Abstract

Expressions for the phase of reflection from a photorefractive phase-conjugate mirror are obtained as a function of the intensity and phase of the pump and the probe beams. The phase is independent of these parameters in common photorefractive conditions in which the index grating is spatially shifted 90° with respect to the light-interference pattern. Multiple solutions exist for the phase and intensity of the reflection at large coupling strength. Oscillation conditions involving frequency detuning are obtained for the double phase-conjugate resonator (resonator formed with two phase-conjugate mirrors).

© 1986 Optical Society of America

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  1. For a review see A. Yariv, IEEE J. Quantum Electron. QE-14, 650 (1978); IEEE J. Quantum Electron. QE-15, 256, 523 (1979); R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1982).
    [CrossRef]
  2. J. O. White, A. Yariv, Appl. Phys. Lett. 37, 5 (1980).
    [CrossRef]
  3. S. K. Kwong, M. Cronin-Golomb, A. Yariv, Appl. Phys. Lett. 45, 1016 (1984).
    [CrossRef]
  4. B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
    [CrossRef] [PubMed]
  5. M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, Opt. Lett. 7, 313 (1982).
    [CrossRef] [PubMed]
  6. J. H. Marburger, J. F. Lam, Appl. Phys. Lett. 34, 389 (1979).
    [CrossRef]
  7. J. F. Lam, W. P. Brown, Opt. Lett. 5, 61 (1980).
    [CrossRef] [PubMed]
  8. M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, A. Yariv, Opt. Lett. 10, 353 (1985).
    [CrossRef] [PubMed]
  9. P. Yeh, M. Khoshrevisan, M. D. Ewbank, J. M. Tracy, J. Opt. Soc. Am. A 1, 1212 (A) (1984).
  10. H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1964).
  11. In photorefractive media, for example, q depends on parameters such as crystal orientation, grating period, charge-carrier concentration, and the angle of incidence a.
  12. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum. Electron. QE-20, 12 (1984).
    [CrossRef]
  13. Ph. Refregier, L. Solyman, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985); A. Yariv, S. K. Kwong, Opt. Lett. 10, 454 (1985).
    [CrossRef] [PubMed]
  14. J. Feinberg, D. Heiman, A. R. Tanguay, R. W. Hellwarth, J. Appl. Phys. 51, 1297 (1980).
    [CrossRef]
  15. B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, R. Neurgaonkar, Appl. Phys. Lett. 40, 863 (1982).
    [CrossRef]

1985 (2)

M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, A. Yariv, Opt. Lett. 10, 353 (1985).
[CrossRef] [PubMed]

Ph. Refregier, L. Solyman, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985); A. Yariv, S. K. Kwong, Opt. Lett. 10, 454 (1985).
[CrossRef] [PubMed]

1984 (3)

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

P. Yeh, M. Khoshrevisan, M. D. Ewbank, J. M. Tracy, J. Opt. Soc. Am. A 1, 1212 (A) (1984).

S. K. Kwong, M. Cronin-Golomb, A. Yariv, Appl. Phys. Lett. 45, 1016 (1984).
[CrossRef]

1982 (2)

M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, Opt. Lett. 7, 313 (1982).
[CrossRef] [PubMed]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, R. Neurgaonkar, Appl. Phys. Lett. 40, 863 (1982).
[CrossRef]

1981 (1)

1980 (3)

J. O. White, A. Yariv, Appl. Phys. Lett. 37, 5 (1980).
[CrossRef]

J. F. Lam, W. P. Brown, Opt. Lett. 5, 61 (1980).
[CrossRef] [PubMed]

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

1979 (1)

J. H. Marburger, J. F. Lam, Appl. Phys. Lett. 34, 389 (1979).
[CrossRef]

1978 (1)

For a review see A. Yariv, IEEE J. Quantum Electron. QE-14, 650 (1978); IEEE J. Quantum Electron. QE-15, 256, 523 (1979); R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1982).
[CrossRef]

1964 (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1964).

Brown, W. P.

Cronin-Golomb, M.

M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, A. Yariv, Opt. Lett. 10, 353 (1985).
[CrossRef] [PubMed]

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

S. K. Kwong, M. Cronin-Golomb, A. Yariv, Appl. Phys. Lett. 45, 1016 (1984).
[CrossRef]

M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, Opt. Lett. 7, 313 (1982).
[CrossRef] [PubMed]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, R. Neurgaonkar, Appl. Phys. Lett. 40, 863 (1982).
[CrossRef]

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

Ewbank, M. D.

P. Yeh, M. Khoshrevisan, M. D. Ewbank, J. M. Tracy, J. Opt. Soc. Am. A 1, 1212 (A) (1984).

Feinberg, J.

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

Fischer, B.

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]

Huignard, J. P.

Ph. Refregier, L. Solyman, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985); A. Yariv, S. K. Kwong, Opt. Lett. 10, 454 (1985).
[CrossRef] [PubMed]

Khoshrevisan, M.

P. Yeh, M. Khoshrevisan, M. D. Ewbank, J. M. Tracy, J. Opt. Soc. Am. A 1, 1212 (A) (1984).

Kogelnik, H.

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1964).

Kwong, S. K.

Lam, J. F.

J. F. Lam, W. P. Brown, Opt. Lett. 5, 61 (1980).
[CrossRef] [PubMed]

J. H. Marburger, J. F. Lam, Appl. Phys. Lett. 34, 389 (1979).
[CrossRef]

Marburger, J. H.

J. H. Marburger, J. F. Lam, Appl. Phys. Lett. 34, 389 (1979).
[CrossRef]

Neurgaonkar, R.

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, R. Neurgaonkar, Appl. Phys. Lett. 40, 863 (1982).
[CrossRef]

Rajbenbach, H.

Ph. Refregier, L. Solyman, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985); A. Yariv, S. K. Kwong, Opt. Lett. 10, 454 (1985).
[CrossRef] [PubMed]

Refregier, Ph.

Ph. Refregier, L. Solyman, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985); A. Yariv, S. K. Kwong, Opt. Lett. 10, 454 (1985).
[CrossRef] [PubMed]

Solyman, L.

Ph. Refregier, L. Solyman, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985); A. Yariv, S. K. Kwong, Opt. Lett. 10, 454 (1985).
[CrossRef] [PubMed]

Tanguay, A. R.

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

Tracy, J. M.

P. Yeh, M. Khoshrevisan, M. D. Ewbank, J. M. Tracy, J. Opt. Soc. Am. A 1, 1212 (A) (1984).

White, J. O.

M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, A. Yariv, Opt. Lett. 10, 353 (1985).
[CrossRef] [PubMed]

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

M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, Opt. Lett. 7, 313 (1982).
[CrossRef] [PubMed]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, R. Neurgaonkar, Appl. Phys. Lett. 40, 863 (1982).
[CrossRef]

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

J. O. White, A. Yariv, Appl. Phys. Lett. 37, 5 (1980).
[CrossRef]

Yariv, A.

M. Cronin-Golomb, B. Fischer, S. K. Kwong, J. O. White, A. Yariv, Opt. Lett. 10, 353 (1985).
[CrossRef] [PubMed]

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

S. K. Kwong, M. Cronin-Golomb, A. Yariv, Appl. Phys. Lett. 45, 1016 (1984).
[CrossRef]

M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, Opt. Lett. 7, 313 (1982).
[CrossRef] [PubMed]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, R. Neurgaonkar, Appl. Phys. Lett. 40, 863 (1982).
[CrossRef]

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

J. O. White, A. Yariv, Appl. Phys. Lett. 37, 5 (1980).
[CrossRef]

For a review see A. Yariv, IEEE J. Quantum Electron. QE-14, 650 (1978); IEEE J. Quantum Electron. QE-15, 256, 523 (1979); R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1982).
[CrossRef]

Yeh, P.

P. Yeh, M. Khoshrevisan, M. D. Ewbank, J. M. Tracy, J. Opt. Soc. Am. A 1, 1212 (A) (1984).

Appl. Phys. Lett. (4)

J. O. White, A. Yariv, Appl. Phys. Lett. 37, 5 (1980).
[CrossRef]

S. K. Kwong, M. Cronin-Golomb, A. Yariv, Appl. Phys. Lett. 45, 1016 (1984).
[CrossRef]

J. H. Marburger, J. F. Lam, Appl. Phys. Lett. 34, 389 (1979).
[CrossRef]

B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, R. Neurgaonkar, Appl. Phys. Lett. 40, 863 (1982).
[CrossRef]

Bell Syst. Tech. J. (1)

H. Kogelnik, Bell Syst. Tech. J. 48, 2909 (1964).

IEEE J. Quantum Electron. (1)

For a review see A. Yariv, IEEE J. Quantum Electron. QE-14, 650 (1978); IEEE J. Quantum Electron. QE-15, 256, 523 (1979); R. A. Fisher, ed., Optical Phase Conjugation (Academic, New York, 1982).
[CrossRef]

IEEE J. Quantum. Electron. (1)

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

J. Appl. Phys. (2)

Ph. Refregier, L. Solyman, H. Rajbenbach, J. P. Huignard, J. Appl. Phys. 58, 45 (1985); A. Yariv, S. K. Kwong, Opt. Lett. 10, 454 (1985).
[CrossRef] [PubMed]

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

J. Opt. Soc. Am. A (1)

P. Yeh, M. Khoshrevisan, M. D. Ewbank, J. M. Tracy, J. Opt. Soc. Am. A 1, 1212 (A) (1984).

Opt. Lett. (4)

Other (1)

In photorefractive media, for example, q depends on parameters such as crystal orientation, grating period, charge-carrier concentration, and the angle of incidence a.

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Figures (3)

Fig. 1
Fig. 1

Schematic diagram of nonlinear four-wave mixing in a nonlinear medium. A1 and A2 are the pumping beams, A3 is the phase-conjugate output, and A4 is the probe beam.

Fig. 2
Fig. 2

Numerical curves of ψ3 versus ln q for various In r and ϕ. |γl| was chosen to be 6. For each of the curves, the range of ψ3 is from 0 to 2π and from −5 to 5 for In q.

Fig. 3
Fig. 3

Schematic diagram of a double phase-conjugate resonator.

Equations (26)

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E j = A j ( r ) exp [ i ( k j · r - ω t ) ] + c . c .
A j ( r ) = A j ( r ) exp [ i ψ j ( r ) ] ,             j = 1 , 4 ,
d A 1 d z = - γ I 0 ( A 1 A 4 * + A 2 * A 3 ) A 4 ,
d A 2 * d z = - γ I 0 ( A 1 A 4 * + A 2 * A 3 ) A 3 * ,
d A 3 d z = γ I 0 ( A 1 A 4 * + A 2 * A 3 ) A 2 ,
d A 4 * d z = γ I 0 ( A 1 A 4 * + A 2 * A 3 ) A 1 * ,
I 0 = I 1 + I 2 + I 3 + I 4 ,
I j = A j 2 .
d A 3 d z = γ I 0 [ A 2 2 A 3 + ( A 1 A 2 ) A 4 * ] ,
d A 4 * d z = γ I 0 [ A 1 2 A 4 * + ( A 1 * A 2 * ) A 3 ] .
A 3 ( z ) = A 4 * ( 0 ) A 1 / A 2 * r - 1 e - γ l + 1 { exp [ γ ( z - l ) ] - 1 } ,
A 4 * ( z ) = A 4 * ( 0 ) 1 r - 1 e - γ l + 1 { r - 1 exp [ γ ( z - l ) ] + 1 } ,
r = A 2 A 2 * A 1 A 1 * = I 2 I 1 .
ψ 3 ( 0 ) = ψ 1 ( 0 ) + ψ 2 ( l ) - ψ 4 ( 0 ) + Im ln [ e - γ l - 1 r - 1 e - γ l + 1 ] .
ψ 3 ( 0 ) = Im ln [ A 1 * ( 0 ) A 2 ( 0 ) A 3 ( 0 ) A 4 * ( 0 ) ] + ψ 1 ( 0 ) + ψ 2 ( 0 ) - ψ 4 ( 0 ) .
A 1 ( z ) A 2 * ( z ) = - { [ Δ - ( Δ 2 + 4 c 2 ) 1 / 2 ] D e - μ z - [ Δ + ( Δ 2 + 4 c 2 ) 1 / 2 ] D - 1 e μ z 2 c * ( D e - μ z - D - 1 e μ z ) } ,
A 3 ( z ) A 4 * ( z ) = { [ Δ - ( Δ 2 + 4 c 2 ) 1 / 2 ] E e - μ z - [ Δ + ( Δ 2 + 4 c 2 ) 1 / 2 ] E - 1 e μ z 2 c * ( E e - μ z - E - 1 e μ z ) } ,
Δ = I 2 + I 3 - I 1 - I 4 , μ = γ ( Δ 2 + 4 c 2 ) 1 / 2 2 I 0 , D = [ Δ + ( Δ 2 + 4 c 2 ) 1 / 2 + 2 c 2 / I 2 ( l ) Δ - ( Δ 2 + 4 c 2 ) 1 / 2 + 2 c 2 / I 2 ( l ) ] 1 / 2 e μ l , E = [ Δ + ( Δ 2 + 4 c 2 ) 1 / 2 Δ - ( Δ 2 + 4 c 2 ) 1 / 2 ] 1 / 2 e μ l .
[ c 2 - I 1 ( 0 ) I 2 ( l ) ] Δ T + ( Δ 2 + 4 c 2 ) 1 / 2 2 + 4 c 2 T 2 I 4 ( 0 ) I 2 ( l ) + 2 c 2 I 4 ( 0 ) ( Δ 2 + 4 c 2 ) 1 / 2 ( T + T * ) = 0 ,
d ( ln A 2 * ) d z = - γ I 0 ( A 1 A 2 * A 3 * A 4 I 4 + I 3 ) ,
ψ 2 ( 0 ) = ψ 2 ( l ) + l 0 { Re ( γ I 0 ) Im [ A 1 ( z ) A 2 * ( z ) A 3 * ( z ) A 4 ( z ) I 4 ( z ) ] + { I 3 ( z ) + Re [ A 1 ( z ) A 2 * ( z ) A 3 * ( z ) A 4 ( z ) I 4 ( z ) ] } Im ( γ I 0 ) } d z ,
Im [ A 1 ( z ) A 2 * ( z ) A 3 * ( z ) A 4 ( z ) ] = 0.
ψ 3 ( 0 ) = ψ 1 ( 0 ) + ψ 2 ( l ) - ψ 4 ( 0 ) ,
γ = i γ 0 1 + i δ τ
Δ ψ = ( ψ g 2 - ψ g 1 ) + ( ψ 21 + ψ 22 ) - ( ψ 11 + ψ 12 ) + 2 δ l c ,
Δ ψ = 2 m π ,

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