Abstract

Photorefractive circuits that are based on double phase-conjugate mirror junctions are studied theoretically. We analyze in detail the configuration of two coupled junctions that is a representative of an experimentally studied class and find double-valued solutions for the oscillating beams. A stability analysis of the solutions is given.

© 1989 Optical Society of America

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References

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  1. H. Jagannath, P. Venkateswarlu, M. C. George, Opt. Lett. 12, 1032 (1987).
    [CrossRef] [PubMed]
  2. S.-K. Kwong, A. Yariv, Opt. Lett. 11, 377 (1986).
    [CrossRef] [PubMed]
  3. M. D. Ewbank, P. Yeh, Khoshnevisan, J. Feinberg, Opt. Lett. 10, 282 (1985).
    [CrossRef] [PubMed]
  4. B. Fischer, S. Sternklar, S. Weiss, Appl. Phys. Lett. 48, 1567 (1986).
    [CrossRef]
  5. S. Weiss, S. Sternklar, B. Fischer, Opt. Lett. 12, 114 (1987); S. Sternklar, S. Weiss, M. Segev, B. Fischer, Opt. Lett. 11, 528 (1986).
    [CrossRef] [PubMed]
  6. A. M. Smout, R. W. Eason, M. G. Gower, Opt. Commun. 59, 77 (1986).
    [CrossRef]
  7. R. W. Eason, A. M. C. Smout, Opt. Lett. 12, 51 (1987).
    [CrossRef] [PubMed]
  8. A. M. C. Smout, A. M. Eason, Opt. Lett. 12, 498 (1987).
    [CrossRef] [PubMed]
  9. M. D. Ewbank, Opt. Lett. 13, 47 (1988).
    [CrossRef] [PubMed]
  10. B. Fischer, S. Sternklar, Appl. Phys. Lett. 51, 74 (1987); S. Sternklar, B. Fischer, Opt. Lett. 12, 711 (1987).
    [CrossRef] [PubMed]
  11. S. Sternklar, S. Weiss, B. Fischer, Opt. Eng. 26, 423 (1986).
  12. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
    [CrossRef]
  13. K. D. Shaw, M. Cronin-Golomb, Opt. Commun. 65, 301 (1988).
    [CrossRef]
  14. L. Solymar, J. M. Heaton, Opt. Commun. 51, 76 (1984).
    [CrossRef]

1988 (2)

K. D. Shaw, M. Cronin-Golomb, Opt. Commun. 65, 301 (1988).
[CrossRef]

M. D. Ewbank, Opt. Lett. 13, 47 (1988).
[CrossRef] [PubMed]

1987 (5)

1986 (4)

S. Sternklar, S. Weiss, B. Fischer, Opt. Eng. 26, 423 (1986).

B. Fischer, S. Sternklar, S. Weiss, Appl. Phys. Lett. 48, 1567 (1986).
[CrossRef]

A. M. Smout, R. W. Eason, M. G. Gower, Opt. Commun. 59, 77 (1986).
[CrossRef]

S.-K. Kwong, A. Yariv, Opt. Lett. 11, 377 (1986).
[CrossRef] [PubMed]

1985 (1)

1984 (2)

L. Solymar, J. M. Heaton, Opt. Commun. 51, 76 (1984).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Cronin-Golomb, M.

K. D. Shaw, M. Cronin-Golomb, Opt. Commun. 65, 301 (1988).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Eason, A. M.

Eason, R. W.

R. W. Eason, A. M. C. Smout, Opt. Lett. 12, 51 (1987).
[CrossRef] [PubMed]

A. M. Smout, R. W. Eason, M. G. Gower, Opt. Commun. 59, 77 (1986).
[CrossRef]

Ewbank, M. D.

Feinberg, J.

Fischer, B.

B. Fischer, S. Sternklar, Appl. Phys. Lett. 51, 74 (1987); S. Sternklar, B. Fischer, Opt. Lett. 12, 711 (1987).
[CrossRef] [PubMed]

S. Weiss, S. Sternklar, B. Fischer, Opt. Lett. 12, 114 (1987); S. Sternklar, S. Weiss, M. Segev, B. Fischer, Opt. Lett. 11, 528 (1986).
[CrossRef] [PubMed]

S. Sternklar, S. Weiss, B. Fischer, Opt. Eng. 26, 423 (1986).

B. Fischer, S. Sternklar, S. Weiss, Appl. Phys. Lett. 48, 1567 (1986).
[CrossRef]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

George, M. C.

Gower, M. G.

A. M. Smout, R. W. Eason, M. G. Gower, Opt. Commun. 59, 77 (1986).
[CrossRef]

Heaton, J. M.

L. Solymar, J. M. Heaton, Opt. Commun. 51, 76 (1984).
[CrossRef]

Jagannath, H.

Khoshnevisan,

Kwong, S.-K.

Shaw, K. D.

K. D. Shaw, M. Cronin-Golomb, Opt. Commun. 65, 301 (1988).
[CrossRef]

Smout, A. M.

A. M. Smout, R. W. Eason, M. G. Gower, Opt. Commun. 59, 77 (1986).
[CrossRef]

Smout, A. M. C.

Solymar, L.

L. Solymar, J. M. Heaton, Opt. Commun. 51, 76 (1984).
[CrossRef]

Sternklar, S.

B. Fischer, S. Sternklar, Appl. Phys. Lett. 51, 74 (1987); S. Sternklar, B. Fischer, Opt. Lett. 12, 711 (1987).
[CrossRef] [PubMed]

S. Weiss, S. Sternklar, B. Fischer, Opt. Lett. 12, 114 (1987); S. Sternklar, S. Weiss, M. Segev, B. Fischer, Opt. Lett. 11, 528 (1986).
[CrossRef] [PubMed]

S. Sternklar, S. Weiss, B. Fischer, Opt. Eng. 26, 423 (1986).

B. Fischer, S. Sternklar, S. Weiss, Appl. Phys. Lett. 48, 1567 (1986).
[CrossRef]

Venkateswarlu, P.

Weiss, S.

S. Weiss, S. Sternklar, B. Fischer, Opt. Lett. 12, 114 (1987); S. Sternklar, S. Weiss, M. Segev, B. Fischer, Opt. Lett. 11, 528 (1986).
[CrossRef] [PubMed]

S. Sternklar, S. Weiss, B. Fischer, Opt. Eng. 26, 423 (1986).

B. Fischer, S. Sternklar, S. Weiss, Appl. Phys. Lett. 48, 1567 (1986).
[CrossRef]

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Yariv, A.

S.-K. Kwong, A. Yariv, Opt. Lett. 11, 377 (1986).
[CrossRef] [PubMed]

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Yeh, P.

Appl. Phys. Lett. (2)

B. Fischer, S. Sternklar, S. Weiss, Appl. Phys. Lett. 48, 1567 (1986).
[CrossRef]

B. Fischer, S. Sternklar, Appl. Phys. Lett. 51, 74 (1987); S. Sternklar, B. Fischer, Opt. Lett. 12, 711 (1987).
[CrossRef] [PubMed]

IEEE J. Quantum Electron. (1)

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
[CrossRef]

Opt. Commun. (3)

K. D. Shaw, M. Cronin-Golomb, Opt. Commun. 65, 301 (1988).
[CrossRef]

L. Solymar, J. M. Heaton, Opt. Commun. 51, 76 (1984).
[CrossRef]

A. M. Smout, R. W. Eason, M. G. Gower, Opt. Commun. 59, 77 (1986).
[CrossRef]

Opt. Eng. (1)

S. Sternklar, S. Weiss, B. Fischer, Opt. Eng. 26, 423 (1986).

Opt. Lett. (7)

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Figures (4)

Fig. 1
Fig. 1

The DPCM junction.

Fig. 2
Fig. 2

(a) 2F-DPCM and two other equivalent configurations with (b) one and (c) two reflections from the crystal surfaces.

Fig. 3
Fig. 3

Intensities of oscillating beams as a function of the input beams ratio s for the 2F-DPCM with a = a′ = 0.86(|γl| = 3) and M = 1. (a) I1 and I1′ (or q and q′), (b) I3 and I3′ (normalized by I4). Our stability analysis shows that the upper branches of the curves for (a) and the lower branches for (b) are unstable.

Fig. 4
Fig. 4

Same as Fig. 3 for a = 0.6, a′ = 0.9, and M = 0.8. Our stability analysis shows that the upper branches of the curves for (a) and the lower branches for (b) are unstable.

Equations (14)

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T ( q ) = I 1 I 4 = I 3 I 2 = a 2 ( q 1 / 2 + q 1 / 2 ) 2 ( q 1 / 2 q 1 / 2 ) 2 4 ,
tanh ( γl 2 a ) = a ,
ρ = I 3 / I 4 = T / q = { 1 a 2 M 1 / 2 ( 1 + a 2 ) ± 2 [ a 2 ( M + 1 ) 1 ] 1 / 2 } 2 .
T ( q ) = I 1 I 4 = I 3 I 2 = a 2 ( q 1 / 2 + q 1 / 2 ) 2 ( q 1 / 2 q 1 / 2 ) 2 4 , T ( q ) = I 1 I 4 = I 3 I 2 = a 2 ( q 1 / 2 + q 1 / 2 ) 2 ( q 1 / 2 q 1 / 2 ) 2 4 ,
M = I 2 / I 1 = I 2 / I 1 ,
s = I 4 / I 4 .
T ( q ) = 1 sM q , T ( q ) = s / Mq .
I 3 / I 3 = s .
A 2 B M a ( 1 a 2 ) < q < A + 2 B M a ( 1 a 2 ) ,
M > [ ( 1 a 2 ) ( 1 a 2 ) ] 1 / 2 / ( a a ) .
τ d [ Δ T ( t ) ] d t + Δ T ( t ) = α Δ q ( t ) , τ d [ Δ T ( t ) ] d t + Δ T ( t ) = α Δ q ( t ) ,
d d t [ Δ q Δ q ] = G [ Δ q Δ q ] ,
G = [ 1 / τ α Mq 0 2 / ( s τ ) αM q 0 2 s / τ 1 / τ ] .
α α M 2 q 0 2 q 0 2 < 1 ,

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