Abstract

Theoretical and experimental results are presented for simultaneous multibeam coupling in photorefractive SBN:Ce. Within a single crystal, multiple signals are amplified through a coupling process that employs a single pump. The coupling gain of each signal results from coupling both between the pump and the signal and between different signals. The amount of gain that each signal receives is dependent on the intensity of the incident signal; thus a competition for the gain exists among the various signals.

© 1988 Optical Society of America

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  1. N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).
    [CrossRef]
  2. J. Feinberg, D. Heinman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
    [CrossRef]
  3. J. P. Huignard, H. Rajbenbach, Ph. Refregier, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 22 (1986).
  4. D. Rak, I. Ledoux, J. P. Huignard, Opt. Commun. 49, 302 (1984).
    [CrossRef]
  5. D. M. Gookin, Opt. Lett. 12, 196 (1987).
    [CrossRef] [PubMed]
  6. V. Markov, S. Odulov, M. Soskin, Opt. Laser Technol. 11, 95 (1979).
    [CrossRef]
  7. H. Rajbenbach, J. P. Huignard, B. Loiseaux, Opt. Commun. 48, 247 (1983).
    [CrossRef]
  8. J. L. deBougrenet de la Tocenaye, P. Pelat-Finet, J. P. Huignard, J. Opt. Soc. Am. B 3, 315 (1986).
    [CrossRef]
  9. D. Z. Anderson, Opt. News 13(12), 16 (1987).
    [CrossRef]
  10. Y. Faiman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).
  11. B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
    [CrossRef] [PubMed]
  12. G. A. Rakuljic, A. Yariv, R. Neurgaonkar, Opt. Eng. 25, 1212 (1986).
  13. J. B. Thaxler, M. Kestigian, Appl. Opt. 13, 913 (1974).
    [CrossRef]
  14. J. Ma, L. Liu, S. Wu, Z. Wang, L. Xu, B. Shu, “Electrocontrolled beam coupling and bistable behavior in SBN:Ce crystals,” Appl. Phys. Lett. (to be published).
  15. D. Z. Anderson, Opt. Lett. 11, 56 (1986).
    [CrossRef] [PubMed]

1987

1986

D. Z. Anderson, Opt. Lett. 11, 56 (1986).
[CrossRef] [PubMed]

Y. Faiman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).

G. A. Rakuljic, A. Yariv, R. Neurgaonkar, Opt. Eng. 25, 1212 (1986).

J. L. deBougrenet de la Tocenaye, P. Pelat-Finet, J. P. Huignard, J. Opt. Soc. Am. B 3, 315 (1986).
[CrossRef]

J. P. Huignard, H. Rajbenbach, Ph. Refregier, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 22 (1986).

1984

D. Rak, I. Ledoux, J. P. Huignard, Opt. Commun. 49, 302 (1984).
[CrossRef]

1983

H. Rajbenbach, J. P. Huignard, B. Loiseaux, Opt. Commun. 48, 247 (1983).
[CrossRef]

1981

1980

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

1979

N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).
[CrossRef]

V. Markov, S. Odulov, M. Soskin, Opt. Laser Technol. 11, 95 (1979).
[CrossRef]

1974

Anderson, D. Z.

Cronin-Golomb, M.

deBougrenet de la Tocenaye, J. L.

Faiman, Y.

Y. Faiman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).

Feinberg, J.

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

Fischer, B.

Gookin, D. M.

Heinman, D.

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

Hellwarth, R. W.

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

Huignard, J. P.

J. P. Huignard, H. Rajbenbach, Ph. Refregier, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 22 (1986).

J. L. deBougrenet de la Tocenaye, P. Pelat-Finet, J. P. Huignard, J. Opt. Soc. Am. B 3, 315 (1986).
[CrossRef]

D. Rak, I. Ledoux, J. P. Huignard, Opt. Commun. 49, 302 (1984).
[CrossRef]

H. Rajbenbach, J. P. Huignard, B. Loiseaux, Opt. Commun. 48, 247 (1983).
[CrossRef]

Kestigian, M.

Khuktarev, N. V.

N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).
[CrossRef]

Klancnik, E.

Y. Faiman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).

Ledoux, I.

D. Rak, I. Ledoux, J. P. Huignard, Opt. Commun. 49, 302 (1984).
[CrossRef]

Lee, S. H.

Y. Faiman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).

Liu, L.

J. Ma, L. Liu, S. Wu, Z. Wang, L. Xu, B. Shu, “Electrocontrolled beam coupling and bistable behavior in SBN:Ce crystals,” Appl. Phys. Lett. (to be published).

Loiseaux, B.

H. Rajbenbach, J. P. Huignard, B. Loiseaux, Opt. Commun. 48, 247 (1983).
[CrossRef]

Ma, J.

J. Ma, L. Liu, S. Wu, Z. Wang, L. Xu, B. Shu, “Electrocontrolled beam coupling and bistable behavior in SBN:Ce crystals,” Appl. Phys. Lett. (to be published).

Markov, V.

V. Markov, S. Odulov, M. Soskin, Opt. Laser Technol. 11, 95 (1979).
[CrossRef]

Markov, V. B.

N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).
[CrossRef]

Neurgaonkar, R.

G. A. Rakuljic, A. Yariv, R. Neurgaonkar, Opt. Eng. 25, 1212 (1986).

Odulov, S.

V. Markov, S. Odulov, M. Soskin, Opt. Laser Technol. 11, 95 (1979).
[CrossRef]

Odulov, S. G.

N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).
[CrossRef]

Pelat-Finet, P.

Rajbenbach, H.

J. P. Huignard, H. Rajbenbach, Ph. Refregier, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 22 (1986).

H. Rajbenbach, J. P. Huignard, B. Loiseaux, Opt. Commun. 48, 247 (1983).
[CrossRef]

Rak, D.

D. Rak, I. Ledoux, J. P. Huignard, Opt. Commun. 49, 302 (1984).
[CrossRef]

Rakuljic, G. A.

G. A. Rakuljic, A. Yariv, R. Neurgaonkar, Opt. Eng. 25, 1212 (1986).

Refregier, Ph.

J. P. Huignard, H. Rajbenbach, Ph. Refregier, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 22 (1986).

Shu, B.

J. Ma, L. Liu, S. Wu, Z. Wang, L. Xu, B. Shu, “Electrocontrolled beam coupling and bistable behavior in SBN:Ce crystals,” Appl. Phys. Lett. (to be published).

Soskin, M.

V. Markov, S. Odulov, M. Soskin, Opt. Laser Technol. 11, 95 (1979).
[CrossRef]

Soskin, M. S.

N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).
[CrossRef]

Tanguay, A. R.

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

Thaxler, J. B.

Vinetskii, L.

N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).
[CrossRef]

Wang, Z.

J. Ma, L. Liu, S. Wu, Z. Wang, L. Xu, B. Shu, “Electrocontrolled beam coupling and bistable behavior in SBN:Ce crystals,” Appl. Phys. Lett. (to be published).

White, J. O.

Wu, S.

J. Ma, L. Liu, S. Wu, Z. Wang, L. Xu, B. Shu, “Electrocontrolled beam coupling and bistable behavior in SBN:Ce crystals,” Appl. Phys. Lett. (to be published).

Xu, L.

J. Ma, L. Liu, S. Wu, Z. Wang, L. Xu, B. Shu, “Electrocontrolled beam coupling and bistable behavior in SBN:Ce crystals,” Appl. Phys. Lett. (to be published).

Yariv, A.

G. A. Rakuljic, A. Yariv, R. Neurgaonkar, Opt. Eng. 25, 1212 (1986).

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
[CrossRef] [PubMed]

Appl. Opt.

Ferroelectrics

N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, L. Vinetskii, Ferroelectrics 22, 949, 961 (1979).
[CrossRef]

J. Appl. Phys.

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

J. Opt. Soc. Am. B

Opt. Commun.

D. Rak, I. Ledoux, J. P. Huignard, Opt. Commun. 49, 302 (1984).
[CrossRef]

H. Rajbenbach, J. P. Huignard, B. Loiseaux, Opt. Commun. 48, 247 (1983).
[CrossRef]

Opt. Eng.

Y. Faiman, E. Klancnik, S. H. Lee, Opt. Eng. 25, 228 (1986).

G. A. Rakuljic, A. Yariv, R. Neurgaonkar, Opt. Eng. 25, 1212 (1986).

Opt. Laser Technol.

V. Markov, S. Odulov, M. Soskin, Opt. Laser Technol. 11, 95 (1979).
[CrossRef]

Opt. Lett.

Opt. News

D. Z. Anderson, Opt. News 13(12), 16 (1987).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

J. P. Huignard, H. Rajbenbach, Ph. Refregier, Proc. Soc. Photo-Opt. Instrum. Eng. 613, 22 (1986).

Other

J. Ma, L. Liu, S. Wu, Z. Wang, L. Xu, B. Shu, “Electrocontrolled beam coupling and bistable behavior in SBN:Ce crystals,” Appl. Phys. Lett. (to be published).

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Figures (5)

Fig. 1
Fig. 1

Geometry for multiwave coupling. ER and Esj (j = 1, 2, …, N) are the pump wave and the signal wave, respectively.

Fig. 2
Fig. 2

Plot of coupling constant γRj as a function of α and αj. The beams are of extraordinary polarization.

Fig. 3
Fig. 3

R(R′) as a function of the signal-beam intensity ratio β(β′). Is1(0)/IR(0) = 0.1 for curve R–β, Is2(0)/IR(0) = 0.1 for curve R′–β′, α = α1 = 30°, and α2 = 32°.

Fig. 4
Fig. 4

Signal intensity increment ΔIsi with the unity of IR(0) as a function of the signal-beam intensity ratio β. Is1(0)/IR(0) = 0.05, α = α1 = 30°. 1 and 2 indicate signals Is1 and Is2 respectively.

Fig. 5
Fig. 5

Experimental arrangement for three beams coupling in the photorefractive SBN:Ce crystal. M’s, mirrors; BS1 and BS2, beam splitters; D, detector.

Equations (12)

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E R ( r , t ) = A R ( r ) exp [ i ( k R · r - ω t ) ] e R , E s j ( r , t ) = A s j ( r ) exp [ i ( k s j · r - ω t ) ] e s j ,             j = 1 , 2 , , N ,
n = n ¯ + ( A R * / 2 I 0 ) i = 1 N n R j exp ( i ϕ R j ) A s j × exp [ i ( k s j - k R ) · r ] + ( 1 / 2 I 0 ) i > j n i j × exp ( i ϕ i j ) A s i A s j * exp [ i ( k s i - k s j ) · r ] + c . c . ,
n R j = r eff j E , t g ϕ R j = π / 2.
E = ( k B T k g / q ) / [ 1 + ( k g / k 0 ) 2 ] ( e s j · e R ) ,
r eff j = ½ { n 0 4 r 13 [ cos ( α j + α ) - cos ( α j - α ) ] + 4 n e 2 n 0 2 r 42 cos [ ½ ( α j - α ) ] + n 0 4 r 33 [ cos ( α j + α ) + cos ( α j - α ) ] } cos [ ½ ( α j - α ) ]
d I R / d z = - j = 1 N ( 2 / I 0 ) ( cos α j / cos α ) γ R j I s j I R ,
d I s j / d z = ( 2 / I 0 ) γ R j I R I s j + [ i = 1 ( i < j ) N ( 2 / I 0 ) γ i j I s i ] I s j - [ i = 1 ( i > j ) N ( 2 / I 0 ) γ i j I s i ] I s j ,             j = 1 , 2 , , N ,
γ R j = ω n R j / ( 2 c n ¯ cos α j ) ,
γ i j = ω n i j / ( 2 c n ¯ cos α j ) ,             γ i j / γ j i = cos α i / cos α j .
I R ( z ) I 0 I R ( 0 ) exp ( - 2 γ R z ) / [ I s 1 ( 0 ) + I s 2 ( 0 ) + I R ( 0 ) exp ( - 2 γ R z ) ] ,
I s 1 ( z ) = I s 1 ( 0 ) I 0 ( a 1 + b 1 ) [ j = 1 2 I s j ( 0 ) exp ( 2 γ R z ) + I R ( 0 ) ] - ( a 1 + b 1 ) exp ( 2 γ R 1 z ) ,
I s 2 ( z ) = I s 2 ( 0 ) I 0 ( a 2 - b 2 ) [ j = 1 2 I s j ( 0 ) exp ( 2 γ R z ) + I R ( 0 ) ] - ( a 2 - b 2 ) exp ( 2 γ R 2 z ) .

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