Abstract

A novel, to our knowledge, liquid-crystal panel suitable for real-time holographic purposes has been prepared. A nematic liquid-crystal layer sandwiched between photoconducting polymeric layers, when exposed to a sinusoidal light-intensity pattern, shows efficient formation of refractive-index gratings. The unique feature of the presented panel is its ability to switch energy from beam to beam in a manner similar to the charge-diffusion-controlled photorefractive effect. In a two-wave-mixing experiment multiple orders of diffraction are present, and a very high two-beam coupling-gain ratio (2.5) and a net exponential gain coefficient of Γ = 931 cm-1 have been measured. This gain was achieved in samples biased by a dc external electric field and tilted with respect to the beam-incidence bisector at 45°. The time constants for grating formation and erasure in the studied system are functions of the applied voltage and can be made as short as a few milliseconds under favorable conditions. The mechanism of beam coupling is linked with an electric-field-driven reorientation of the nematic director as a result of a spatially modulated space-charge field created by light in a photoconducting poly(3-octyl)thiophene polymeric layer.

© 1998 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  42. Data supplied with the E7 liquid crystal by Merck KGaA, D-64271 Darmstadt, Germany.
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    [CrossRef]
  47. L. Wang, G. Moddel, “Resolution limits from charge transport in optically addressed spatial light modulators,” J. Appl. Phys. 78, 69–73 (1995).
    [CrossRef]
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    [CrossRef]

1997 (1)

P. Tayebati, E. Canoglu, C. Hantzis, R. N. Sacks, “High-speed all-semiconductor optically addressed spatial light modulator,” Appl. Phys. Lett. 71, 1610–1612 (1997).
[CrossRef]

1996 (6)

J. Contzen, G. Heppke, H. S. Kitzerow, D. Kruerke, H. Schmid, “Storage of laser-induced holographic gratings in discotic liquid crystals,” Appl. Phys. B Laser Opt. 63, 605–608 (1996).

Y. Okada-Shudo, I. Yamaguhi, H. Tomioka, H. Sasabe, “Real-time image processing using polarization discrimination of bacteriorhodopsin,” Synthet. Metals 81, 147–149 (1996).
[CrossRef]

S. Bartkiewicz, A. Miniewicz, “Mechanism of optical recording in doped liquid crystals,” Adv. Mater. Opt. Electron. 6, 219–224 (1996).
[CrossRef]

I. C. Khoo, “Orientational photorefractive effects in nematic liquid crystals films,” IEEE J. Quantum Electron. 32, 525–534 (1996).
[CrossRef]

C. Sentein, B. Mouanda, A. Rosilio, C. Rosilio, “Influence of stereoregularity on the photoinitiated electrical conductivity of poly(3-alkylthiophenes),” Synthet. Metals 83, 27–37 (1996).
[CrossRef]

S. Bartkiewicz, A. Miniewicz, A. Januszko, J. Parka, “Dye-doped liquid crystal composite for real-time holography,” Pure Appl. Opt. 5, 799–809 (1996).
[CrossRef]

1995 (5)

I. C. Khoo, “Holographic grating formation in dye- and fullerene C60-doped nematic liquid-crystal film,” Opt. Lett. 20, 2137–2139 (1995).
[CrossRef] [PubMed]

S. Bartkiewicz, A. Miniewicz, “Methylene blue sensitized poly(methyl methacrylate) matrix: a novel holographic material,” Appl. Opt. 34, 5175–5178 (1995).
[CrossRef] [PubMed]

L. Wang, G. Moddel, “Resolution limits from charge transport in optically addressed spatial light modulators,” J. Appl. Phys. 78, 69–73 (1995).
[CrossRef]

G. P. Wiederrecht, B. A. Yoon, M. R. Wasielewski, “High photorefractive gain in nematic liquid crystals doped with electron donor and acceptor molecules,” Science 270, 1794–1797 (1995).
[CrossRef]

D. M. Burland, G. C. Bjorklund, W. E. Moerner, S. M. Silence, J. J. Stankus, “Photorefractive polymer—A status report,” Pure Appl. Chem. 67, 33–38 (1995).
[CrossRef]

1994 (9)

M. Liphardt, A. Goonesekera, B. E. Jones, S. Ducharme, J. M. Takacs, L. Zhang, “High-performance photorefractive polymers,” Science 263, 367–369 (1994).
[CrossRef] [PubMed]

E. V. Rudenko, A. V. Sukhov, “Optically induced space charge field in nematics and orientational nonlinearity,” (in Russian) JETP 105, 1621–1634 (1994).

H. Li, Y. Liang, I. C. Khoo, “Transient laser induced orthogonal director-axis reorientation in dye-doped liquid crystals (DDLC),” Mol. Cryst. Liq. Cryst. 251, 85–92 (1994).
[CrossRef]

P. R. Barbier, L. Wang, G. Moddel, “Thin-film photosensor design for liquid crystal spatial light modulators,” Opt. Eng. 33, 1322–1329 (1994).
[CrossRef]

N. Hawiltschek, E. Gärtner, P. Gussek, F. Reichel, “Properties and application of liquid crystal spatial light modulators in optical signal processing,” Exp. Tech. Phys. 40, 199–239 (1994).

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, N. Peyghambarian, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–499 (1994).
[CrossRef]

I. Jánossy, “Molecular interpretation of the absorption-induced optical reorientation of nematic liquid crystals,” Phys. Rev. E 49, 2957–2963 (1994).
[CrossRef]

I. C. Khoo, H. Li, Y. Liang, “Observation of orientational photorefractive effects in nematic liquid crystals,” Opt. Lett. 19, 1723–1725 (1994).
[CrossRef] [PubMed]

H. Seiberle, M. Schadt, “LC-conductivity and cell parameters; their influence on twisted nematic and supertwisted nematic liquid crystal displays,” Mol. Cryst. Liq. Cryst. 239, 229–244 (1994).
[CrossRef]

1993 (3)

J.-M. Nunzi, F. Charra, N. Pfeffer, “Optimization of an ultrafast OASLM using photoexcitations in organic thin films: the incoherent-to-coherent conversion efficiency of spectral concentration,” J. Phys. III (France) 3, 1401–1411 (1993).
[CrossRef]

I. C. Khoo, H. Li, Y. Liang, “Optically induced extraordinarily large negative orientational nonlinearity in dye-doped liquid crystal,” IEEE J. Quantum Electron. 29, 1444–1447 (1993).
[CrossRef]

C. Carré, D. J. Lougnot, “Photopolymers for holographic recording: from standard to self-processing materials,” J. Phys. III 3, 1445–1460 (1993).

1992 (6)

B. G. Sfez, E. V. K. Rao, Y. I. Nissim, J. L. Oudar, “Operation of nonlinear GaAs/AlGaAs multiple quantum well microresonators fabricated using alloy-mixing techniques,” Appl. Phys. Lett. 60, 607–609 (1992).
[CrossRef]

T. Kurokawa, S. Fukushima, “Spatial light modulators using ferroelectric liquid crystals,” Opt. Quantum Electron. 24, 1151–1163 (1992).
[CrossRef]

A. G. Chen, D. J. Brady, “Real-time holography in azo-dye-doped liquid crystals,” Opt. Lett. 17, 441–443 (1992).
[CrossRef] [PubMed]

S. Boj, G. Pauliat, G. Roosen, “Dynamic holographic memory showing readout, refreshing, and updating capabilities,” Opt. Lett. 17, 438–440 (1992).
[CrossRef] [PubMed]

I. Jánossy, T. Kôsa, “Influence of anthraquinone dyes on optical reorientation of nematic liquid crystals,” Opt. Lett. 17, 1183–1185 (1992).
[CrossRef] [PubMed]

N. T. Binh, M. Gailberger, H. Bassler, “Photoconduction in poly(3-alkylthiophene). I. Charge carrier generation,” Synthet. Metals 47, 77–86 (1992).
[CrossRef]

1991 (4)

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[CrossRef]

C. C. Mao, K. M. Johnson, G. Moddel, “Optical phase conjugation using optically addressed chiral smectic liquid crystal spatial light modulators,” Ferroelectrics 114, 45–53 (1991).
[CrossRef]

D. Oesterhelt, C. Bräuchle, N. Hampp, “Bacteriorhodopsin: a biological material for information processing,” Q. Rev. Biophys. 24, 425–478 (1991).
[CrossRef] [PubMed]

R. K. Kostuk, J. W. Goodman, “Refractive index modulation mechanism in bleached silver halide holograms,” Appl. Opt. 30, 369–371 (1991).
[CrossRef] [PubMed]

1990 (1)

I. Jánossy, A. D. Lloyd, B. S. Wherrett, “Anomalous optical Fréedericksz transition in an absorbing liquid crystal,” Mol. Cryst. Liq. Cryst. 179, 1–12 (1990).

1988 (2)

A. Miniewicz, S. Bartkiewicz, F. Kajzar, “On the dynamics of coherent amplification of light observed in liquid crystal panel with photoconducting polymeric layers,” Nonlin. Opt. 19, 157–175 (1988).

P. Hariharan, C. M. Chidley, “Photographic phase holograms: spatial frequency effects with conventional and reversal bleaches,” Appl. Opt. 27, 3065–3067 (1988).
[CrossRef] [PubMed]

1974 (1)

W. R. Roach, “Resolution of electro-optic light valves,” IEEE Trans. Electron Devices ED-21, 453–459 (1974).
[CrossRef]

1971 (1)

1970 (1)

Barbier, P. R.

P. R. Barbier, L. Wang, G. Moddel, “Thin-film photosensor design for liquid crystal spatial light modulators,” Opt. Eng. 33, 1322–1329 (1994).
[CrossRef]

Bartkiewicz, S.

S. Bartkiewicz, A. Miniewicz, “Mechanism of optical recording in doped liquid crystals,” Adv. Mater. Opt. Electron. 6, 219–224 (1996).
[CrossRef]

S. Bartkiewicz, A. Miniewicz, A. Januszko, J. Parka, “Dye-doped liquid crystal composite for real-time holography,” Pure Appl. Opt. 5, 799–809 (1996).
[CrossRef]

S. Bartkiewicz, A. Miniewicz, “Methylene blue sensitized poly(methyl methacrylate) matrix: a novel holographic material,” Appl. Opt. 34, 5175–5178 (1995).
[CrossRef] [PubMed]

A. Miniewicz, S. Bartkiewicz, F. Kajzar, “On the dynamics of coherent amplification of light observed in liquid crystal panel with photoconducting polymeric layers,” Nonlin. Opt. 19, 157–175 (1988).

A. Miniewicz, S. Bartkiewicz, A. Januszko, J. Parka, “Dye-doped liquid crystal for real-time holography: nematic reorientation induced by photoconductivity,” in Photoactive Organic Materials Science and Application, Vol. 3/9 of NATO ASI Series, F. Kajzar, V. M. Agranovich, C. Y.-C. Lee, eds. (Kluwer, Dordrecht, the Netherlands, 1996), pp. 487–500.
[CrossRef]

A. Miniewicz, S. Bartkiewicz, W. Turalski, A. Januszko, “Dye-doped liquid crystals for real-time holography,” in Electrical and Related Properties of Organic Solids, Vol. 3/24 of NATO ASI Series, R. W. Munn, A. Miniewicz, B. Kuchta, eds. (Kluwer, Dordrecht, the Netherlands, 1997), pp. 323–337.
[CrossRef]

Bassler, H.

N. T. Binh, M. Gailberger, H. Bassler, “Photoconduction in poly(3-alkylthiophene). I. Charge carrier generation,” Synthet. Metals 47, 77–86 (1992).
[CrossRef]

Binh, N. T.

N. T. Binh, M. Gailberger, H. Bassler, “Photoconduction in poly(3-alkylthiophene). I. Charge carrier generation,” Synthet. Metals 47, 77–86 (1992).
[CrossRef]

Bjorklund, G. C.

D. M. Burland, G. C. Bjorklund, W. E. Moerner, S. M. Silence, J. J. Stankus, “Photorefractive polymer—A status report,” Pure Appl. Chem. 67, 33–38 (1995).
[CrossRef]

Boj, S.

Brady, D. J.

Bräuchle, C.

D. Oesterhelt, C. Bräuchle, N. Hampp, “Bacteriorhodopsin: a biological material for information processing,” Q. Rev. Biophys. 24, 425–478 (1991).
[CrossRef] [PubMed]

Burland, D. M.

D. M. Burland, G. C. Bjorklund, W. E. Moerner, S. M. Silence, J. J. Stankus, “Photorefractive polymer—A status report,” Pure Appl. Chem. 67, 33–38 (1995).
[CrossRef]

Canoglu, E.

P. Tayebati, E. Canoglu, C. Hantzis, R. N. Sacks, “High-speed all-semiconductor optically addressed spatial light modulator,” Appl. Phys. Lett. 71, 1610–1612 (1997).
[CrossRef]

Carré, C.

C. Carré, D. J. Lougnot, “Photopolymers for holographic recording: from standard to self-processing materials,” J. Phys. III 3, 1445–1460 (1993).

Charra, F.

J.-M. Nunzi, F. Charra, N. Pfeffer, “Optimization of an ultrafast OASLM using photoexcitations in organic thin films: the incoherent-to-coherent conversion efficiency of spectral concentration,” J. Phys. III (France) 3, 1401–1411 (1993).
[CrossRef]

Chemla, D. S.

D. A. B. Miller, D. S. Chemla, S. Schmitt-Rink, “Electric field dependence of opticle properties of semiconductor quantum wells: physics and applications,” in Optical Nonlinearities and Instabilities in Semiconductors, H. Haug, ed. (Academic, Boston, Mass., 1988), pp. 325–359.
[CrossRef]

Chen, A. G.

Chidley, C. M.

Colbrum, W. S.

Contzen, J.

J. Contzen, G. Heppke, H. S. Kitzerow, D. Kruerke, H. Schmid, “Storage of laser-induced holographic gratings in discotic liquid crystals,” Appl. Phys. B Laser Opt. 63, 605–608 (1996).

Ducharme, S.

M. Liphardt, A. Goonesekera, B. E. Jones, S. Ducharme, J. M. Takacs, L. Zhang, “High-performance photorefractive polymers,” Science 263, 367–369 (1994).
[CrossRef] [PubMed]

Eichler, H. J.

H. J. Eichler, P. Günter, D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986).
[CrossRef]

Fukushima, S.

T. Kurokawa, S. Fukushima, “Spatial light modulators using ferroelectric liquid crystals,” Opt. Quantum Electron. 24, 1151–1163 (1992).
[CrossRef]

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[CrossRef]

Gailberger, M.

N. T. Binh, M. Gailberger, H. Bassler, “Photoconduction in poly(3-alkylthiophene). I. Charge carrier generation,” Synthet. Metals 47, 77–86 (1992).
[CrossRef]

Gärtner, E.

N. Hawiltschek, E. Gärtner, P. Gussek, F. Reichel, “Properties and application of liquid crystal spatial light modulators in optical signal processing,” Exp. Tech. Phys. 40, 199–239 (1994).

Goodman, J. W.

Goonesekera, A.

M. Liphardt, A. Goonesekera, B. E. Jones, S. Ducharme, J. M. Takacs, L. Zhang, “High-performance photorefractive polymers,” Science 263, 367–369 (1994).
[CrossRef] [PubMed]

Günter, P.

H. J. Eichler, P. Günter, D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986).
[CrossRef]

Gussek, P.

N. Hawiltschek, E. Gärtner, P. Gussek, F. Reichel, “Properties and application of liquid crystal spatial light modulators in optical signal processing,” Exp. Tech. Phys. 40, 199–239 (1994).

Haines, K. A.

Hampp, N.

D. Oesterhelt, C. Bräuchle, N. Hampp, “Bacteriorhodopsin: a biological material for information processing,” Q. Rev. Biophys. 24, 425–478 (1991).
[CrossRef] [PubMed]

Hantzis, C.

P. Tayebati, E. Canoglu, C. Hantzis, R. N. Sacks, “High-speed all-semiconductor optically addressed spatial light modulator,” Appl. Phys. Lett. 71, 1610–1612 (1997).
[CrossRef]

Hariharan, P.

Harper, J. S.

Hawiltschek, N.

N. Hawiltschek, E. Gärtner, P. Gussek, F. Reichel, “Properties and application of liquid crystal spatial light modulators in optical signal processing,” Exp. Tech. Phys. 40, 199–239 (1994).

Heppke, G.

J. Contzen, G. Heppke, H. S. Kitzerow, D. Kruerke, H. Schmid, “Storage of laser-induced holographic gratings in discotic liquid crystals,” Appl. Phys. B Laser Opt. 63, 605–608 (1996).

Jánossy, I.

I. Jánossy, “Molecular interpretation of the absorption-induced optical reorientation of nematic liquid crystals,” Phys. Rev. E 49, 2957–2963 (1994).
[CrossRef]

I. Jánossy, T. Kôsa, “Influence of anthraquinone dyes on optical reorientation of nematic liquid crystals,” Opt. Lett. 17, 1183–1185 (1992).
[CrossRef] [PubMed]

I. Jánossy, A. D. Lloyd, B. S. Wherrett, “Anomalous optical Fréedericksz transition in an absorbing liquid crystal,” Mol. Cryst. Liq. Cryst. 179, 1–12 (1990).

Januszko, A.

S. Bartkiewicz, A. Miniewicz, A. Januszko, J. Parka, “Dye-doped liquid crystal composite for real-time holography,” Pure Appl. Opt. 5, 799–809 (1996).
[CrossRef]

A. Miniewicz, S. Bartkiewicz, W. Turalski, A. Januszko, “Dye-doped liquid crystals for real-time holography,” in Electrical and Related Properties of Organic Solids, Vol. 3/24 of NATO ASI Series, R. W. Munn, A. Miniewicz, B. Kuchta, eds. (Kluwer, Dordrecht, the Netherlands, 1997), pp. 323–337.
[CrossRef]

A. Miniewicz, S. Bartkiewicz, A. Januszko, J. Parka, “Dye-doped liquid crystal for real-time holography: nematic reorientation induced by photoconductivity,” in Photoactive Organic Materials Science and Application, Vol. 3/9 of NATO ASI Series, F. Kajzar, V. M. Agranovich, C. Y.-C. Lee, eds. (Kluwer, Dordrecht, the Netherlands, 1996), pp. 487–500.
[CrossRef]

Johnson, K. M.

C. C. Mao, K. M. Johnson, G. Moddel, “Optical phase conjugation using optically addressed chiral smectic liquid crystal spatial light modulators,” Ferroelectrics 114, 45–53 (1991).
[CrossRef]

Jones, B. E.

M. Liphardt, A. Goonesekera, B. E. Jones, S. Ducharme, J. M. Takacs, L. Zhang, “High-performance photorefractive polymers,” Science 263, 367–369 (1994).
[CrossRef] [PubMed]

Kajzar, F.

A. Miniewicz, S. Bartkiewicz, F. Kajzar, “On the dynamics of coherent amplification of light observed in liquid crystal panel with photoconducting polymeric layers,” Nonlin. Opt. 19, 157–175 (1988).

Khoo, I. C.

I. C. Khoo, “Orientational photorefractive effects in nematic liquid crystals films,” IEEE J. Quantum Electron. 32, 525–534 (1996).
[CrossRef]

I. C. Khoo, “Holographic grating formation in dye- and fullerene C60-doped nematic liquid-crystal film,” Opt. Lett. 20, 2137–2139 (1995).
[CrossRef] [PubMed]

H. Li, Y. Liang, I. C. Khoo, “Transient laser induced orthogonal director-axis reorientation in dye-doped liquid crystals (DDLC),” Mol. Cryst. Liq. Cryst. 251, 85–92 (1994).
[CrossRef]

I. C. Khoo, H. Li, Y. Liang, “Observation of orientational photorefractive effects in nematic liquid crystals,” Opt. Lett. 19, 1723–1725 (1994).
[CrossRef] [PubMed]

I. C. Khoo, H. Li, Y. Liang, “Optically induced extraordinarily large negative orientational nonlinearity in dye-doped liquid crystal,” IEEE J. Quantum Electron. 29, 1444–1447 (1993).
[CrossRef]

I. C. Khoo, Liquid Crystals Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).

Kippelen, B.

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, N. Peyghambarian, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–499 (1994).
[CrossRef]

Kitzerow, H. S.

J. Contzen, G. Heppke, H. S. Kitzerow, D. Kruerke, H. Schmid, “Storage of laser-induced holographic gratings in discotic liquid crystals,” Appl. Phys. B Laser Opt. 63, 605–608 (1996).

Kôsa, T.

Kostuk, R. K.

Kruerke, D.

J. Contzen, G. Heppke, H. S. Kitzerow, D. Kruerke, H. Schmid, “Storage of laser-induced holographic gratings in discotic liquid crystals,” Appl. Phys. B Laser Opt. 63, 605–608 (1996).

Kurokawa, T.

T. Kurokawa, S. Fukushima, “Spatial light modulators using ferroelectric liquid crystals,” Opt. Quantum Electron. 24, 1151–1163 (1992).
[CrossRef]

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[CrossRef]

Li, H.

I. C. Khoo, H. Li, Y. Liang, “Observation of orientational photorefractive effects in nematic liquid crystals,” Opt. Lett. 19, 1723–1725 (1994).
[CrossRef] [PubMed]

H. Li, Y. Liang, I. C. Khoo, “Transient laser induced orthogonal director-axis reorientation in dye-doped liquid crystals (DDLC),” Mol. Cryst. Liq. Cryst. 251, 85–92 (1994).
[CrossRef]

I. C. Khoo, H. Li, Y. Liang, “Optically induced extraordinarily large negative orientational nonlinearity in dye-doped liquid crystal,” IEEE J. Quantum Electron. 29, 1444–1447 (1993).
[CrossRef]

Liang, Y.

H. Li, Y. Liang, I. C. Khoo, “Transient laser induced orthogonal director-axis reorientation in dye-doped liquid crystals (DDLC),” Mol. Cryst. Liq. Cryst. 251, 85–92 (1994).
[CrossRef]

I. C. Khoo, H. Li, Y. Liang, “Observation of orientational photorefractive effects in nematic liquid crystals,” Opt. Lett. 19, 1723–1725 (1994).
[CrossRef] [PubMed]

I. C. Khoo, H. Li, Y. Liang, “Optically induced extraordinarily large negative orientational nonlinearity in dye-doped liquid crystal,” IEEE J. Quantum Electron. 29, 1444–1447 (1993).
[CrossRef]

Liphardt, M.

M. Liphardt, A. Goonesekera, B. E. Jones, S. Ducharme, J. M. Takacs, L. Zhang, “High-performance photorefractive polymers,” Science 263, 367–369 (1994).
[CrossRef] [PubMed]

Lloyd, A. D.

I. Jánossy, A. D. Lloyd, B. S. Wherrett, “Anomalous optical Fréedericksz transition in an absorbing liquid crystal,” Mol. Cryst. Liq. Cryst. 179, 1–12 (1990).

Lougnot, D. J.

C. Carré, D. J. Lougnot, “Photopolymers for holographic recording: from standard to self-processing materials,” J. Phys. III 3, 1445–1460 (1993).

Mao, C. C.

C. C. Mao, K. M. Johnson, G. Moddel, “Optical phase conjugation using optically addressed chiral smectic liquid crystal spatial light modulators,” Ferroelectrics 114, 45–53 (1991).
[CrossRef]

Meerholz, K.

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, N. Peyghambarian, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–499 (1994).
[CrossRef]

Miller, D. A. B.

D. A. B. Miller, D. S. Chemla, S. Schmitt-Rink, “Electric field dependence of opticle properties of semiconductor quantum wells: physics and applications,” in Optical Nonlinearities and Instabilities in Semiconductors, H. Haug, ed. (Academic, Boston, Mass., 1988), pp. 325–359.
[CrossRef]

Miniewicz, A.

S. Bartkiewicz, A. Miniewicz, “Mechanism of optical recording in doped liquid crystals,” Adv. Mater. Opt. Electron. 6, 219–224 (1996).
[CrossRef]

S. Bartkiewicz, A. Miniewicz, A. Januszko, J. Parka, “Dye-doped liquid crystal composite for real-time holography,” Pure Appl. Opt. 5, 799–809 (1996).
[CrossRef]

S. Bartkiewicz, A. Miniewicz, “Methylene blue sensitized poly(methyl methacrylate) matrix: a novel holographic material,” Appl. Opt. 34, 5175–5178 (1995).
[CrossRef] [PubMed]

A. Miniewicz, S. Bartkiewicz, F. Kajzar, “On the dynamics of coherent amplification of light observed in liquid crystal panel with photoconducting polymeric layers,” Nonlin. Opt. 19, 157–175 (1988).

A. Miniewicz, S. Bartkiewicz, A. Januszko, J. Parka, “Dye-doped liquid crystal for real-time holography: nematic reorientation induced by photoconductivity,” in Photoactive Organic Materials Science and Application, Vol. 3/9 of NATO ASI Series, F. Kajzar, V. M. Agranovich, C. Y.-C. Lee, eds. (Kluwer, Dordrecht, the Netherlands, 1996), pp. 487–500.
[CrossRef]

A. Miniewicz, S. Bartkiewicz, W. Turalski, A. Januszko, “Dye-doped liquid crystals for real-time holography,” in Electrical and Related Properties of Organic Solids, Vol. 3/24 of NATO ASI Series, R. W. Munn, A. Miniewicz, B. Kuchta, eds. (Kluwer, Dordrecht, the Netherlands, 1997), pp. 323–337.
[CrossRef]

Moddel, G.

L. Wang, G. Moddel, “Resolution limits from charge transport in optically addressed spatial light modulators,” J. Appl. Phys. 78, 69–73 (1995).
[CrossRef]

P. R. Barbier, L. Wang, G. Moddel, “Thin-film photosensor design for liquid crystal spatial light modulators,” Opt. Eng. 33, 1322–1329 (1994).
[CrossRef]

C. C. Mao, K. M. Johnson, G. Moddel, “Optical phase conjugation using optically addressed chiral smectic liquid crystal spatial light modulators,” Ferroelectrics 114, 45–53 (1991).
[CrossRef]

Moerner, W. E.

D. M. Burland, G. C. Bjorklund, W. E. Moerner, S. M. Silence, J. J. Stankus, “Photorefractive polymer—A status report,” Pure Appl. Chem. 67, 33–38 (1995).
[CrossRef]

Mouanda, B.

C. Sentein, B. Mouanda, A. Rosilio, C. Rosilio, “Influence of stereoregularity on the photoinitiated electrical conductivity of poly(3-alkylthiophenes),” Synthet. Metals 83, 27–37 (1996).
[CrossRef]

Nissim, Y. I.

B. G. Sfez, E. V. K. Rao, Y. I. Nissim, J. L. Oudar, “Operation of nonlinear GaAs/AlGaAs multiple quantum well microresonators fabricated using alloy-mixing techniques,” Appl. Phys. Lett. 60, 607–609 (1992).
[CrossRef]

Nunzi, J.-M.

J.-M. Nunzi, F. Charra, N. Pfeffer, “Optimization of an ultrafast OASLM using photoexcitations in organic thin films: the incoherent-to-coherent conversion efficiency of spectral concentration,” J. Phys. III (France) 3, 1401–1411 (1993).
[CrossRef]

Oesterhelt, D.

D. Oesterhelt, C. Bräuchle, N. Hampp, “Bacteriorhodopsin: a biological material for information processing,” Q. Rev. Biophys. 24, 425–478 (1991).
[CrossRef] [PubMed]

Ohno, M.

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[CrossRef]

Okada-Shudo, Y.

Y. Okada-Shudo, I. Yamaguhi, H. Tomioka, H. Sasabe, “Real-time image processing using polarization discrimination of bacteriorhodopsin,” Synthet. Metals 81, 147–149 (1996).
[CrossRef]

Oudar, J. L.

B. G. Sfez, E. V. K. Rao, Y. I. Nissim, J. L. Oudar, “Operation of nonlinear GaAs/AlGaAs multiple quantum well microresonators fabricated using alloy-mixing techniques,” Appl. Phys. Lett. 60, 607–609 (1992).
[CrossRef]

Parka, J.

S. Bartkiewicz, A. Miniewicz, A. Januszko, J. Parka, “Dye-doped liquid crystal composite for real-time holography,” Pure Appl. Opt. 5, 799–809 (1996).
[CrossRef]

A. Miniewicz, S. Bartkiewicz, A. Januszko, J. Parka, “Dye-doped liquid crystal for real-time holography: nematic reorientation induced by photoconductivity,” in Photoactive Organic Materials Science and Application, Vol. 3/9 of NATO ASI Series, F. Kajzar, V. M. Agranovich, C. Y.-C. Lee, eds. (Kluwer, Dordrecht, the Netherlands, 1996), pp. 487–500.
[CrossRef]

Pauliat, G.

Pennington, K. S.

Peyghambarian, N.

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, N. Peyghambarian, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–499 (1994).
[CrossRef]

Pfeffer, N.

J.-M. Nunzi, F. Charra, N. Pfeffer, “Optimization of an ultrafast OASLM using photoexcitations in organic thin films: the incoherent-to-coherent conversion efficiency of spectral concentration,” J. Phys. III (France) 3, 1401–1411 (1993).
[CrossRef]

Pohl, D. W.

H. J. Eichler, P. Günter, D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986).
[CrossRef]

Rao, E. V. K.

B. G. Sfez, E. V. K. Rao, Y. I. Nissim, J. L. Oudar, “Operation of nonlinear GaAs/AlGaAs multiple quantum well microresonators fabricated using alloy-mixing techniques,” Appl. Phys. Lett. 60, 607–609 (1992).
[CrossRef]

Reichel, F.

N. Hawiltschek, E. Gärtner, P. Gussek, F. Reichel, “Properties and application of liquid crystal spatial light modulators in optical signal processing,” Exp. Tech. Phys. 40, 199–239 (1994).

Roach, W. R.

W. R. Roach, “Resolution of electro-optic light valves,” IEEE Trans. Electron Devices ED-21, 453–459 (1974).
[CrossRef]

Roosen, G.

Rosilio, A.

C. Sentein, B. Mouanda, A. Rosilio, C. Rosilio, “Influence of stereoregularity on the photoinitiated electrical conductivity of poly(3-alkylthiophenes),” Synthet. Metals 83, 27–37 (1996).
[CrossRef]

Rosilio, C.

C. Sentein, B. Mouanda, A. Rosilio, C. Rosilio, “Influence of stereoregularity on the photoinitiated electrical conductivity of poly(3-alkylthiophenes),” Synthet. Metals 83, 27–37 (1996).
[CrossRef]

Rudenko, E. V.

E. V. Rudenko, A. V. Sukhov, “Optically induced space charge field in nematics and orientational nonlinearity,” (in Russian) JETP 105, 1621–1634 (1994).

Sacks, R. N.

P. Tayebati, E. Canoglu, C. Hantzis, R. N. Sacks, “High-speed all-semiconductor optically addressed spatial light modulator,” Appl. Phys. Lett. 71, 1610–1612 (1997).
[CrossRef]

Sandalphon,

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, N. Peyghambarian, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–499 (1994).
[CrossRef]

Sasabe, H.

Y. Okada-Shudo, I. Yamaguhi, H. Tomioka, H. Sasabe, “Real-time image processing using polarization discrimination of bacteriorhodopsin,” Synthet. Metals 81, 147–149 (1996).
[CrossRef]

Schadt, M.

H. Seiberle, M. Schadt, “LC-conductivity and cell parameters; their influence on twisted nematic and supertwisted nematic liquid crystal displays,” Mol. Cryst. Liq. Cryst. 239, 229–244 (1994).
[CrossRef]

Schmid, H.

J. Contzen, G. Heppke, H. S. Kitzerow, D. Kruerke, H. Schmid, “Storage of laser-induced holographic gratings in discotic liquid crystals,” Appl. Phys. B Laser Opt. 63, 605–608 (1996).

Schmitt-Rink, S.

D. A. B. Miller, D. S. Chemla, S. Schmitt-Rink, “Electric field dependence of opticle properties of semiconductor quantum wells: physics and applications,” in Optical Nonlinearities and Instabilities in Semiconductors, H. Haug, ed. (Academic, Boston, Mass., 1988), pp. 325–359.
[CrossRef]

Seiberle, H.

H. Seiberle, M. Schadt, “LC-conductivity and cell parameters; their influence on twisted nematic and supertwisted nematic liquid crystal displays,” Mol. Cryst. Liq. Cryst. 239, 229–244 (1994).
[CrossRef]

Sentein, C.

C. Sentein, B. Mouanda, A. Rosilio, C. Rosilio, “Influence of stereoregularity on the photoinitiated electrical conductivity of poly(3-alkylthiophenes),” Synthet. Metals 83, 27–37 (1996).
[CrossRef]

Sfez, B. G.

B. G. Sfez, E. V. K. Rao, Y. I. Nissim, J. L. Oudar, “Operation of nonlinear GaAs/AlGaAs multiple quantum well microresonators fabricated using alloy-mixing techniques,” Appl. Phys. Lett. 60, 607–609 (1992).
[CrossRef]

Silence, S. M.

D. M. Burland, G. C. Bjorklund, W. E. Moerner, S. M. Silence, J. J. Stankus, “Photorefractive polymer—A status report,” Pure Appl. Chem. 67, 33–38 (1995).
[CrossRef]

Stankus, J. J.

D. M. Burland, G. C. Bjorklund, W. E. Moerner, S. M. Silence, J. J. Stankus, “Photorefractive polymer—A status report,” Pure Appl. Chem. 67, 33–38 (1995).
[CrossRef]

Sukhov, A. V.

E. V. Rudenko, A. V. Sukhov, “Optically induced space charge field in nematics and orientational nonlinearity,” (in Russian) JETP 105, 1621–1634 (1994).

Takacs, J. M.

M. Liphardt, A. Goonesekera, B. E. Jones, S. Ducharme, J. M. Takacs, L. Zhang, “High-performance photorefractive polymers,” Science 263, 367–369 (1994).
[CrossRef] [PubMed]

Tayebati, P.

P. Tayebati, E. Canoglu, C. Hantzis, R. N. Sacks, “High-speed all-semiconductor optically addressed spatial light modulator,” Appl. Phys. Lett. 71, 1610–1612 (1997).
[CrossRef]

Tomioka, H.

Y. Okada-Shudo, I. Yamaguhi, H. Tomioka, H. Sasabe, “Real-time image processing using polarization discrimination of bacteriorhodopsin,” Synthet. Metals 81, 147–149 (1996).
[CrossRef]

Turalski, W.

A. Miniewicz, S. Bartkiewicz, W. Turalski, A. Januszko, “Dye-doped liquid crystals for real-time holography,” in Electrical and Related Properties of Organic Solids, Vol. 3/24 of NATO ASI Series, R. W. Munn, A. Miniewicz, B. Kuchta, eds. (Kluwer, Dordrecht, the Netherlands, 1997), pp. 323–337.
[CrossRef]

Volodin, B. L.

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, N. Peyghambarian, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–499 (1994).
[CrossRef]

Wang, L.

L. Wang, G. Moddel, “Resolution limits from charge transport in optically addressed spatial light modulators,” J. Appl. Phys. 78, 69–73 (1995).
[CrossRef]

P. R. Barbier, L. Wang, G. Moddel, “Thin-film photosensor design for liquid crystal spatial light modulators,” Opt. Eng. 33, 1322–1329 (1994).
[CrossRef]

Wasielewski, M. R.

G. P. Wiederrecht, B. A. Yoon, M. R. Wasielewski, “High photorefractive gain in nematic liquid crystals doped with electron donor and acceptor molecules,” Science 270, 1794–1797 (1995).
[CrossRef]

Wherrett, B. S.

I. Jánossy, A. D. Lloyd, B. S. Wherrett, “Anomalous optical Fréedericksz transition in an absorbing liquid crystal,” Mol. Cryst. Liq. Cryst. 179, 1–12 (1990).

Wiederrecht, G. P.

G. P. Wiederrecht, B. A. Yoon, M. R. Wasielewski, “High photorefractive gain in nematic liquid crystals doped with electron donor and acceptor molecules,” Science 270, 1794–1797 (1995).
[CrossRef]

Yamaguhi, I.

Y. Okada-Shudo, I. Yamaguhi, H. Tomioka, H. Sasabe, “Real-time image processing using polarization discrimination of bacteriorhodopsin,” Synthet. Metals 81, 147–149 (1996).
[CrossRef]

Yeh, P.

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

Yoon, B. A.

G. P. Wiederrecht, B. A. Yoon, M. R. Wasielewski, “High photorefractive gain in nematic liquid crystals doped with electron donor and acceptor molecules,” Science 270, 1794–1797 (1995).
[CrossRef]

Zhang, L.

M. Liphardt, A. Goonesekera, B. E. Jones, S. Ducharme, J. M. Takacs, L. Zhang, “High-performance photorefractive polymers,” Science 263, 367–369 (1994).
[CrossRef] [PubMed]

(in Russian) JETP (1)

E. V. Rudenko, A. V. Sukhov, “Optically induced space charge field in nematics and orientational nonlinearity,” (in Russian) JETP 105, 1621–1634 (1994).

Adv. Mater. Opt. Electron. (1)

S. Bartkiewicz, A. Miniewicz, “Mechanism of optical recording in doped liquid crystals,” Adv. Mater. Opt. Electron. 6, 219–224 (1996).
[CrossRef]

Appl. Opt. (5)

Appl. Phys. B Laser Opt. (1)

J. Contzen, G. Heppke, H. S. Kitzerow, D. Kruerke, H. Schmid, “Storage of laser-induced holographic gratings in discotic liquid crystals,” Appl. Phys. B Laser Opt. 63, 605–608 (1996).

Appl. Phys. Lett. (3)

B. G. Sfez, E. V. K. Rao, Y. I. Nissim, J. L. Oudar, “Operation of nonlinear GaAs/AlGaAs multiple quantum well microresonators fabricated using alloy-mixing techniques,” Appl. Phys. Lett. 60, 607–609 (1992).
[CrossRef]

P. Tayebati, E. Canoglu, C. Hantzis, R. N. Sacks, “High-speed all-semiconductor optically addressed spatial light modulator,” Appl. Phys. Lett. 71, 1610–1612 (1997).
[CrossRef]

S. Fukushima, T. Kurokawa, M. Ohno, “Real-time hologram construction and reconstruction using a high-resolution spatial light modulator,” Appl. Phys. Lett. 58, 787–789 (1991).
[CrossRef]

Exp. Tech. Phys. (1)

N. Hawiltschek, E. Gärtner, P. Gussek, F. Reichel, “Properties and application of liquid crystal spatial light modulators in optical signal processing,” Exp. Tech. Phys. 40, 199–239 (1994).

Ferroelectrics (1)

C. C. Mao, K. M. Johnson, G. Moddel, “Optical phase conjugation using optically addressed chiral smectic liquid crystal spatial light modulators,” Ferroelectrics 114, 45–53 (1991).
[CrossRef]

IEEE J. Quantum Electron. (2)

I. C. Khoo, “Orientational photorefractive effects in nematic liquid crystals films,” IEEE J. Quantum Electron. 32, 525–534 (1996).
[CrossRef]

I. C. Khoo, H. Li, Y. Liang, “Optically induced extraordinarily large negative orientational nonlinearity in dye-doped liquid crystal,” IEEE J. Quantum Electron. 29, 1444–1447 (1993).
[CrossRef]

IEEE Trans. Electron Devices (1)

W. R. Roach, “Resolution of electro-optic light valves,” IEEE Trans. Electron Devices ED-21, 453–459 (1974).
[CrossRef]

J. Appl. Phys. (1)

L. Wang, G. Moddel, “Resolution limits from charge transport in optically addressed spatial light modulators,” J. Appl. Phys. 78, 69–73 (1995).
[CrossRef]

J. Phys. III (1)

C. Carré, D. J. Lougnot, “Photopolymers for holographic recording: from standard to self-processing materials,” J. Phys. III 3, 1445–1460 (1993).

J. Phys. III (France) (1)

J.-M. Nunzi, F. Charra, N. Pfeffer, “Optimization of an ultrafast OASLM using photoexcitations in organic thin films: the incoherent-to-coherent conversion efficiency of spectral concentration,” J. Phys. III (France) 3, 1401–1411 (1993).
[CrossRef]

Mol. Cryst. Liq. Cryst. (3)

H. Li, Y. Liang, I. C. Khoo, “Transient laser induced orthogonal director-axis reorientation in dye-doped liquid crystals (DDLC),” Mol. Cryst. Liq. Cryst. 251, 85–92 (1994).
[CrossRef]

H. Seiberle, M. Schadt, “LC-conductivity and cell parameters; their influence on twisted nematic and supertwisted nematic liquid crystal displays,” Mol. Cryst. Liq. Cryst. 239, 229–244 (1994).
[CrossRef]

I. Jánossy, A. D. Lloyd, B. S. Wherrett, “Anomalous optical Fréedericksz transition in an absorbing liquid crystal,” Mol. Cryst. Liq. Cryst. 179, 1–12 (1990).

Nature (1)

K. Meerholz, B. L. Volodin, Sandalphon, B. Kippelen, N. Peyghambarian, “A photorefractive polymer with high optical gain and diffraction efficiency near 100%,” Nature 371, 497–499 (1994).
[CrossRef]

Nonlin. Opt. (1)

A. Miniewicz, S. Bartkiewicz, F. Kajzar, “On the dynamics of coherent amplification of light observed in liquid crystal panel with photoconducting polymeric layers,” Nonlin. Opt. 19, 157–175 (1988).

Opt. Eng. (1)

P. R. Barbier, L. Wang, G. Moddel, “Thin-film photosensor design for liquid crystal spatial light modulators,” Opt. Eng. 33, 1322–1329 (1994).
[CrossRef]

Opt. Lett. (5)

Opt. Quantum Electron. (1)

T. Kurokawa, S. Fukushima, “Spatial light modulators using ferroelectric liquid crystals,” Opt. Quantum Electron. 24, 1151–1163 (1992).
[CrossRef]

Phys. Rev. E (1)

I. Jánossy, “Molecular interpretation of the absorption-induced optical reorientation of nematic liquid crystals,” Phys. Rev. E 49, 2957–2963 (1994).
[CrossRef]

Pure Appl. Chem. (1)

D. M. Burland, G. C. Bjorklund, W. E. Moerner, S. M. Silence, J. J. Stankus, “Photorefractive polymer—A status report,” Pure Appl. Chem. 67, 33–38 (1995).
[CrossRef]

Pure Appl. Opt. (1)

S. Bartkiewicz, A. Miniewicz, A. Januszko, J. Parka, “Dye-doped liquid crystal composite for real-time holography,” Pure Appl. Opt. 5, 799–809 (1996).
[CrossRef]

Q. Rev. Biophys. (1)

D. Oesterhelt, C. Bräuchle, N. Hampp, “Bacteriorhodopsin: a biological material for information processing,” Q. Rev. Biophys. 24, 425–478 (1991).
[CrossRef] [PubMed]

Science (2)

M. Liphardt, A. Goonesekera, B. E. Jones, S. Ducharme, J. M. Takacs, L. Zhang, “High-performance photorefractive polymers,” Science 263, 367–369 (1994).
[CrossRef] [PubMed]

G. P. Wiederrecht, B. A. Yoon, M. R. Wasielewski, “High photorefractive gain in nematic liquid crystals doped with electron donor and acceptor molecules,” Science 270, 1794–1797 (1995).
[CrossRef]

Synthet. Metals (3)

Y. Okada-Shudo, I. Yamaguhi, H. Tomioka, H. Sasabe, “Real-time image processing using polarization discrimination of bacteriorhodopsin,” Synthet. Metals 81, 147–149 (1996).
[CrossRef]

C. Sentein, B. Mouanda, A. Rosilio, C. Rosilio, “Influence of stereoregularity on the photoinitiated electrical conductivity of poly(3-alkylthiophenes),” Synthet. Metals 83, 27–37 (1996).
[CrossRef]

N. T. Binh, M. Gailberger, H. Bassler, “Photoconduction in poly(3-alkylthiophene). I. Charge carrier generation,” Synthet. Metals 47, 77–86 (1992).
[CrossRef]

Other (8)

Data supplied with the E7 liquid crystal by Merck KGaA, D-64271 Darmstadt, Germany.

H. J. Eichler, P. Günter, D. W. Pohl, Laser-Induced Dynamic Gratings (Springer-Verlag, Berlin, 1986).
[CrossRef]

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, New York, 1993).

I. C. Khoo, Liquid Crystals Physical Properties and Nonlinear Optical Phenomena (Wiley, New York, 1995).

A. Miniewicz, S. Bartkiewicz, W. Turalski, A. Januszko, “Dye-doped liquid crystals for real-time holography,” in Electrical and Related Properties of Organic Solids, Vol. 3/24 of NATO ASI Series, R. W. Munn, A. Miniewicz, B. Kuchta, eds. (Kluwer, Dordrecht, the Netherlands, 1997), pp. 323–337.
[CrossRef]

A. Miniewicz, S. Bartkiewicz, A. Januszko, J. Parka, “Dye-doped liquid crystal for real-time holography: nematic reorientation induced by photoconductivity,” in Photoactive Organic Materials Science and Application, Vol. 3/9 of NATO ASI Series, F. Kajzar, V. M. Agranovich, C. Y.-C. Lee, eds. (Kluwer, Dordrecht, the Netherlands, 1996), pp. 487–500.
[CrossRef]

P. Günter, J.-P. Huignard, eds., Photorefractive Materials and their Applications (Springer-Verlag, Berlin, 1988), Vols. 1 and 2.
[CrossRef]

D. A. B. Miller, D. S. Chemla, S. Schmitt-Rink, “Electric field dependence of opticle properties of semiconductor quantum wells: physics and applications,” in Optical Nonlinearities and Instabilities in Semiconductors, H. Haug, ed. (Academic, Boston, Mass., 1988), pp. 325–359.
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Scheme of the two-wave-mixing experimental geometry. The sample is tilted at an angle 45° relative to the bisector of the incident beams, which are p polarized. The grating wave vector is along the x axis, and the external electric field E a is applied at -45° to the z axis. The wave-mixing angle is 2θ = 2.2°.

Fig. 2
Fig. 2

Diffraction efficiency η measured for a LC sample as a function of the incidence angle β for various laser powers I 0: curve A: 40 mW; curve B: 20 mW; curve C: 10 mW; and curve D: 5 mW. Other parameters: Λ = 10 μm, V = 3 V, and d = 10 μm.

Fig. 3
Fig. 3

Dependence of the beam-coupling ratio g as a function of the pump-beam power I 20 in a LC sample for an incident intensity ratio of m = 10. Other experimental parameters are the same as for Fig. 2.

Fig. 4
Fig. 4

Dependence of the beam-coupling ratio g on the incident intensity ratio in a LC sample.

Fig. 5
Fig. 5

Beam-coupling ratio g as a function of the externally applied voltage U a (LC layer thickness of d = 10 μm).

Fig. 6
Fig. 6

Some typical examples of oscilloscope traces of grating build-up and erasure kinetics taken at externally applied dc voltages of 7 and 20 V, respectively. The chopper is placed on beam I 20 and the light detector at the first-order diffraction spot of beam I 1 (the lower part of the beam scheme shown in Fig. 1).

Equations (4)

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I x = I 0 1 + M   cos Kx ,
n e eff x ,   y ,   z = n e n o ( n o 2 sin 2 ϕ E z x ,   y ,   z + n e 2 cos 2 ϕ E z x ,   y ,   z ) ½ ,
Γ = 1 d / cos   β ln gm m - g + 1 ,
f E = Δ 4 π n ˆ · E n ˆ × E

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