Abstract

The photorefractive gain and time response of n-doped and p-doped BaTiO3 were compared in the visible, λ =514 nm, and in the infrared, λ=830 nm. Two-beam coupling experiments were conducted for beam ratios between 3600:1, 5000:1, and 8000:1. In both infrared and visible it was observed that the measured gains were higher for the p-BaTiO3 by an order of magnitude or more. When the gain was high, a temporal memory effect was observed, suggesting that the time dependence of the space-charge field is determined by the history of the modulation depth. This effect is shown to be consistent with the Kukhtarev equations for a single carrier. Low-gain behavior was observed at all interaction angles for both crystals in the IR. In the visible the high-gain temporal memory effect is reported for the p-BaTiO3.

© 1998 Optical Society of America

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  1. N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).
  2. A. M. Glass, Opt. Eng. (Bellingham) 17, 470 (1978).
    [CrossRef]
  3. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [CrossRef]
  4. T. G. Pencheva, M. P. Petrov, and S. I. Stepanov, Opt. Commun. 40, (1982).
    [CrossRef]
  5. G. C. Valley and M. B. Klein, Opt. Eng. (Bellingham) 22, 704 (1983).
    [CrossRef]
  6. D. Erbschloe, L. Solymar, J. Takacs, and T. Wilson, IEEE J. Quantum Electron. 24, 820 (1988).
    [CrossRef]
  7. J. H. Hong, A. E. Chiou, and P. Yeh, Appl. Opt. 29, 3026 (1990).
    [CrossRef] [PubMed]
  8. J. Joseph, P. K. C. Pillai, and K. Singh, Appl. Opt. 30, 3315 (1991).
    [CrossRef] [PubMed]
  9. G. Charmaine Gilbreath, J. Lightwave Technol. 9, 105 (1991).
    [CrossRef]
  10. Y. H. Lee, IEEE J. Quantum Electron. 27, 2488 (1991).
    [CrossRef]
  11. C. Xu, D. Statman, and J. K. McIver, J. Opt. Soc. Am. B 9, 1825 (1992).
    [CrossRef]
  12. M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-24, 12 (1984).
    [CrossRef]
  13. R. W. Boyd, Nonlinear Optics (Academic, New York, 1992).
  14. V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, Sov. Phys. Usp. 22, 742 (1979).
    [CrossRef]
  15. D. Statman and G. C. Gilbreath, J. Nonlin. Opt. Phys. Mater. 5, 9 (1996).
    [CrossRef]
  16. F. P. Strohkendl and R. W. Hellwarth, J. Appl. Phys. 62, 2450 (1987).
    [CrossRef]
  17. F. P. Strohkendl, P. Tayebati, and R. W. Hellwarth, J. Appl. Phys. 66, 6024 (1989).
    [CrossRef]
  18. A. E. Attard and T. X. Brown, Appl. Opt. 25, 3253 (1986).
    [CrossRef]
  19. R. Magnusson and T. K. Gaylord, J. Appl. Phys. 47, 190 (1976).
    [CrossRef]
  20. D. Statman and J. C. Lombardi, Laser 96 Conference Proceedings (STS, McLean, Va., 1997).
  21. E. Serrano, V. López, M. Carrascosa, and F. Aqulló-López, J. Opt. Soc. Am. B 11, 670 (1994).
    [CrossRef]
  22. It should be noted that, in scaled coordinates, the length Ld is equivalent to the diffusion field Ed used by some authors.

1996 (1)

D. Statman and G. C. Gilbreath, J. Nonlin. Opt. Phys. Mater. 5, 9 (1996).
[CrossRef]

1994 (1)

1992 (1)

1991 (3)

G. Charmaine Gilbreath, J. Lightwave Technol. 9, 105 (1991).
[CrossRef]

Y. H. Lee, IEEE J. Quantum Electron. 27, 2488 (1991).
[CrossRef]

J. Joseph, P. K. C. Pillai, and K. Singh, Appl. Opt. 30, 3315 (1991).
[CrossRef] [PubMed]

1990 (1)

1989 (1)

F. P. Strohkendl, P. Tayebati, and R. W. Hellwarth, J. Appl. Phys. 66, 6024 (1989).
[CrossRef]

1988 (1)

D. Erbschloe, L. Solymar, J. Takacs, and T. Wilson, IEEE J. Quantum Electron. 24, 820 (1988).
[CrossRef]

1987 (1)

F. P. Strohkendl and R. W. Hellwarth, J. Appl. Phys. 62, 2450 (1987).
[CrossRef]

1986 (1)

1984 (1)

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-24, 12 (1984).
[CrossRef]

1983 (1)

G. C. Valley and M. B. Klein, Opt. Eng. (Bellingham) 22, 704 (1983).
[CrossRef]

1979 (2)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[CrossRef]

1978 (1)

A. M. Glass, Opt. Eng. (Bellingham) 17, 470 (1978).
[CrossRef]

1976 (2)

N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).

R. Magnusson and T. K. Gaylord, J. Appl. Phys. 47, 190 (1976).
[CrossRef]

Aqulló-López, F.

Attard, A. E.

Brown, T. X.

Carrascosa, M.

Chiou, A. E.

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-24, 12 (1984).
[CrossRef]

Erbschloe, D.

D. Erbschloe, L. Solymar, J. Takacs, and T. Wilson, IEEE J. Quantum Electron. 24, 820 (1988).
[CrossRef]

Fischer, B.

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-24, 12 (1984).
[CrossRef]

Gaylord, T. K.

R. Magnusson and T. K. Gaylord, J. Appl. Phys. 47, 190 (1976).
[CrossRef]

Gilbreath, G. C.

D. Statman and G. C. Gilbreath, J. Nonlin. Opt. Phys. Mater. 5, 9 (1996).
[CrossRef]

Gilbreath, G. Charmaine

G. Charmaine Gilbreath, J. Lightwave Technol. 9, 105 (1991).
[CrossRef]

Glass, A. M.

A. M. Glass, Opt. Eng. (Bellingham) 17, 470 (1978).
[CrossRef]

Hellwarth, R. W.

F. P. Strohkendl, P. Tayebati, and R. W. Hellwarth, J. Appl. Phys. 66, 6024 (1989).
[CrossRef]

F. P. Strohkendl and R. W. Hellwarth, J. Appl. Phys. 62, 2450 (1987).
[CrossRef]

Hong, J. H.

Joseph, J.

Klein, M. B.

G. C. Valley and M. B. Klein, Opt. Eng. (Bellingham) 22, 704 (1983).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[CrossRef]

N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).

Lee, Y. H.

Y. H. Lee, IEEE J. Quantum Electron. 27, 2488 (1991).
[CrossRef]

López, V.

Magnusson, R.

R. Magnusson and T. K. Gaylord, J. Appl. Phys. 47, 190 (1976).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

McIver, J. K.

Odulov, S. G.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Pillai, P. K. C.

Serrano, E.

Singh, K.

Solymar, L.

D. Erbschloe, L. Solymar, J. Takacs, and T. Wilson, IEEE J. Quantum Electron. 24, 820 (1988).
[CrossRef]

Soskin, M. S.

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[CrossRef]

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

Statman, D.

D. Statman and G. C. Gilbreath, J. Nonlin. Opt. Phys. Mater. 5, 9 (1996).
[CrossRef]

C. Xu, D. Statman, and J. K. McIver, J. Opt. Soc. Am. B 9, 1825 (1992).
[CrossRef]

Strohkendl, F. P.

F. P. Strohkendl, P. Tayebati, and R. W. Hellwarth, J. Appl. Phys. 66, 6024 (1989).
[CrossRef]

F. P. Strohkendl and R. W. Hellwarth, J. Appl. Phys. 62, 2450 (1987).
[CrossRef]

Takacs, J.

D. Erbschloe, L. Solymar, J. Takacs, and T. Wilson, IEEE J. Quantum Electron. 24, 820 (1988).
[CrossRef]

Tayebati, P.

F. P. Strohkendl, P. Tayebati, and R. W. Hellwarth, J. Appl. Phys. 66, 6024 (1989).
[CrossRef]

Valley, G. C.

G. C. Valley and M. B. Klein, Opt. Eng. (Bellingham) 22, 704 (1983).
[CrossRef]

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[CrossRef]

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-24, 12 (1984).
[CrossRef]

Wilson, T.

D. Erbschloe, L. Solymar, J. Takacs, and T. Wilson, IEEE J. Quantum Electron. 24, 820 (1988).
[CrossRef]

Xu, C.

Yariv, A.

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-24, 12 (1984).
[CrossRef]

Yeh, P.

Appl. Opt. (3)

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, Ferroelectrics 22, 949 (1979).
[CrossRef]

IEEE J. Quantum Electron. (3)

D. Erbschloe, L. Solymar, J. Takacs, and T. Wilson, IEEE J. Quantum Electron. 24, 820 (1988).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, IEEE J. Quantum Electron. QE-24, 12 (1984).
[CrossRef]

Y. H. Lee, IEEE J. Quantum Electron. 27, 2488 (1991).
[CrossRef]

J. Appl. Phys. (3)

R. Magnusson and T. K. Gaylord, J. Appl. Phys. 47, 190 (1976).
[CrossRef]

F. P. Strohkendl and R. W. Hellwarth, J. Appl. Phys. 62, 2450 (1987).
[CrossRef]

F. P. Strohkendl, P. Tayebati, and R. W. Hellwarth, J. Appl. Phys. 66, 6024 (1989).
[CrossRef]

J. Lightwave Technol. (1)

G. Charmaine Gilbreath, J. Lightwave Technol. 9, 105 (1991).
[CrossRef]

J. Nonlin. Opt. Phys. Mater. (1)

D. Statman and G. C. Gilbreath, J. Nonlin. Opt. Phys. Mater. 5, 9 (1996).
[CrossRef]

J. Opt. Soc. Am. B (2)

Opt. Eng. (Bellingham) (2)

G. C. Valley and M. B. Klein, Opt. Eng. (Bellingham) 22, 704 (1983).
[CrossRef]

A. M. Glass, Opt. Eng. (Bellingham) 17, 470 (1978).
[CrossRef]

Sov. Phys. Usp. (1)

V. L. Vinetskii, N. V. Kukhtarev, S. G. Odulov, and M. S. Soskin, Sov. Phys. Usp. 22, 742 (1979).
[CrossRef]

Sov. Tech. Phys. Lett. (1)

N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).

Other (4)

T. G. Pencheva, M. P. Petrov, and S. I. Stepanov, Opt. Commun. 40, (1982).
[CrossRef]

R. W. Boyd, Nonlinear Optics (Academic, New York, 1992).

D. Statman and J. C. Lombardi, Laser 96 Conference Proceedings (STS, McLean, Va., 1997).

It should be noted that, in scaled coordinates, the length Ld is equivalent to the diffusion field Ed used by some authors.

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Figures (12)

Fig. 1
Fig. 1

Experimental setup: P, polarizer; BS, beam splitter; M1, mirror 1; M2, mirror 2; ND, neutral-density filter; A, aperture; PD, photodiode.

Fig. 2
Fig. 2

Experimental geometry.

Fig. 3
Fig. 3

Time dependence of gain for low-gain conditions: p-BaTiO3 λ=830 nm, θ=53°, β=0°. Laser power, 40 mW.

Fig. 4
Fig. 4

Time dependence of gain for high-gain conditions: p-BaTiO3 λ=514 nm, θ=30°, β=0°. Laser power, 25 mW.

Fig. 5
Fig. 5

Net gain (γ-2α) versus grating spacing, 2[sin(θ/2)]: λ=830 nm, β=0. Closed circles, p-BaTiO3; open circles, n-BaTiO3. Fits give trap density of 0.66×1016 cm-3 for both p- and n-BaTiO3. Fits also give effective electro-optic coefficients of 98 pm/A for p-BaTiO3 and 65 pm/V for n-BaTiO3 and loss coefficients of 0 cm-1 for p-BaTiO3 and 1.12 cm-1 for n-BaTiO3.

Fig. 6
Fig. 6

Net gain (γ-2α) versus grating spacing, 2[sin(θ/2)]: λ=514 nm, β=0. Closed circles, p-BaTiO3; open circles, n-BaTiO3. Fits give trap density of 1.2×1016 cm-3 for both p- and n-BaTiO3. Fits also give effective electro-optic coefficients of 240 pm/V for p-BaTiO3 and 110 pm/V for n-BaTiO3 and loss coefficients of 1.79 cm-1 for p-BaTiO3 and 1.01 cm-1 for n-BaTiO3.

Fig. 7
Fig. 7

Δn for low-gain two-beam coupling: p-BaTiO3 λ=830 nm, θ=53°, β=0°. Laser power, 40 mW.

Fig. 8
Fig. 8

Δn for high-gain two-beam coupling: p-BaTiO3 λ=514 nm, θ=30°, β=0°. Laser power, 25 mW.

Fig. 9
Fig. 9

Rate constants for p-BaTiO3 versus grating spacing at λ=830 nm.

Fig. 10
Fig. 10

Rate constants for n-BaTiO3 versus grating spacing at λ=830 nm.

Fig. 11
Fig. 11

Rate constants for p-BaTiO3 versus grating spacing at λ=514 nm.

Fig. 12
Fig. 12

Rate constants for n-BaTiO3 versus grating spacing at λ=514 nm.

Tables (4)

Tables Icon

Table 1 Gain and Fit Parameters to Δn=c+a exp(-kt)+b exp(-lt) for p-BaTiO3 in the IR

Tables Icon

Table 2 Gain and Fit Parameters to Δn=c+a exp(-kt)+b exp(-lt) for n-BaTiO3 in the IR

Tables Icon

Table 3 Fit Parameters to Δn=c+a exp(-kt)+b exp(-lt) for p-BaTiO3 in the Visible

Tables Icon

Table 4 Gain and Fit Parameters to Δn=c+a exp(-kt)+b exp(-lt) for n-BaTiO3 in the Visible

Equations (14)

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

dE1dτ=-f0(ND-1)1+Ld21/τR+Ld2 E1-m2 Ld21+Ld2,
Δn=12n3reffE1,
dA1dz=πλ cos(θ/2)ΔnA2-αA1,
dA2dz=-πλ cos(θ/2)Δn*A1-αA2,
I1=I10I0(I0-I10)exp[-(γ-2α)d]+I10exp(2αd),
γ=2πλ cos(θ/2) Δnm
γ-2α=cosθ/2dlnI1(I0-I10)I10[I0-I1 exp(2αd)]=cosθ/2dlnGR1+R-G exp(2αd).
E1(z, t)=f0(ND-1)Ld21/τR+Ld20tm(z, s)×exp[-κ(t-s)]ds,
κ=f0(ND-1)1+Ld21/τR+Ld2.
E1(z, t)=Ld21+Ld2m(z)[1-exp(-κτ)].
E1(z, τ)=Ld21+Ld2m(z, 0)×1-γγ-κ exp(-κτ)+κγ-κ exp(-γτ).
η=πΔndλ cos θ/22.
E1=2λ cos θ/2πn3reffd G-1R.
Δn=a exp(-kt)+b exp(-lt)+c.

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