Abstract

Holographic gratings in photorefractive crystals that are based on charge redistribution inevitably decay as a result of ionic and electronic conduction. Under certain and restricted conditions these decay times can be acceptably long. Relevant decay rates and transient hologram field expressions are derived with special reference to LiNbO3. Some experimental data are presented.

© 1995 Optical Society of America

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References

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  1. G. Montemezzani, M. Zgonik, P. Günter, J. Opt. Soc. Am. B 10, 171 (1993).
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  2. S. Orlov, D. Psaltis, R. R. Neurgaonkar, Appl. Phys. Lett. 63, 2466 (1993).
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  3. M. Carrascosa, F. Agullo-Lopez, J. Opt. Soc. Am. B 7, 2317 (1990).
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  4. R. Matull, R. A. Rupp, J. Phys. D 21, 1556 (1988).
    [CrossRef]
  5. D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, Appl. Phys. Lett. 26, 182 (1975).
    [CrossRef]
  6. A. Yariv, V. Leyva, G. A. Rakuljic, in Technical Digest, 1994 IEEE Nonlinear Optics, Materials, Fundamentals, and Applications (Institute of Electrical and Electronics Engineers, New York, 1994), paper PD6.
  7. V. Leyva, G. A. Rakuljic, B. O’Conner, Appl. Phys. Lett. 65, 1079 (1994).
    [CrossRef]

1994 (1)

V. Leyva, G. A. Rakuljic, B. O’Conner, Appl. Phys. Lett. 65, 1079 (1994).
[CrossRef]

1993 (2)

G. Montemezzani, M. Zgonik, P. Günter, J. Opt. Soc. Am. B 10, 171 (1993).
[CrossRef]

S. Orlov, D. Psaltis, R. R. Neurgaonkar, Appl. Phys. Lett. 63, 2466 (1993).
[CrossRef]

1990 (1)

1988 (1)

R. Matull, R. A. Rupp, J. Phys. D 21, 1556 (1988).
[CrossRef]

1975 (1)

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, Appl. Phys. Lett. 26, 182 (1975).
[CrossRef]

Agullo-Lopez, F.

Amodei, J. J.

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, Appl. Phys. Lett. 26, 182 (1975).
[CrossRef]

Burke, W. J.

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, Appl. Phys. Lett. 26, 182 (1975).
[CrossRef]

Carrascosa, M.

Günter, P.

Leyva, V.

V. Leyva, G. A. Rakuljic, B. O’Conner, Appl. Phys. Lett. 65, 1079 (1994).
[CrossRef]

A. Yariv, V. Leyva, G. A. Rakuljic, in Technical Digest, 1994 IEEE Nonlinear Optics, Materials, Fundamentals, and Applications (Institute of Electrical and Electronics Engineers, New York, 1994), paper PD6.

Matull, R.

R. Matull, R. A. Rupp, J. Phys. D 21, 1556 (1988).
[CrossRef]

Montemezzani, G.

Neurgaonkar, R. R.

S. Orlov, D. Psaltis, R. R. Neurgaonkar, Appl. Phys. Lett. 63, 2466 (1993).
[CrossRef]

O’Conner, B.

V. Leyva, G. A. Rakuljic, B. O’Conner, Appl. Phys. Lett. 65, 1079 (1994).
[CrossRef]

Orlov, S.

S. Orlov, D. Psaltis, R. R. Neurgaonkar, Appl. Phys. Lett. 63, 2466 (1993).
[CrossRef]

Phillips, W.

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, Appl. Phys. Lett. 26, 182 (1975).
[CrossRef]

Psaltis, D.

S. Orlov, D. Psaltis, R. R. Neurgaonkar, Appl. Phys. Lett. 63, 2466 (1993).
[CrossRef]

Rakuljic, G. A.

V. Leyva, G. A. Rakuljic, B. O’Conner, Appl. Phys. Lett. 65, 1079 (1994).
[CrossRef]

A. Yariv, V. Leyva, G. A. Rakuljic, in Technical Digest, 1994 IEEE Nonlinear Optics, Materials, Fundamentals, and Applications (Institute of Electrical and Electronics Engineers, New York, 1994), paper PD6.

Rupp, R. A.

R. Matull, R. A. Rupp, J. Phys. D 21, 1556 (1988).
[CrossRef]

Staebler, D. L.

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, Appl. Phys. Lett. 26, 182 (1975).
[CrossRef]

Yariv, A.

A. Yariv, V. Leyva, G. A. Rakuljic, in Technical Digest, 1994 IEEE Nonlinear Optics, Materials, Fundamentals, and Applications (Institute of Electrical and Electronics Engineers, New York, 1994), paper PD6.

Zgonik, M.

Appl. Phys. Lett. (3)

S. Orlov, D. Psaltis, R. R. Neurgaonkar, Appl. Phys. Lett. 63, 2466 (1993).
[CrossRef]

D. L. Staebler, W. J. Burke, W. Phillips, J. J. Amodei, Appl. Phys. Lett. 26, 182 (1975).
[CrossRef]

V. Leyva, G. A. Rakuljic, B. O’Conner, Appl. Phys. Lett. 65, 1079 (1994).
[CrossRef]

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

J. Phys. D (1)

R. Matull, R. A. Rupp, J. Phys. D 21, 1556 (1988).
[CrossRef]

Other (1)

A. Yariv, V. Leyva, G. A. Rakuljic, in Technical Digest, 1994 IEEE Nonlinear Optics, Materials, Fundamentals, and Applications (Institute of Electrical and Electronics Engineers, New York, 1994), paper PD6.

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Figures (2)

Fig. 1
Fig. 1

Typical life history of a hologram in a photorefractive material.

Fig. 2
Fig. 2

Diffraction efficiency versus time of two holograms recorded and stored in Fe-doped LiNbO3 at 110 °C. The grating spacing is ~0.34 μm. The initial (t = 0) diffraction efficiencies were ~30% (upper curve, circles) and ~12% (lower curve, squares). Because of ionic compensation (fast stage of the decay) the reflection efficiency decreases by a factor of ~100 for both holograms. It continues to decay further in the dark at a much slower rate because of conduction by thermally excited electrons.

Equations (11)

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E 1 = i e K ( N d 1 + + n i 1 - n e 1 ) ,
N d 1 + t = - ( σ / h ν I 0 + β ) N d N a N d 1 + - γ e N a n e 1 ,
n e 1 t = [ - ( σ / h ν I 0 + β ) N d N a + μ e n e 0 e + i k σ I 0 K e ] N d 1 + + μ n e 0 e n i 1 - ( γ e N a + μ n e 0 e + D e K 2 + i μ e K E 0 ) n e 1 ,
n i 1 t = - ( μ i n i 0 e + D i K 2 + i μ i K E 0 ) n i 1 + μ i n i 0 e ( n e 1 - N d 1 + ) ,
E 1 ( I ) ( t ) = E 1 ( 0 ) ( 0 ) { D i K 2 + i K μ i E 0 ω i + D i K 2 + i K μ i E 0 + ω i ω i + D i K 2 + i K μ i E 0 × exp [ - ( ω i + D i K 2 + i K μ i E 0 ) t ] } ,
E 1 ( 1 ) = D i K 2 + i K μ i E 0 ω i + D i K 2 + i K μ i E 0 E 1 ( 0 ) .
E 1 ( II ) ( t ) = i e K [ N d 1 + ( t ) + n i 1 ( t ) ] = E 1 ( 0 ) D i K 2 ω i + D i K 2 × exp [ - ω e ( D i K 2 D i K 2 + ω i + K 2 d 2 ) t ] ω e = e μ e n e 0 = e μ e ( σ / h ν I 0 + β ) ( N d - N a ) γ e N a , d 2 N d k T N a ( N d - N a ) e 2 ,
E 1 ( III ) ( t ) = i e K { E d - i E p . v . N a / N d E d + E q - i E p . v . N a / N d n i 1 ( t 1 ) + [ N d 1 + ( t 1 ) + E q E d + E q - i E p . v . N a / N d n i 1 ( t 1 ) ] × exp ( - ω i t ) } , ω 1 ω e [ 1 + K 2 d 2 - i E p . v . E q ( N a N d ) ] ,
E 1 ( 2 ) = i e K n i 1 ( t 1 ) E d - i E p . v . N a / N d E d + E q - i E p . v . N a / N d ,
n i 1 ( IV ) ( t ) = n i 1 ( t 2 ) exp { - [ ω i ( ω 1 - ω e ω 1 ) + D i K 2 ] t }
E 1 ( IV ) ( t ) = i e K ( E d - i E p . v . N a / N d E d + E q - i E p . v . N a / N d ) n i 1 ( t 1 ) × exp { - [ ω i ( ω 1 - ω e ω 1 ) + D i K 2 ] t } .

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