Abstract

We present the theoretical and experimental results of photorefractive two-beam coupling in Cr-doped strontium barium niobate:60, using thermal excitation (i.e., dark conductivity) to model the experimentally observed temperature-dependent behavior of the two-beam coupling constant and response time.

© 1989 Optical Society of America

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  1. G. A. Rakuljic, K. Sayano, A. Agranat, A. Yariv, R. R. Neurgaonkar, Appl. Phys. Lett. 53, 1465 (1988).
    [CrossRef]
  2. L. J. Cheng, A. Partovi, Appl. Phys. Lett. 49, 1456 (1986).
    [CrossRef]
  3. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, Opt. Commun. 23, 338 (1977).
    [CrossRef]
  4. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, Ferroelectrics 22, 949 (1979).
    [CrossRef]
  5. N. V. Kukhtarev, Sov. Tech. Phys. Lett. 2, 438 (1976).
  6. M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, J. Feinberg, J. Appl. Phys. 62, 374 (1987).
    [CrossRef]
  7. G. C. Valley, M. B. Klein, Opt. Eng. 22, 704 (1983).
  8. J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
    [CrossRef]

1988 (1)

G. A. Rakuljic, K. Sayano, A. Agranat, A. Yariv, R. R. Neurgaonkar, Appl. Phys. Lett. 53, 1465 (1988).
[CrossRef]

1987 (1)

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, J. Feinberg, J. Appl. Phys. 62, 374 (1987).
[CrossRef]

1986 (1)

L. J. Cheng, A. Partovi, Appl. Phys. Lett. 49, 1456 (1986).
[CrossRef]

1983 (1)

G. C. Valley, M. B. Klein, Opt. Eng. 22, 704 (1983).

1980 (1)

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

1979 (1)

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

1977 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, Opt. Commun. 23, 338 (1977).
[CrossRef]

1976 (1)

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

Agranat, A.

G. A. Rakuljic, K. Sayano, A. Agranat, A. Yariv, R. R. Neurgaonkar, Appl. Phys. Lett. 53, 1465 (1988).
[CrossRef]

Cheng, L. J.

L. J. Cheng, A. Partovi, Appl. Phys. Lett. 49, 1456 (1986).
[CrossRef]

Cory, W. K.

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, J. Feinberg, J. Appl. Phys. 62, 374 (1987).
[CrossRef]

Ewbank, M. D.

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, J. Feinberg, J. Appl. Phys. 62, 374 (1987).
[CrossRef]

Feinberg, J.

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, J. Feinberg, J. Appl. Phys. 62, 374 (1987).
[CrossRef]

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Heiman, D.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Hellwarth, R. W.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Klein, M. B.

G. C. Valley, M. B. Klein, Opt. Eng. 22, 704 (1983).

Kukhtarev, N. V.

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

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, Opt. Commun. 23, 338 (1977).
[CrossRef]

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

Markov, V. B.

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

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, Opt. Commun. 23, 338 (1977).
[CrossRef]

Neurgaonkar, R. R.

G. A. Rakuljic, K. Sayano, A. Agranat, A. Yariv, R. R. Neurgaonkar, Appl. Phys. Lett. 53, 1465 (1988).
[CrossRef]

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, J. Feinberg, J. Appl. Phys. 62, 374 (1987).
[CrossRef]

Odulov, S. G.

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

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, Opt. Commun. 23, 338 (1977).
[CrossRef]

Partovi, A.

L. J. Cheng, A. Partovi, Appl. Phys. Lett. 49, 1456 (1986).
[CrossRef]

Rakuljic, G. A.

G. A. Rakuljic, K. Sayano, A. Agranat, A. Yariv, R. R. Neurgaonkar, Appl. Phys. Lett. 53, 1465 (1988).
[CrossRef]

Sayano, K.

G. A. Rakuljic, K. Sayano, A. Agranat, A. Yariv, R. R. Neurgaonkar, Appl. Phys. Lett. 53, 1465 (1988).
[CrossRef]

Soskin, M. S.

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

Tanguay, A. R.

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Valley, G. C.

G. C. Valley, M. B. Klein, Opt. Eng. 22, 704 (1983).

Vinetski, V. L.

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

Yariv, A.

G. A. Rakuljic, K. Sayano, A. Agranat, A. Yariv, R. R. Neurgaonkar, Appl. Phys. Lett. 53, 1465 (1988).
[CrossRef]

Appl. Phys. Lett. (2)

G. A. Rakuljic, K. Sayano, A. Agranat, A. Yariv, R. R. Neurgaonkar, Appl. Phys. Lett. 53, 1465 (1988).
[CrossRef]

L. J. Cheng, A. Partovi, Appl. Phys. Lett. 49, 1456 (1986).
[CrossRef]

Ferroelectrics (1)

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

J. Appl. Phys. (2)

M. D. Ewbank, R. R. Neurgaonkar, W. K. Cory, J. Feinberg, J. Appl. Phys. 62, 374 (1987).
[CrossRef]

J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
[CrossRef]

Opt. Commun. (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, Opt. Commun. 23, 338 (1977).
[CrossRef]

Opt. Eng. (1)

G. C. Valley, M. B. Klein, Opt. Eng. 22, 704 (1983).

Sov. Tech. Phys. Lett. (1)

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

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Figures (5)

Fig. 1
Fig. 1

Experimental values of the steady-state photorefractive two-beam coupling constant Γ of the SBN:60:Cr crystal as a function of temperature. For the experiments λ = 514.5 nm, λg = 1 μm, I1(0)/I2(0) = 10, and I1(0) = 0.150 W/cm2. The solid curve represents the theoretical value of Γ versus the temperature for some typical material constants.

Fig. 2
Fig. 2

Γ as a function of the total intensity for 293 and 313 K, with the best fit shown by the solid curves.

Fig. 3
Fig. 3

Response time τ of the SBN:60:Cr crystal as defined by the rise time for Γ to reach Γsteady state (1 − e−1). The data are for λ = 514.5 μm, λg = 1 μm, I1(0)/I2(0) = 10, and I1(0) = 0.150 W/cm2.

Fig. 4
Fig. 4

Experimentally measured relative dielectric constant r for the SBN:60:Cr sample obtained by measuring the low-frequency capacitance of the crystal.

Fig. 5
Fig. 5

Theoretical value of Γ from T = 120 K to room temperature showing the peak at some optimum temperature T0 for curve (a), the best fit to the experimentally obtained points, with hνβ/sI0 = 2 × 105; curve (b), low dark conductivity, with hνβ/sI0 = 3 × 103; and curve (c), high dark conductivity, with hνβ/sI0 = 2 × 107.

Equations (13)

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Γ = 1 l ln [ I 2 ( l ) I 1 ( 0 ) I 1 ( l ) I 2 ( 0 ) ] ,
N + t = ( s I 0 h ν + β ) N - γ n N + ,
β exp ( - E β / k T ) .
Γ = R e ( i ω 2 c l r eff n 0 3 E sc ) ,
E sc = i E N m ( E 0 + i E d ) ( 1 - e - t / τ ) [ E 0 + i ( E d + E N ) ] ( 1 + h ν s I 0 β ) ,
τ = t 0 E 0 + i ( E d + E μ ) E 0 + i ( E d + E N ) ,
t 0 = h ν N A s I 0 ( 1 + h ν s I 0 β ) ( N 0 - N A ) ,
E N = e N A k ( 1 + N A N 0 - N A ) - 1 ,
E d = k B T k e ,
E μ = γ N A μ k .
Γ 1 1 + K / I 0 ,
Γ = Γ 0 ( T T + B / ) [ 1 1 + A exp ( - E β / k B T ) ] ,
τ = τ 0 ( T + C / μ T + B / ) [ 1 1 + A exp ( - E β / k B T ) ] .

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