Abstract

We propose a mathematical model for the movement in absorbing materials of photorefractive holograms under feedback constraints. We use this model to analyze the speed of a fringe-locked running hologram in photorefractive sillenite crystals that usually exhibit a strong absorption effect. Fringe-locked experiments permit us to compute the quantum efficiency for the photogeneration of charge carriers in photorefractive crystals if the effect of bulk absorption and the effective value of the externally applied field are adequately taken into consideration. A Bi12TiO20 sample was measured with the 532-nm laser wavelength, and a quantum efficiency of Φ=0.37 was obtained. Disregarding absorption leads to large errors in Φ.

© 2000 Optical Society of America

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References

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  1. S. I. Stepanov, V. V. Kulikov, and M. P. Petrov, “ ‘Running’ holograms in photorefractive Bi12TiO20 crystals,” Opt. Commun. 44, 19–23 (1982).
    [CrossRef]
  2. G. Hamel de Montchenault, B. Loiseaux, and J. P. Huignard, “Moving grating during erasure in photorefractive Bi12SiO20 crystals,” Electron. Lett. 22, 1030–1032 (1986).
    [CrossRef]
  3. J. Frejlich, P. M. Garcia, and L. Cescato, “Adaptive fringe-locked running hologram in photorefractive crystals: errata,” Opt. Lett. 15, 1247 (1990).
    [CrossRef] [PubMed]
  4. P. M. Garcia, L. Cescato, and J. Frejlich, “Phase-shift measurement in photorefractive holographic recording,” J. Appl. Phys. 66, 47–49 (1989).
    [CrossRef]
  5. A. A. Freschi, P. M. Garcia, and J. Frejlich, “Charge-carrier diffusion length in photorefractive crystals computed from the initial hologram phase shift,” Appl. Phys. Lett. 71, 2427–2429 (1997).
    [CrossRef]
  6. A. A. Freschi, P. M. Garcia, and J. Frejlich, “Phase-controlled photorefractive running holograms,” Opt. Commun. 143, 257–260 (1997).
    [CrossRef]
  7. S. Stepanov and P. Petrov, Photorefractive Materials and Their Applications I, P. Günter and J.-P Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 263–289.
    [CrossRef]
  8. E. Shamonina, K. H. Ringhofer, P. M. Garcia, A. A. Freschi, and J. Frejlich, “Shape-asymmetry of the diffraction efficiency in Bi12TiO20 crystals: the simultaneous influence of absorption and higher harmonics,” Opt. Commun. 141, 132–136 (1997).
    [CrossRef]
  9. 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]
  10. 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]
  11. C. H. Kwak, S. Y. Park, H. K. Lee, and E.-H. Lee, “Exact solution of two-wave coupling for photorefractive and photochromic gratings in photorefractive materials,” Opt. Commun. 79, 349–352 (1990).
    [CrossRef]
  12. A. A. Kamshilin and M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
    [CrossRef]

1997

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

A. A. Freschi, P. M. Garcia, and J. Frejlich, “Phase-controlled photorefractive running holograms,” Opt. Commun. 143, 257–260 (1997).
[CrossRef]

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

1990

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

C. H. Kwak, S. Y. Park, H. K. Lee, and E.-H. Lee, “Exact solution of two-wave coupling for photorefractive and photochromic gratings in photorefractive materials,” Opt. Commun. 79, 349–352 (1990).
[CrossRef]

1989

P. M. Garcia, L. Cescato, and J. Frejlich, “Phase-shift measurement in photorefractive holographic recording,” J. Appl. Phys. 66, 47–49 (1989).
[CrossRef]

1986

G. Hamel de Montchenault, B. Loiseaux, and J. P. Huignard, “Moving grating during erasure in photorefractive Bi12SiO20 crystals,” Electron. Lett. 22, 1030–1032 (1986).
[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]

1985

A. A. Kamshilin and M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

1982

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

Cescato, L.

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

P. M. Garcia, L. Cescato, and J. Frejlich, “Phase-shift measurement in photorefractive holographic recording,” J. Appl. Phys. 66, 47–49 (1989).
[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]

Frejlich, J.

A. A. Freschi, P. M. Garcia, and J. Frejlich, “Phase-controlled photorefractive running holograms,” Opt. Commun. 143, 257–260 (1997).
[CrossRef]

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

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

P. M. Garcia, L. Cescato, and J. Frejlich, “Phase-shift measurement in photorefractive holographic recording,” J. Appl. Phys. 66, 47–49 (1989).
[CrossRef]

Freschi, A. A.

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

A. A. Freschi, P. M. Garcia, and J. Frejlich, “Phase-controlled photorefractive running holograms,” Opt. Commun. 143, 257–260 (1997).
[CrossRef]

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

Garcia, P. M.

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 efficiency 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, “Phase-controlled photorefractive running holograms,” Opt. Commun. 143, 257–260 (1997).
[CrossRef]

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

P. M. Garcia, L. Cescato, and J. Frejlich, “Phase-shift measurement in photorefractive holographic recording,” J. Appl. Phys. 66, 47–49 (1989).
[CrossRef]

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]

Hamel de Montchenault, G.

G. Hamel de Montchenault, B. Loiseaux, and J. P. Huignard, “Moving grating during erasure in photorefractive Bi12SiO20 crystals,” Electron. Lett. 22, 1030–1032 (1986).
[CrossRef]

Huignard, J. P.

G. Hamel de Montchenault, B. Loiseaux, and J. P. Huignard, “Moving grating during erasure in photorefractive Bi12SiO20 crystals,” Electron. Lett. 22, 1030–1032 (1986).
[CrossRef]

Kamshilin, A. A.

A. A. Kamshilin and M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[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]

Kwak, C. H.

C. H. Kwak, S. Y. Park, H. K. Lee, and E.-H. Lee, “Exact solution of two-wave coupling for photorefractive and photochromic gratings in photorefractive materials,” Opt. Commun. 79, 349–352 (1990).
[CrossRef]

Lee, E.-H.

C. H. Kwak, S. Y. Park, H. K. Lee, and E.-H. Lee, “Exact solution of two-wave coupling for photorefractive and photochromic gratings in photorefractive materials,” Opt. Commun. 79, 349–352 (1990).
[CrossRef]

Lee, H. K.

C. H. Kwak, S. Y. Park, H. K. Lee, and E.-H. Lee, “Exact solution of two-wave coupling for photorefractive and photochromic gratings in photorefractive materials,” Opt. Commun. 79, 349–352 (1990).
[CrossRef]

Loiseaux, B.

G. Hamel de Montchenault, B. Loiseaux, and J. P. Huignard, “Moving grating during erasure in photorefractive Bi12SiO20 crystals,” Electron. Lett. 22, 1030–1032 (1986).
[CrossRef]

Park, S. Y.

C. H. Kwak, S. Y. Park, H. K. Lee, and E.-H. Lee, “Exact solution of two-wave coupling for photorefractive and photochromic gratings in photorefractive materials,” Opt. Commun. 79, 349–352 (1990).
[CrossRef]

Petrov, M. P.

A. A. Kamshilin and M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

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

Ringhofer, K. H.

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

Shamonina, E.

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 efficiency in Bi12TiO20 crystals: the simultaneous influence of absorption and higher harmonics,” Opt. Commun. 141, 132–136 (1997).
[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]

Appl. Phys. Lett.

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

Electron. Lett.

G. Hamel de Montchenault, B. Loiseaux, and J. P. Huignard, “Moving grating during erasure in photorefractive Bi12SiO20 crystals,” Electron. Lett. 22, 1030–1032 (1986).
[CrossRef]

J. Appl. Phys.

P. M. Garcia, L. Cescato, and J. Frejlich, “Phase-shift measurement in photorefractive holographic recording,” J. Appl. Phys. 66, 47–49 (1989).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Commun.

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]

C. H. Kwak, S. Y. Park, H. K. Lee, and E.-H. Lee, “Exact solution of two-wave coupling for photorefractive and photochromic gratings in photorefractive materials,” Opt. Commun. 79, 349–352 (1990).
[CrossRef]

A. A. Kamshilin and M. P. Petrov, “Continuous reconstruction of holographic interferograms through anisotropic diffraction in photorefractive crystals,” Opt. Commun. 53, 23–26 (1985).
[CrossRef]

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

A. A. Freschi, P. M. Garcia, and J. Frejlich, “Phase-controlled photorefractive running holograms,” Opt. Commun. 143, 257–260 (1997).
[CrossRef]

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

Opt. Lett.

Other

S. Stepanov and P. Petrov, Photorefractive Materials and Their Applications I, P. Günter and J.-P Huignard, eds., Vol. 61 of Topics in Applied Physics (Springer-Verlag, Berlin, 1988), pp. 263–289.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Experimental setup: G, glass plate; BTO, Bi12TiO20 crystal; VA, applied voltage; D1,D2, photodetectors; LA-Ω, lock-in amplifier tuned to frequency Ω; INT, integrator; HV, high-voltage source amplifier driving piezo-electric supported mirror PZT; OSC, oscillator producing the Ω-frequency signal used to modulate the phase of beam IS0; BS, beam splitter; M, mirror.

Fig. 2
Fig. 2

Experimentally measured detuning Kv measured in a fringe-locked experiment (filled circles) as a function of the ratio of applied to diffusion fields E/ED. The best fit (continuous curve) to the implicit relations in Eq. (19) leads to ξ=0.73 and Φ=0.36 for the parameters LD=0.14 μm and ls=0.065 μm. The theoretical fit (dashed curve) to the simplified Eq. (11), where absorption is not taken into account, leads to Φ=0.15 when all other conditions are unchanged.

Equations (25)

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IΩ=4J1(ψd)IR0IS0η(1-η)sin φ,
I2Ω=4J2(ψd)IR0IS0η(1-η)cos φ.
VΩ=Aη(1-η)sin φ,V2Ω=Aη(1-η)cos φ,
tan φ=VΩ/V2Ω
sin φ=12sinh(Γd/4)-cosh(Γd/4)[cosh2(Γd/4)-cos2(γd/4)]1/2sinγd2,
Γ=-2πn3reffλ cos θI(Eeff),
γ=-2πn3reffλ cos θR(Eeff),tan ϕ=Γγ,
Eeff
=-E+iED1+K2lS2-iKlE-iτMKv(1+K2LD2-iKLE),
ED=K kBTq,lS2=kBTε0q2(ND)eff,lE=ε0Eq(ND)eff,
LD2=Dτ,D=μkBT/q,
(ND)eff=ND+(ND-ND+)ND,LE=μτE,
τM=ε0hνdqμτΦIabs.
R(Eeff)=-E(1+K2ls2-K2LEvτM)-ED[KlE+KvτM(1+K2LD2)](1+K2ls2-K2LEvτM)2+[KlE+KvτM(1+K2LD2)]2.
v=1KτMEEDE2K2LD2+ED2(1+K2LD2).
-dIdz=αI0exp(-αz),
τM(z)=τM(0)exp(αz),
IS(z)z=Γ(z) IR(z)IS(z)IR(z)+IS(z),
ψS(z)z=-γ(z)2IR(z)IR(z)+IS(z),
1IS(z)IS(z)z=Γ(z),
ψS(z)z=-γ(z)2.
1d0dR[Eeff(z)]dz=0.
4ac-b2τM(0)Kv[exp(αd)-1]2c+2aτM2(0)K2v2exp(αd)+bτM(0)Kv[exp(αd)+1]
=tanx4ac-b22cg+xbαd-12lnaτM2(0)K2v2exp(2αd)+bτM(0)Kv exp(αd)+caτM2(0)K2v2+bτM(0)Kv+c
for4acb2,

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