Abstract

Scattering due to noisy gratings produced by randomly distributed charge particles in photorefractive crystals is considered. The scattering cross section is analyzed in terms of the fluctuation of the refractive index introduced by the random space-charge field through the Pockels effect. We also consider the noise in photo-refractive gratings due to such scattering. A signal-to-noise ratio of 1 leads to a minimum modulation depth for an index grating.

© 1991 Optical Society of America

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References

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  1. See, for example, P. Yeh, IEEE J. Quantum Electron 25, 484 (1989).
    [CrossRef]
  2. A. Chiou, P. Yeh, Appl. Opt. 29, 1111 (1990).
    [CrossRef] [PubMed]
  3. See, for example, P. Yeh, A. E. Chiou, J. Hong, P. Bechwith, T. Chang, M. Khoshnevisan, Opt. Eng. 28, 328 (1989).
  4. J. H. Hong, S. Campbell, P. Yeh, Appl. Opt. 29, 3019 (1990).
    [CrossRef] [PubMed]
  5. I. McMichael, P. Beckwith, P. Yeh, Opt. Lett. 12, 1023 (1987), and references therein.
    [CrossRef] [PubMed]
  6. R. McGraw, Phys. Rev. A 42, 2235 (1990).
    [CrossRef]
  7. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 418–422.
  8. See, for example, A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).
  9. See, for example, C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1976).
  10. J. Feinberg, J. Opt. Soc. Am. 72, 46 (1982).
    [CrossRef]
  11. H. Rajbenbach, A. Delboulbé, J. P. Huignard, Opt. Lett. 14, 1275 (1989).
    [CrossRef] [PubMed]
  12. J. Joseph, P. K. C. Pillai, K. Singh, Opt. Commun. 80, 84 (1990).
    [CrossRef]

1990 (4)

1989 (3)

See, for example, P. Yeh, IEEE J. Quantum Electron 25, 484 (1989).
[CrossRef]

H. Rajbenbach, A. Delboulbé, J. P. Huignard, Opt. Lett. 14, 1275 (1989).
[CrossRef] [PubMed]

See, for example, P. Yeh, A. E. Chiou, J. Hong, P. Bechwith, T. Chang, M. Khoshnevisan, Opt. Eng. 28, 328 (1989).

1987 (1)

1982 (1)

Bechwith, P.

See, for example, P. Yeh, A. E. Chiou, J. Hong, P. Bechwith, T. Chang, M. Khoshnevisan, Opt. Eng. 28, 328 (1989).

Beckwith, P.

Campbell, S.

Chang, T.

See, for example, P. Yeh, A. E. Chiou, J. Hong, P. Bechwith, T. Chang, M. Khoshnevisan, Opt. Eng. 28, 328 (1989).

Chiou, A.

Chiou, A. E.

See, for example, P. Yeh, A. E. Chiou, J. Hong, P. Bechwith, T. Chang, M. Khoshnevisan, Opt. Eng. 28, 328 (1989).

Delboulbé, A.

Feinberg, J.

Hong, J.

See, for example, P. Yeh, A. E. Chiou, J. Hong, P. Bechwith, T. Chang, M. Khoshnevisan, Opt. Eng. 28, 328 (1989).

Hong, J. H.

Huignard, J. P.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 418–422.

Joseph, J.

J. Joseph, P. K. C. Pillai, K. Singh, Opt. Commun. 80, 84 (1990).
[CrossRef]

Khoshnevisan, M.

See, for example, P. Yeh, A. E. Chiou, J. Hong, P. Bechwith, T. Chang, M. Khoshnevisan, Opt. Eng. 28, 328 (1989).

Kittel, C.

See, for example, C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1976).

McGraw, R.

R. McGraw, Phys. Rev. A 42, 2235 (1990).
[CrossRef]

McMichael, I.

Pillai, P. K. C.

J. Joseph, P. K. C. Pillai, K. Singh, Opt. Commun. 80, 84 (1990).
[CrossRef]

Rajbenbach, H.

Singh, K.

J. Joseph, P. K. C. Pillai, K. Singh, Opt. Commun. 80, 84 (1990).
[CrossRef]

Yariv, A.

See, for example, A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Yeh, P.

A. Chiou, P. Yeh, Appl. Opt. 29, 1111 (1990).
[CrossRef] [PubMed]

J. H. Hong, S. Campbell, P. Yeh, Appl. Opt. 29, 3019 (1990).
[CrossRef] [PubMed]

See, for example, P. Yeh, IEEE J. Quantum Electron 25, 484 (1989).
[CrossRef]

See, for example, P. Yeh, A. E. Chiou, J. Hong, P. Bechwith, T. Chang, M. Khoshnevisan, Opt. Eng. 28, 328 (1989).

I. McMichael, P. Beckwith, P. Yeh, Opt. Lett. 12, 1023 (1987), and references therein.
[CrossRef] [PubMed]

See, for example, A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

Appl. Opt. (2)

IEEE J. Quantum Electron (1)

See, for example, P. Yeh, IEEE J. Quantum Electron 25, 484 (1989).
[CrossRef]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

J. Joseph, P. K. C. Pillai, K. Singh, Opt. Commun. 80, 84 (1990).
[CrossRef]

Opt. Eng. (1)

See, for example, P. Yeh, A. E. Chiou, J. Hong, P. Bechwith, T. Chang, M. Khoshnevisan, Opt. Eng. 28, 328 (1989).

Opt. Lett. (2)

Phys. Rev. A (1)

R. McGraw, Phys. Rev. A 42, 2235 (1990).
[CrossRef]

Other (3)

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 418–422.

See, for example, A. Yariv, P. Yeh, Optical Waves in Crystals (Wiley, New York, 1984).

See, for example, C. Kittel, Introduction to Solid State Physics (Wiley, New York, 1976).

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Equations (16)

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d σ d Ω = S 2 ,
S = k 2 4 π d r p * · [ ( Δ ) - 1 p ] exp [ i ( k - k ) · r ] ,
Δ = - ( r E sc ) 0 ,
· dc E sc = ρ ,
S = - e k 2 4 π 0 p * · [ ( r Kp ) ] K · dc · K F ,
F = 1 e ρ ( r ) exp ( i K · r ) d r ,
ρ ( r ) = e i = 1 N [ δ ( r - r i ) - δ ( r - x i ) ] ,
p ( r , x ) = 1 V k D 2 4 π exp ( - k D r - x ) r - x
k D 2 = e 2 ( N / V ) k B T dc ,
F 2 = 2 N K 2 K 2 + k D 2 ,
d σ d Ω = 2 e 2 N k 4 ( 4 π 0 ) 2 | p * · [ ( r Kp ) ] K · dc · K | 2 K 2 K 2 + k D 2 .
d σ d Ω = 2 e 2 N k 4 ( 4 π ) 2 | n 2 p * · [ ( r K ) p ] K dc | 2 1 K 2 + k D 2 .
p ( r , x ) = 1 V ( 1 + m cos K g · r ) k D 2 4 π exp ( - k D r - x ) r - x
d σ d Ω = e 2 k 4 ( 4 π 0 ) 2 | p * · [ ( r Kp ) ] K · dc · K | 2 × { | m N 2 K 2 K 2 + k D 2 sinc [ ( u - u g ) L x ] × sinc [ ( v - v g ) L y ] sinc [ ( w - w g ) L z ] | 2 + 2 N K 2 K 2 + k D 2 } ,
SNR = ( m N 2 K 2 K 2 + k D 2 ) 2 2 N K 2 K 2 + k D 2 ,
σ = ( κ L z ) 2 L x L y cos θ .

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