wang, “Innovative Sensitizer DiPBI Outperforms PCBM,” Adv. Mater.24, 2104–2108 (2012).
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H. Qian, Z. Wang, W. Yue, and D. Zhu, “Exceptional Coupling of Tetrachloroperylene Bisimide: Combination of Ullmann Reaction and C–H Transformation,” J. Am. Chem. Soc.129, 10664–10665 (2007).
[CrossRef] [PubMed]

A. Lv, S. R. Puniredd, J. Zhang, Z. Li, H. Zhu, W. Jiang, H. Dong, Y. He, L. Jiang, Y. Li, W. Pisula, Q. Meng, W. Hu, and Z. Wang, “High Mobility Air Stable Organic Single Crystal Transistors of a n-Type Diperylene Bisimide,” Adv. Mater. (to be published).
[PubMed]

Wright, D.

A. Grunnet-Jepsen, D. Wright, B. Smith, M. Bratcher, M. DeClue, J. Siegel, and W. Moerner, “Spectroscopic determination of trap density in C-60-sensitized photorefractive polymers,” Chem. Phys. Lett.291, 553–561 (1998).
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P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
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Ye, J.

M.-M. Shi, H.-Z. Chen, J.-Z. Sun, J. Ye, and M. Wang, “Excellent ambipolar photoconductivity of PVK film doped with fluoroperylene diimide,” Chem. Phys. Lett.381, 666–671 (2003).
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Yeh, P.

P. Yeh, “Two-Wave Mixing in Nonlinear Media,” IEEE J. Quantum. Electron.25, 97–132 (1989).
[CrossRef]

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G. B. Jung, M. Yoshida, T. Mutai, R. Fujimura, S. Ashihara, T. Shimura, K. Araki, and K. Kuroda, “High-speed TPD-based Photorefractive Polymer Composites,” Sen’i Gakkaishi60, 193–197 (2004).
[CrossRef] [PubMed]

Yue, W.

H. Qian, Z. Wang, W. Yue, and D. Zhu, “Exceptional Coupling of Tetrachloroperylene Bisimide: Combination of Ullmann Reaction and C–H Transformation,” J. Am. Chem. Soc.129, 10664–10665 (2007).
[CrossRef] [PubMed]

Zhang, J.

J. Zhang and K. Singer, “Homogeneous photorefractive polymer/nematogen composite,” Appl. Phys. Lett.72, 2948–2950 (1998).
[CrossRef]

A. Lv, S. R. Puniredd, J. Zhang, Z. Li, H. Zhu, W. Jiang, H. Dong, Y. He, L. Jiang, Y. Li, W. Pisula, Q. Meng, W. Hu, and Z. Wang, “High Mobility Air Stable Organic Single Crystal Transistors of a n-Type Diperylene Bisimide,” Adv. Mater. (to be published).
[PubMed]

Zhu, D.

H. Qian, Z. Wang, W. Yue, and D. Zhu, “Exceptional Coupling of Tetrachloroperylene Bisimide: Combination of Ullmann Reaction and C–H Transformation,” J. Am. Chem. Soc.129, 10664–10665 (2007).
[CrossRef] [PubMed]

Zhu, H.

A. Lv, S. R. Puniredd, J. Zhang, Z. Li, H. Zhu, W. Jiang, H. Dong, Y. He, L. Jiang, Y. Li, W. Pisula, Q. Meng, W. Hu, and Z. Wang, “High Mobility Air Stable Organic Single Crystal Transistors of a n-Type Diperylene Bisimide,” Adv. Mater. (to be published).
[PubMed]

Adv. Mater.

S. Köber, M. Salvador, and K. Meerholz, “Organic Photorefractive Materials and Applications,” Adv. Mater.23, 4725–4763 (2011).
[CrossRef]

K. Ditte, W. Jiang, T. Schemme, C. Denz, and Z. Wang, “Innovative Sensitizer DiPBI Outperforms PCBM,” Adv. Mater.24, 2104–2108 (2012).
[CrossRef] [PubMed]

Annu. Rev. Mater. Sci.

W. Moerner, A. Grunnet-Jepsen, and C. Thompson, “Photorefractive Polymers,” Annu. Rev. Mater. Sci.27, 585–623 (1997).
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Appl. Phys. B: Lasers Opt.

K. Buse, “Light-induced charge transport processes in photorefractive crystals II: Materials,” Appl. Phys. B: Lasers Opt.64, 391–407 (1997).
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Appl. Phys. Lett.

J. Zhang and K. Singer, “Homogeneous photorefractive polymer/nematogen composite,” Appl. Phys. Lett.72, 2948–2950 (1998).
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Chem. Mater.

K. Ogino, T. Nomura, T. Shichi, S.-H. Park, H. Sato, T. Aoyama, and T. Wada, “Synthesis of Polymers Having Tetraphenyldiaminobiphenyl Units for a Host Polymer of Photorefractive Composite,” Chem. Mater.9, 2768–2775 (1997).
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H. J. Bolink, V. V. Krasnikov, P. H. J. Kouwer, and G. Hadziioannou, “A Novel Polyaryl Ether Based Photorefractive Composite,” Chem. Mater.10, 3951–3957 (1998).
[CrossRef]

Chem. Phys. Lett.

A. Grunnet-Jepsen, D. Wright, B. Smith, M. Bratcher, M. DeClue, J. Siegel, and W. Moerner, “Spectroscopic determination of trap density in C-60-sensitized photorefractive polymers,” Chem. Phys. Lett.291, 553–561 (1998).
[CrossRef]

M.-M. Shi, H.-Z. Chen, J.-Z. Sun, J. Ye, and M. Wang, “Excellent ambipolar photoconductivity of PVK film doped with fluoroperylene diimide,” Chem. Phys. Lett.381, 666–671 (2003).
[CrossRef]

Chem. Rev.

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

O. Ostroverkhova and W. Moerner, “Organic photorefractives: Mechanisms, materials, and applications,” Chem. Rev.104, 3267–3314 (2004).
[CrossRef] [PubMed]

IEEE J. Quantum. Electron.

P. Yeh, “Two-Wave Mixing in Nonlinear Media,” IEEE J. Quantum. Electron.25, 97–132 (1989).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron.

C. Denz, K.-O. Müller, T. Heimann, and T. Tschudi, “Volume holographic storage demonstrator based on phase-coded multiplexing,” IEEE J. Sel. Top. Quantum Electron.4, 832–839 (1998).
[CrossRef]

J. Am. Chem. Soc.

H. Qian, Z. Wang, W. Yue, and D. Zhu, “Exceptional Coupling of Tetrachloroperylene Bisimide: Combination of Ullmann Reaction and C–H Transformation,” J. Am. Chem. Soc.129, 10664–10665 (2007).
[CrossRef] [PubMed]

J. Appl. Phys.

O. Ostroverkhova and K. Singer, “Space-charge dynamics in photorefractive polymers,” J. Appl. Phys.92, 1727–1743 (2002).
[CrossRef]

J. Chem. Educ.

D. F. Swinehart, “The Beer-Lambert Law,” J. Chem. Educ.39, 333–335 (1962).
[CrossRef]

J. Chem. Phys.

E. Hendrickx, B. Kippelen, S. Thayumanavan, S. R. Marder, A. Persoons, and N. Peyghambarian, “High photogeneration efficiency of charge-transfer complexes formed between low ionization potential arylamines and C60,” J. Chem. Phys.112, 9557–9561 (2000).
[CrossRef]

D. V. Steenwinckel, E. Hendrickx, and A. Persoons, “Dynamics and steady-state properties of photorefractive poly(N-vinylcarbazole)-based composites sensitized with (2,4,7-trinitro-9-fluorenylidene)malononitrile in a 0–3 wt % range,” J. Chem. Phys.114, 9557–9564 (2001).
[CrossRef]

J. Mater. Chem.

J. Thomas, R. A. Norwood, and N. Peyghambarian, “Non-linear optical polymers for photorefractive applications,” J. Mater. Chem.19, 7476–7489 (2009).
[CrossRef]

Nature

P.-A. Blanche, A. Bablumian, R. Voorakaranam, C. Christenson, W. Lin, T. Gu, D. Flores, P. Wang, W.-Y. Hsieh, M. Kathaperumal, B. Rachwal, O. Siddiqui, J. Thomas, R. A. Norwood, M. Yamamoto, and N. Peyghambarian, “Holographic three-dimensional telepresence using large-area photorefractive polymer,” Nature468, 80–83 (2010).
[CrossRef] [PubMed]

Opt. Express

Phys. Rev. B

T. K. Däubler, R. Bittner, K. Meerholz, V. Cimrová, and D. Neher, “Charge carrier photogeneration, trapping, and space-charge field formation in PVK-based photorefractive materials,” Phys. Rev. B61, 13515–13527 (2000).
[CrossRef]

Pure Appl. Chem.

F. Khan, A.-M. Hor, and P. R. Sundararajan, “Morphological reasoning for the enhanced charge carrier mobility of a hole transport molecule in polystyrene,” Pure Appl. Chem.76, 1509–1520 (2004).
[CrossRef]

Sen’i Gakkaishi

G. B. Jung, M. Yoshida, T. Mutai, R. Fujimura, S. Ashihara, T. Shimura, K. Araki, and K. Kuroda, “High-speed TPD-based Photorefractive Polymer Composites,” Sen’i Gakkaishi60, 193–197 (2004).
[CrossRef] [PubMed]

Solid State Commun.

S. R. Mohan and M. Joshi, “Field dependence of hole mobility in TPD-doped polystyrene,” Solid State Commun.139, 181–185 (2006).
[CrossRef]

Thin Solid Films

J. Morgado, L. Alccer, M. Esteves, N. Pires, and B. Gigante, “New stylbene-based arylamines with dehydroabietic acid methyl ester moieties for organic light-emitting diodes,” Thin Solid Films515, 7697–7700 (2007).
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A. Lv, S. R. Puniredd, J. Zhang, Z. Li, H. Zhu, W. Jiang, H. Dong, Y. He, L. Jiang, Y. Li, W. Pisula, Q. Meng, W. Hu, and Z. Wang, “High Mobility Air Stable Organic Single Crystal Transistors of a n-Type Diperylene Bisimide,” Adv. Mater. (to be published).
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P. Günter and J.-P. Huignard, Photorefractive Materials and their Applications 1: Basic Effects (Springer, 2006).
[CrossRef]

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Figures (3)

Fig. 1
Fig. 1

Absorption spectra of samples containing PS:TPD or PVK as hole transporter.

Fig. 2
Fig. 2

Comparison of the internal photocurrent efficiency of samples containing PS:TPD or PVK as hole transporter in dependence on the applied electric field.

Fig. 3
Fig. 3

Dependence of the two-beam coupling gain coefficient on the applied electric field for PS:TPD and PVK containing samples.

Tables (1)

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Table 1 Energy Levels of the Components 5CB [21], PVK [22], TPD [23], and DiPBI [24]

Equations (3)

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σ ph = I ph a E ext .
ϕ int = σ ph E ext h ν e α d W ,
Γ = 1 L [ ln ( γ b ) ln ( 1 + b γ ) ] ,

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