Abstract

We report a theoretical model for a photorefractive running hologram in bulk-absorbing materials in the presence of self-diffraction and use this model to analyze experiments for photorefractive materials characterization. A nonperturbative technique that allows one to measure at the same time the diffraction efficiency and the output beam’s phase shift is reported, and its advantages are discussed. We use this technique and apply the theoretical model to compute some parameters for the electron-charge carriers (Debye screening length ls0.03 µm, diffusion length LD0.14 µm, and photoexcitation quantum efficiency Φ0.45) at the 514.5-nm-wavelength laser line for a nominally undoped Bi12TiO20 crystal. Particular experimental features are detected and assumed to be consequences of hole–electron competition in this sample.

© 2001 Optical Society of America

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  31. S. Mallick and D. Rouède, “Influence of the polarization direction on the two-beam coupling in photorefractive Bi12SiO20: diffusion regime,” Appl. Phys. B 43, 239–245 (1987).
    [CrossRef]
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    [CrossRef]
  34. S. Bian and J. Frejlich, “Photorefractive response time measurement in GaAs using phase modulation in two-wave mixing,” Opt. Lett. 19, 1702–1704 (1994).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  37. J. Feinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
    [CrossRef]
  38. I. de Oliveira and J. Frejlich, “Dielectric relaxation time measurement in absorbing photorefractive materials,” Opt. Commun. 178, 251–255 (2000).
    [CrossRef]
  39. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]

2000 (2)

1999 (1)

1998 (1)

1997 (4)

J. Frejlich, P. M. Garcia, K. H. Ringhofer, and E. Shamonina, “Phase modulation in two-wave mixing for dynamically recorded gratings in photorefractive materials,” J. Opt. Soc. Am. B 14, 1741–1749 (1997).
[CrossRef]

E. Shamonina, K. H. Ringhofer, P. M. Garcia, A. A. Freschi, and J. Frejlich, “Shape-asymmetry of the diffraction effi-ciency in Bi12TiO20 crystals: the simultaneous influence of absorption and higher harmonics,” Opt. Commun. 141, 132–136 (1997).
[CrossRef]

K. Buse, “Light-induced charge transport processes in photorefractive crystals. I.:Models and experimental methods,” Appl. Phys. B 64, 273–291 (1997).
[CrossRef]

A. A. Freschi, P. M. Garcia, and J. Frejlich, “Charge-carriers diffusion length in photorefractive crystals computed from the initial hologram phase shift,” Appl. Phys. Lett. 71, 2427–2429 (1997).
[CrossRef]

1995 (5)

1994 (2)

1993 (1)

1992 (1)

J. Frejlich and P. M. Garcia, “Quasi-permanent hole-photorefractive and photochromic effects in Bi12TiO20 crystals,” Appl. Phys. A 55, 49–54 (1992).
[CrossRef]

1991 (1)

D. J. Webb and L. Solymar, “The effects of optical activity and absorption on two-wave mixing in Bi12SiO20,” Opt. Commun. 83, 287–294 (1991).
[CrossRef]

1990 (1)

1989 (1)

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP: Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3798–3813 (1989).
[CrossRef]

1988 (1)

1987 (3)

S. Mallick and D. Rouède, “Influence of the polarization direction on the two-beam coupling in photorefractive Bi12SiO20: diffusion regime,” Appl. Phys. B 43, 239–245 (1987).
[CrossRef]

G. Pauliat, M. Allain, J. C. Launay, and G. Roosen, “Optical evidence of a photorefractive effect due to holes in Bi12GeO20 crystals,” Opt. Commun. 61, 321–324 (1987).
[CrossRef]

J. Kumar, G. Albanese, and W. H. Steier, “Measurement of two-wave mixing gain in GaAs with a moving grating,” Opt. Commun. 63, 191–193 (1987).
[CrossRef]

1986 (2)

P. D. Foote and T. J. Hall, “Influence of optical activity on two beam coupling constants in photorefractive Bi12SiO20,” Opt. Commun. 57, 201–206 (1986).
[CrossRef]

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 11, 312–314 (1986).
[CrossRef]

1985 (2)

Ph. Refregier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect: a review,” Prog. Quantum Electron. 10, 77–146 (1985).
[CrossRef]

1984 (1)

1983 (1)

1982 (1)

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “‘Running’ holograms in photorefractive Bi12TiO20 crystals,” Opt. Commun. 44, 19–23 (1982).
[CrossRef]

1981 (2)

J.-P. Huignard and A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

J.-P. Huignard and A. Marrakchi, “Two-wave mixing and energy transfer in Bi12SiO20 crystals: application to image amplification and vibrational analysis,” Opt. Lett. 6, 622–624 (1981).
[CrossRef] [PubMed]

1980 (1)

J. Feinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

1979 (1)

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

1969 (1)

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

Albanese, G.

J. Kumar, G. Albanese, and W. H. Steier, “Measurement of two-wave mixing gain in GaAs with a moving grating,” Opt. Commun. 63, 191–193 (1987).
[CrossRef]

Allain, M.

G. Pauliat, M. Allain, J. C. Launay, and G. Roosen, “Optical evidence of a photorefractive effect due to holes in Bi12GeO20 crystals,” Opt. Commun. 61, 321–324 (1987).
[CrossRef]

Andreeta, J. P.

V. V. Prokofiev, J. F. Carvalho, J. P. Andreeta, N. J. H. Gallo, A. C. Hernandes, J. Frejlich, A. A. Freschi, P. M. Garcia, J. Maracaiba, A. A. Kamshilin, and T. Jaaskelainen, “Growth and characterization of photorefractive Bi12TiO20 single crystals,” Cryst. Res. Technol. 30, 171–176 (1995).
[CrossRef]

Aubrecht, I.

Bian, S.

Brost, G.

Buse, K.

K. Buse, “Light-induced charge transport processes in photorefractive crystals. I.:Models and experimental methods,” Appl. Phys. B 64, 273–291 (1997).
[CrossRef]

Carvalho, J. F.

V. V. Prokofiev, J. F. Carvalho, J. P. Andreeta, N. J. H. Gallo, A. C. Hernandes, J. Frejlich, A. A. Freschi, P. M. Garcia, J. Maracaiba, A. A. Kamshilin, and T. Jaaskelainen, “Growth and characterization of photorefractive Bi12TiO20 single crystals,” Cryst. Res. Technol. 30, 171–176 (1995).
[CrossRef]

Cescato, L.

Connors, L. M.

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect: a review,” Prog. Quantum Electron. 10, 77–146 (1985).
[CrossRef]

de Oliveira, I.

I. de Oliveira and J. Frejlich, “Dielectric relaxation time measurement in absorbing photorefractive materials,” Opt. Commun. 178, 251–255 (2000).
[CrossRef]

Ellin, H. C.

Feinberg, J.

J. Feinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

Foote, P. D.

P. D. Foote and T. J. Hall, “Influence of optical activity on two beam coupling constants in photorefractive Bi12SiO20,” Opt. Commun. 57, 201–206 (1986).
[CrossRef]

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect: a review,” Prog. Quantum Electron. 10, 77–146 (1985).
[CrossRef]

Frejlich, J.

I. de Oliveira and J. Frejlich, “Dielectric relaxation time measurement in absorbing photorefractive materials,” Opt. Commun. 178, 251–255 (2000).
[CrossRef]

J. Frejlich, A. A. Freschi, P. M. Garcia, E. Shamonina, V. Ya. Gayvoronsky, and K. H. Ringhofer, “Feedback-controlled running holograms in strongly absorbing photorefractive materials,” J. Opt. Soc. Am. B 17, 1517–1521 (2000).
[CrossRef]

E. Shamonina, K. H. Ringhofer, P. M. Garcia, A. A. Freschi, and J. Frejlich, “Shape-asymmetry of the diffraction effi-ciency in Bi12TiO20 crystals: the simultaneous influence of absorption and higher harmonics,” Opt. Commun. 141, 132–136 (1997).
[CrossRef]

A. A. Freschi, P. M. Garcia, and J. Frejlich, “Charge-carriers diffusion length in photorefractive crystals computed from the initial hologram phase shift,” Appl. Phys. Lett. 71, 2427–2429 (1997).
[CrossRef]

J. Frejlich, P. M. Garcia, K. H. Ringhofer, and E. Shamonina, “Phase modulation in two-wave mixing for dynamically recorded gratings in photorefractive materials,” J. Opt. Soc. Am. B 14, 1741–1749 (1997).
[CrossRef]

V. V. Prokofiev, J. F. Carvalho, J. P. Andreeta, N. J. H. Gallo, A. C. Hernandes, J. Frejlich, A. A. Freschi, P. M. Garcia, J. Maracaiba, A. A. Kamshilin, and T. Jaaskelainen, “Growth and characterization of photorefractive Bi12TiO20 single crystals,” Cryst. Res. Technol. 30, 171–176 (1995).
[CrossRef]

S. Bian and J. Frejlich, “Actively stabilized holographic recording for the measurement of photorefractive properties of a Ti-doped KNSBN crystal,” J. Opt. Soc. Am. B 12, 2060–2065 (1995).
[CrossRef]

S. Bian and J. Frejlich, “Photorefractive response time measurement in GaAs using phase modulation in two-wave mixing,” Opt. Lett. 19, 1702–1704 (1994).
[CrossRef] [PubMed]

J. Frejlich and P. M. Garcia, “Quasi-permanent hole-photorefractive and photochromic effects in Bi12TiO20 crystals,” Appl. Phys. A 55, 49–54 (1992).
[CrossRef]

J. Frejlich, P. M. Garcia, and L. Cescato, “Adaptive fringe-locked running hologram in photorefractive crystals: errata,” Opt. Lett. 15, 1247 (1990).
[CrossRef] [PubMed]

Freschi, A. A.

J. Frejlich, A. A. Freschi, P. M. Garcia, E. Shamonina, V. Ya. Gayvoronsky, and K. H. Ringhofer, “Feedback-controlled running holograms in strongly absorbing photorefractive materials,” J. Opt. Soc. Am. B 17, 1517–1521 (2000).
[CrossRef]

E. Shamonina, K. H. Ringhofer, P. M. Garcia, A. A. Freschi, and J. Frejlich, “Shape-asymmetry of the diffraction effi-ciency in Bi12TiO20 crystals: the simultaneous influence of absorption and higher harmonics,” Opt. Commun. 141, 132–136 (1997).
[CrossRef]

A. A. Freschi, P. M. Garcia, and J. Frejlich, “Charge-carriers diffusion length in photorefractive crystals computed from the initial hologram phase shift,” Appl. Phys. Lett. 71, 2427–2429 (1997).
[CrossRef]

V. V. Prokofiev, J. F. Carvalho, J. P. Andreeta, N. J. H. Gallo, A. C. Hernandes, J. Frejlich, A. A. Freschi, P. M. Garcia, J. Maracaiba, A. A. Kamshilin, and T. Jaaskelainen, “Growth and characterization of photorefractive Bi12TiO20 single crystals,” Cryst. Res. Technol. 30, 171–176 (1995).
[CrossRef]

Gallo, N. J. H.

V. V. Prokofiev, J. F. Carvalho, J. P. Andreeta, N. J. H. Gallo, A. C. Hernandes, J. Frejlich, A. A. Freschi, P. M. Garcia, J. Maracaiba, A. A. Kamshilin, and T. Jaaskelainen, “Growth and characterization of photorefractive Bi12TiO20 single crystals,” Cryst. Res. Technol. 30, 171–176 (1995).
[CrossRef]

Garcia, P. M.

J. Frejlich, A. A. Freschi, P. M. Garcia, E. Shamonina, V. Ya. Gayvoronsky, and K. H. Ringhofer, “Feedback-controlled running holograms in strongly absorbing photorefractive materials,” J. Opt. Soc. Am. B 17, 1517–1521 (2000).
[CrossRef]

E. Shamonina, K. H. Ringhofer, P. M. Garcia, A. A. Freschi, and J. Frejlich, “Shape-asymmetry of the diffraction effi-ciency in Bi12TiO20 crystals: the simultaneous influence of absorption and higher harmonics,” Opt. Commun. 141, 132–136 (1997).
[CrossRef]

A. A. Freschi, P. M. Garcia, and J. Frejlich, “Charge-carriers diffusion length in photorefractive crystals computed from the initial hologram phase shift,” Appl. Phys. Lett. 71, 2427–2429 (1997).
[CrossRef]

J. Frejlich, P. M. Garcia, K. H. Ringhofer, and E. Shamonina, “Phase modulation in two-wave mixing for dynamically recorded gratings in photorefractive materials,” J. Opt. Soc. Am. B 14, 1741–1749 (1997).
[CrossRef]

V. V. Prokofiev, J. F. Carvalho, J. P. Andreeta, N. J. H. Gallo, A. C. Hernandes, J. Frejlich, A. A. Freschi, P. M. Garcia, J. Maracaiba, A. A. Kamshilin, and T. Jaaskelainen, “Growth and characterization of photorefractive Bi12TiO20 single crystals,” Cryst. Res. Technol. 30, 171–176 (1995).
[CrossRef]

J. Frejlich and P. M. Garcia, “Quasi-permanent hole-photorefractive and photochromic effects in Bi12TiO20 crystals,” Appl. Phys. A 55, 49–54 (1992).
[CrossRef]

J. Frejlich, P. M. Garcia, and L. Cescato, “Adaptive fringe-locked running hologram in photorefractive crystals: errata,” Opt. Lett. 15, 1247 (1990).
[CrossRef] [PubMed]

Gayvoronsky, V. Ya.

Gravey, P.

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP: Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3798–3813 (1989).
[CrossRef]

Grunnet-Jepsen, A.

Hall, T. J.

P. D. Foote and T. J. Hall, “Influence of optical activity on two beam coupling constants in photorefractive Bi12SiO20,” Opt. Commun. 57, 201–206 (1986).
[CrossRef]

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect: a review,” Prog. Quantum Electron. 10, 77–146 (1985).
[CrossRef]

Harris, M. T.

Heiman, D.

J. Feinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

Hellwarth, R. W.

F. P. Strohkendl, J. M. C. Jonathan, and R. W. Hellwarth, “Hole–electron competition in photorefractive gratings,” Opt. Lett. 11, 312–314 (1986).
[CrossRef]

J. Feinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

Hernandes, A. C.

V. V. Prokofiev, J. F. Carvalho, J. P. Andreeta, N. J. H. Gallo, A. C. Hernandes, J. Frejlich, A. A. Freschi, P. M. Garcia, J. Maracaiba, A. A. Kamshilin, and T. Jaaskelainen, “Growth and characterization of photorefractive Bi12TiO20 single crystals,” Cryst. Res. Technol. 30, 171–176 (1995).
[CrossRef]

Herriau, J. P.

Huignard, J.-P.

B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, and J.-P. Huignard, “High photorefractive gain in two-beam coupling with moving fringes in GaAs:Cr crystals,” Opt. Lett. 13, 327–329 (1988).
[CrossRef] [PubMed]

Ph. Refregier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

J.-P. Huignard and A. Marrakchi, “Two-wave mixing and energy transfer in Bi12SiO20 crystals: application to image amplification and vibrational analysis,” Opt. Lett. 6, 622–624 (1981).
[CrossRef] [PubMed]

J.-P. Huignard and A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

Imbert, B.

Jaaskelainen, T.

V. V. Prokofiev, J. F. Carvalho, J. P. Andreeta, N. J. H. Gallo, A. C. Hernandes, J. Frejlich, A. A. Freschi, P. M. Garcia, J. Maracaiba, A. A. Kamshilin, and T. Jaaskelainen, “Growth and characterization of photorefractive Bi12TiO20 single crystals,” Cryst. Res. Technol. 30, 171–176 (1995).
[CrossRef]

Jaura, R.

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect: a review,” Prog. Quantum Electron. 10, 77–146 (1985).
[CrossRef]

Johansen, P. M.

Jonathan, J. M. C.

Kamshilin, A. A.

V. V. Prokofiev, J. F. Carvalho, J. P. Andreeta, N. J. H. Gallo, A. C. Hernandes, J. Frejlich, A. A. Freschi, P. M. Garcia, J. Maracaiba, A. A. Kamshilin, and T. Jaaskelainen, “Growth and characterization of photorefractive Bi12TiO20 single crystals,” Cryst. Res. Technol. 30, 171–176 (1995).
[CrossRef]

Kogelnik, H.

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

Kukhtarev, N. V.

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

Kulikov, V. V.

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “‘Running’ holograms in photorefractive Bi12TiO20 crystals,” Opt. Commun. 44, 19–23 (1982).
[CrossRef]

Kumar, J.

J. Kumar, G. Albanese, and W. H. Steier, “Measurement of two-wave mixing gain in GaAs with a moving grating,” Opt. Commun. 63, 191–193 (1987).
[CrossRef]

Larkin, J. J.

Launay, J. C.

G. Pauliat, M. Allain, J. C. Launay, and G. Roosen, “Optical evidence of a photorefractive effect due to holes in Bi12GeO20 crystals,” Opt. Commun. 61, 321–324 (1987).
[CrossRef]

Magde, K. M.

Mallick, S.

B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, and J.-P. Huignard, “High photorefractive gain in two-beam coupling with moving fringes in GaAs:Cr crystals,” Opt. Lett. 13, 327–329 (1988).
[CrossRef] [PubMed]

S. Mallick and D. Rouède, “Influence of the polarization direction on the two-beam coupling in photorefractive Bi12SiO20: diffusion regime,” Appl. Phys. B 43, 239–245 (1987).
[CrossRef]

Mann, M.

Maracaiba, J.

V. V. Prokofiev, J. F. Carvalho, J. P. Andreeta, N. J. H. Gallo, A. C. Hernandes, J. Frejlich, A. A. Freschi, P. M. Garcia, J. Maracaiba, A. A. Kamshilin, and T. Jaaskelainen, “Growth and characterization of photorefractive Bi12TiO20 single crystals,” Cryst. Res. Technol. 30, 171–176 (1995).
[CrossRef]

Markov, V. B.

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

Marrakchi, A.

J.-P. Huignard and A. Marrakchi, “Two-wave mixing and energy transfer in Bi12SiO20 crystals: application to image amplification and vibrational analysis,” Opt. Lett. 6, 622–624 (1981).
[CrossRef] [PubMed]

J.-P. Huignard and A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

Norman, J.

Odoulov, S.

Odulov, S. G.

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

Otten, J.

Ozkul, C.

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP: Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3798–3813 (1989).
[CrossRef]

Pauliat, G.

G. Pauliat, M. Allain, J. C. Launay, and G. Roosen, “Optical evidence of a photorefractive effect due to holes in Bi12GeO20 crystals,” Opt. Commun. 61, 321–324 (1987).
[CrossRef]

Pedersen, H. C.

Petrov, M. P.

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “‘Running’ holograms in photorefractive Bi12TiO20 crystals,” Opt. Commun. 44, 19–23 (1982).
[CrossRef]

Picoli, G.

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP: Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3798–3813 (1989).
[CrossRef]

Prokofiev, V. V.

V. V. Prokofiev, J. F. Carvalho, J. P. Andreeta, N. J. H. Gallo, A. C. Hernandes, J. Frejlich, A. A. Freschi, P. M. Garcia, J. Maracaiba, A. A. Kamshilin, and T. Jaaskelainen, “Growth and characterization of photorefractive Bi12TiO20 single crystals,” Cryst. Res. Technol. 30, 171–176 (1995).
[CrossRef]

Rajbenbach, H.

B. Imbert, H. Rajbenbach, S. Mallick, J. P. Herriau, and J.-P. Huignard, “High photorefractive gain in two-beam coupling with moving fringes in GaAs:Cr crystals,” Opt. Lett. 13, 327–329 (1988).
[CrossRef] [PubMed]

Ph. Refregier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Refregier, Ph.

Ph. Refregier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Ringhofer, K. H.

Roosen, G.

G. Pauliat, M. Allain, J. C. Launay, and G. Roosen, “Optical evidence of a photorefractive effect due to holes in Bi12GeO20 crystals,” Opt. Commun. 61, 321–324 (1987).
[CrossRef]

Rouède, D.

S. Mallick and D. Rouède, “Influence of the polarization direction on the two-beam coupling in photorefractive Bi12SiO20: diffusion regime,” Appl. Phys. B 43, 239–245 (1987).
[CrossRef]

Shamonina, E.

Shcherbin, K.

Shumelyuk, A.

Solymar, L.

A. Grunnet-Jepsen, I. Aubrecht, and L. Solymar, “Investigation of the internal field in photorefractive materials and measurement of the effective electro-optic coefficient,” J. Opt. Soc. Am. B 12, 921–929 (1995).
[CrossRef]

I. Aubrecht, H. C. Ellin, A. Grunnet-Jepsen, and L. Solymar, “Space-charge field in photorefractive materials enhanced by moving fringes: comparison of hole–electron transport models,” J. Opt. Soc. Am. B 12, 1918–1923 (1995).
[CrossRef]

D. J. Webb and L. Solymar, “The effects of optical activity and absorption on two-wave mixing in Bi12SiO20,” Opt. Commun. 83, 287–294 (1991).
[CrossRef]

Ph. Refregier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Soskin, M. S.

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

Steier, W. H.

J. Kumar, G. Albanese, and W. H. Steier, “Measurement of two-wave mixing gain in GaAs with a moving grating,” Opt. Commun. 63, 191–193 (1987).
[CrossRef]

Stepanov, S. I.

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “‘Running’ holograms in photorefractive Bi12TiO20 crystals,” Opt. Commun. 44, 19–23 (1982).
[CrossRef]

Strohkendl, F. P.

Sturman, B. I.

Tanguay Jr., A. R.

J. Feinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

Taranov, V.

Valley, G. C.

Vieux, V.

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP: Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3798–3813 (1989).
[CrossRef]

Vinetskii, V. L.

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

Webb, D. J.

D. J. Webb and L. Solymar, “The effects of optical activity and absorption on two-wave mixing in Bi12SiO20,” Opt. Commun. 83, 287–294 (1991).
[CrossRef]

Appl. Opt. (1)

Appl. Phys. A (1)

J. Frejlich and P. M. Garcia, “Quasi-permanent hole-photorefractive and photochromic effects in Bi12TiO20 crystals,” Appl. Phys. A 55, 49–54 (1992).
[CrossRef]

Appl. Phys. B (2)

K. Buse, “Light-induced charge transport processes in photorefractive crystals. I.:Models and experimental methods,” Appl. Phys. B 64, 273–291 (1997).
[CrossRef]

S. Mallick and D. Rouède, “Influence of the polarization direction on the two-beam coupling in photorefractive Bi12SiO20: diffusion regime,” Appl. Phys. B 43, 239–245 (1987).
[CrossRef]

Appl. Phys. Lett. (1)

A. A. Freschi, P. M. Garcia, and J. Frejlich, “Charge-carriers diffusion length in photorefractive crystals computed from the initial hologram phase shift,” Appl. Phys. Lett. 71, 2427–2429 (1997).
[CrossRef]

Bell Syst. Tech. J. (1)

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

Cryst. Res. Technol. (1)

V. V. Prokofiev, J. F. Carvalho, J. P. Andreeta, N. J. H. Gallo, A. C. Hernandes, J. Frejlich, A. A. Freschi, P. M. Garcia, J. Maracaiba, A. A. Kamshilin, and T. Jaaskelainen, “Growth and characterization of photorefractive Bi12TiO20 single crystals,” Cryst. Res. Technol. 30, 171–176 (1995).
[CrossRef]

Ferroelectrics (1)

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

J. Appl. Phys. (3)

J. Feinberg, D. Heiman, A. R. Tanguay, Jr., and R. W. Hellwarth, “Photorefractive effects and light-induced charge migration in barium titanate,” J. Appl. Phys. 51, 1297–1305 (1980).
[CrossRef]

Ph. Refregier, L. Solymar, H. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

G. Picoli, P. Gravey, C. Ozkul, and V. Vieux, “Theory of two-wave mixing gain enhancement in photorefractive InP: Fe: a new mechanism of resonance,” J. Appl. Phys. 66, 3798–3813 (1989).
[CrossRef]

J. Opt. Soc. Am. B (11)

G. C. Valley, “Two-wave mixing with an applied field and a moving grating,” J. Opt. Soc. Am. B 1, 868–873 (1984).
[CrossRef]

G. Brost, K. M. Magde, J. J. Larkin, and M. T. Harris, “Modulation dependence of the photorefractive response with moving gratings: numerical analysis and experiment,” J. Opt. Soc. Am. B 11, 1764–1772 (1994).
[CrossRef]

A. Grunnet-Jepsen, I. Aubrecht, and L. Solymar, “Investigation of the internal field in photorefractive materials and measurement of the effective electro-optic coefficient,” J. Opt. Soc. Am. B 12, 921–929 (1995).
[CrossRef]

B. I. Sturman, E. Shamonina, M. Mann, and K. H. Ringhofer, “Space-charge waves in photorefractive ferroelectrics,” J. Opt. Soc. Am. B 12, 1642–1650 (1995).
[CrossRef]

I. Aubrecht, H. C. Ellin, A. Grunnet-Jepsen, and L. Solymar, “Space-charge field in photorefractive materials enhanced by moving fringes: comparison of hole–electron transport models,” J. Opt. Soc. Am. B 12, 1918–1923 (1995).
[CrossRef]

S. Bian and J. Frejlich, “Actively stabilized holographic recording for the measurement of photorefractive properties of a Ti-doped KNSBN crystal,” J. Opt. Soc. Am. B 12, 2060–2065 (1995).
[CrossRef]

J. Frejlich, P. M. Garcia, K. H. Ringhofer, and E. Shamonina, “Phase modulation in two-wave mixing for dynamically recorded gratings in photorefractive materials,” J. Opt. Soc. Am. B 14, 1741–1749 (1997).
[CrossRef]

G. Brost, J. Norman, S. Odoulov, K. Shcherbin, A. Shumelyuk, and V. Taranov, “Gain spectra of beam coupling in photorefractive semiconductors,” J. Opt. Soc. Am. B 15, 2083–2090 (1998).
[CrossRef]

B. I. Sturman, M. Mann, J. Otten, and K. H. Ringhofer, “Space-charge waves and their parametric excitation,” J. Opt. Soc. Am. B 10, 1919–1932 (1993).
[CrossRef]

J. Frejlich, A. A. Freschi, P. M. Garcia, E. Shamonina, V. Ya. Gayvoronsky, and K. H. Ringhofer, “Feedback-controlled running holograms in strongly absorbing photorefractive materials,” J. Opt. Soc. Am. B 17, 1517–1521 (2000).
[CrossRef]

H. C. Pedersen and P. M. Johansen, “Space-charge wave theory of photorefractive parametric amplification,” J. Opt. Soc. Am. B 16, 1185–1188 (1999).
[CrossRef]

Opt. Commun. (8)

S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “‘Running’ holograms in photorefractive Bi12TiO20 crystals,” Opt. Commun. 44, 19–23 (1982).
[CrossRef]

G. Pauliat, M. Allain, J. C. Launay, and G. Roosen, “Optical evidence of a photorefractive effect due to holes in Bi12GeO20 crystals,” Opt. Commun. 61, 321–324 (1987).
[CrossRef]

J.-P. Huignard and A. Marrakchi, “Coherent signal beam amplification in two-wave mixing experiments with photorefractive Bi12SiO20 crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

J. Kumar, G. Albanese, and W. H. Steier, “Measurement of two-wave mixing gain in GaAs with a moving grating,” Opt. Commun. 63, 191–193 (1987).
[CrossRef]

D. J. Webb and L. Solymar, “The effects of optical activity and absorption on two-wave mixing in Bi12SiO20,” Opt. Commun. 83, 287–294 (1991).
[CrossRef]

E. Shamonina, K. H. Ringhofer, P. M. Garcia, A. A. Freschi, and J. Frejlich, “Shape-asymmetry of the diffraction effi-ciency in Bi12TiO20 crystals: the simultaneous influence of absorption and higher harmonics,” Opt. Commun. 141, 132–136 (1997).
[CrossRef]

I. de Oliveira and J. Frejlich, “Dielectric relaxation time measurement in absorbing photorefractive materials,” Opt. Commun. 178, 251–255 (2000).
[CrossRef]

P. D. Foote and T. J. Hall, “Influence of optical activity on two beam coupling constants in photorefractive Bi12SiO20,” Opt. Commun. 57, 201–206 (1986).
[CrossRef]

Opt. Lett. (5)

Prog. Quantum Electron. (1)

T. J. Hall, R. Jaura, L. M. Connors, and P. D. Foote, “The photorefractive effect: a review,” Prog. Quantum Electron. 10, 77–146 (1985).
[CrossRef]

Other (3)

S. Stepanov and P. Petrov, Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988); Vol. 61, Chap. 9, pp. 263–289.

P. Günter and J.-P. Huignard, Photorefractive Materials and Their Applications I, P. Günter and J.-P. Huignard, eds. (Springer-Verlag, Berlin, 1988); Vol. 61, Chap. 2, pp. 7–73.

I. de Oliveira and J. Frejlich, “Gain and stability in photorefractive holograms under applied electric field,” Phys. Rev. A (to be published).

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Figures (5)

Fig. 1
Fig. 1

Diffraction efficiency (upper) and tan φ (lower) as a function of Kv computed with the experimental parameters K=2.55 µm-1, α=11.65 cm-1, ξE0=4.55 kV/cm, and I0=17.5 mW/cm2. The material parameters are LD=0.22 µm, ls=0.03 µm, β2=40, and Φ=0.4 for electrons (continuous curve), whereas for holes they are LDh=0.16 µm, lsh=0.15 µm, and Φh=0.004 (dashed curve). The resulting electron-to-hole diffraction-efficiency ratio at Kv=0 is ηe/ηh2.4. The thick continuous curve is the overall result.

Fig. 2
Fig. 2

Diffraction efficiency (upper) and tan φ (lower) as a function of Kv computed with K=11.3 µm-1. All other experimental and material parameters and the meaning of thick, thin, and dashed curves are the same as for Fig. 1, with ηe/ηh17 for Kv=0.

Fig. 3
Fig. 3

Experimental two-wave mixing setup with the 514.5-nm laser wavelength: BS, beam splitter; PZT, piezoelectric-supported mirror; OSC, oscillator; D, photodetector; LAΩ and LA 2Ω, lock-in amplifiers tuned to Ω and 2Ω, respectively; HV, high-voltage source driver for the PZT; M, mirror; BTO, Bi12TiO20 crystal; Vo, applied voltage; IR,So and IR,S, irradiance of the interfering beams in front of and behind the crystal, respectively.

Fig. 4
Fig. 4

Diffraction-efficiency (η) experimental data (spots) as a function of detuning Kv and best theoretical fit (continuous curve) to Eq. (20) for ξ=0.96, K=2.55 µm-1, Eo=7.3 kV/cm, β2=41.2, and Io=22.5 mW/cm2. The resulting best-fitting parameters are LD=0.14 µm and Φ=0.45. Data for Kv<0 (small spots) were not used for the fit.

Fig. 5
Fig. 5

Experimental data tan φ (spots) as a function of Kv for the same conditions as in Fig. 4, with the resulting parameter Φ=0.41 from the fit to Eq. (21). Data for Kv<0 (small spots) are also not considered for the fit.

Tables (1)

Tables Icon

Table 1 Experimental Results

Equations (26)

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

Esc=-mEeff,
Eeff=E0+iED1+K2ls2-iKlE-iKvτM(1+K2LD2-iKLE),
τM=ε0hν(kBT/q)qLD2αIΦ,ls2=ε0kBTq2(ND)eff,lE=ε0E0q(ND)eff,
η=2β21+β2 cosh(Γd/2)-cos(γd/2)β2 exp(-Γd/2)+exp(Γd/2),
withΓ=-4πn3reff2λ I {Eeff},γ=-4πn3reff2λ R{Eeff},
ηm2Γd42+γd42,m=2β1+β2,
tan φ=sin(γd/2)1-β21+β2[cosh(Γd/2)-cos(γd/2)]+sinh(Γd/2),
γ=-4πn3reff2λ arKv exp(αz)+craK 2v2 exp(2αz)+bKv exp(αz)+c,
Γ=-4πn3reff2λ aiKv exp(αz)+ciaK2v2 exp(2αz)+bKv exp(αz)+c,
a=[K2LE2+(1+K2LD2)2]τM(0)2,
b=2τM(0)(K2ls2-K2LD2) EoED,
c=(1+K2ls2)2+K2lE2,
ar=-[(1+K2LD2)ED+KLEEo]τM(0),
cr=Eo,
ai=EoτM(0),
ci=EoKlE+ED(1+K2ls2),
τM(0)
=εo(kBT/q)hνqLD2αΦI(0).
0dγdz=γ¯d=-4πn3reff2λ ar-bcr2c 2α4ac-b2×arctan 2aKv exp(αz)+b4ac-b2z=0z=d+-4πn3reff2λ cr2αc×ln exp(2αz)aK2v2 exp(2αz)+bKv exp(αz)+cz=0z=d,
0dΓdz=Γ¯d=-4πn3reff2λ×ai-bci2c 2α4ac-b2×arctan 2aKv exp(αz)+b4ac-b2z=0z=d+-4πn3reff2λ ci2αc×ln exp(2αz)aK2v2 exp(2αz)+bKv exp(αz)+cz=0z=d,
η=2β21+β2 cosh(Γ¯d/2)-cos(γ¯d/2)β2 exp(-Γ¯d/2)+exp(Γ¯d/2),
tan φ=sin(γ¯d/2)1-β21+β2[cosh(Γ¯d/2)-cos(γ¯d/2)]+sinh(Γ¯d/2).
VΩ=AΩKdΩ2ψdIS0IR0η sin φ,
V 2Ω=A2ΩKd2Ω ψd22 IS0IR0η cos φ,
η=1ISIR(KdΩ)2 VΩAΩ2vdKPZTΩ2+2V2ΩA2Ω(vdKPZTΩ)22,
tan φ=VΩV2Ω A2ΩAΩ KPZTΩvd4.

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