Abstract

We present wave-optics calculations of the temporal and spatial evolution from random noise of a double phase-conjugate mirror in photorefractive media that show its image exchange and phase-reversal properties. The calculations show that for values of coupling coefficient times length greater than two the process exhibits excellent conjugation fidelity, behaves as an oscillator, and continues to operate even when the noise required for starting it is set to zero. For values less than two, the double phase-conjugation process exhibits poor fidelity and disappears when the noise is set to zero.

© 1993 Optical Society of America

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References

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  1. S. Weiss, S. Sternklar, B. Fischer, Opt. Lett. 12, 114 (1987); Appl. Phys. Lett. 50, 483 (1987); Opt. Eng. 26, 423 (1987).
    [CrossRef] [PubMed]
  2. A. A. Zozulya, Opt. Lett. 16, 545 (1991); V. V. Eliseev, V. T. Tikhonchuk, A. A. Zozulya, J. Opt. Soc. Am. B 8, 2497 (1991); N. V. Bobodaev, V. V. Eliseev, L. I. Ivleva, A. S. Korshunov, S. S. Orlov, N. M. Polozkov, A. A. Zozulya, J. Opt. Soc. Am. B 9, 1493 (1992); K. D. Shaw, Opt. Commun. 90, 133 (1992); K. D. Shaw, Opt. Commun. 94, 458 (1992).
    [CrossRef] [PubMed]
  3. B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985), Chaps. 2–5.
  4. G. C. Valley, J. Opt. Soc. Am. B 9, 1440 (1992).
    [CrossRef]
  5. M. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990).
    [CrossRef]
  6. M. Segev, D. Engin, A. Yariv, G. C. Valley, Opt. Lett. 18, 956 (1993).
    [CrossRef] [PubMed]
  7. M. Segev, B. Crosignani, A. Yariv, B. Fischer, Phys. Rev. Lett. 68, 923 (1992); B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, G. Salamo, J. Opt. Soc. Am. B 10, 446 (1993).
    [CrossRef] [PubMed]
  8. M. Segev, A. Yariv, Opt. Lett. 16, 1938 (1991).
    [CrossRef] [PubMed]
  9. M. C. Escher, J. L. Locher, The World of M. C. Escher (Abrams, New York, 1971), p. 84.

1993 (1)

1992 (2)

M. Segev, B. Crosignani, A. Yariv, B. Fischer, Phys. Rev. Lett. 68, 923 (1992); B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, G. Salamo, J. Opt. Soc. Am. B 10, 446 (1993).
[CrossRef] [PubMed]

G. C. Valley, J. Opt. Soc. Am. B 9, 1440 (1992).
[CrossRef]

1991 (2)

1990 (1)

M. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990).
[CrossRef]

1987 (1)

Crosignani, B.

M. Segev, B. Crosignani, A. Yariv, B. Fischer, Phys. Rev. Lett. 68, 923 (1992); B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, G. Salamo, J. Opt. Soc. Am. B 10, 446 (1993).
[CrossRef] [PubMed]

Engin, D.

Escher, M. C.

M. C. Escher, J. L. Locher, The World of M. C. Escher (Abrams, New York, 1971), p. 84.

Fischer, B.

M. Segev, B. Crosignani, A. Yariv, B. Fischer, Phys. Rev. Lett. 68, 923 (1992); B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, G. Salamo, J. Opt. Soc. Am. B 10, 446 (1993).
[CrossRef] [PubMed]

M. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990).
[CrossRef]

S. Weiss, S. Sternklar, B. Fischer, Opt. Lett. 12, 114 (1987); Appl. Phys. Lett. 50, 483 (1987); Opt. Eng. 26, 423 (1987).
[CrossRef] [PubMed]

Locher, J. L.

M. C. Escher, J. L. Locher, The World of M. C. Escher (Abrams, New York, 1971), p. 84.

Ophir, Y.

M. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990).
[CrossRef]

Pilipetsky, N. F.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985), Chaps. 2–5.

Segev, M.

M. Segev, D. Engin, A. Yariv, G. C. Valley, Opt. Lett. 18, 956 (1993).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, B. Fischer, Phys. Rev. Lett. 68, 923 (1992); B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, G. Salamo, J. Opt. Soc. Am. B 10, 446 (1993).
[CrossRef] [PubMed]

M. Segev, A. Yariv, Opt. Lett. 16, 1938 (1991).
[CrossRef] [PubMed]

M. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990).
[CrossRef]

Shkunov, V. V.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985), Chaps. 2–5.

Sternklar, S.

Valley, G. C.

Weiss, S.

Yariv, A.

M. Segev, D. Engin, A. Yariv, G. C. Valley, Opt. Lett. 18, 956 (1993).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, A. Yariv, B. Fischer, Phys. Rev. Lett. 68, 923 (1992); B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, G. Salamo, J. Opt. Soc. Am. B 10, 446 (1993).
[CrossRef] [PubMed]

M. Segev, A. Yariv, Opt. Lett. 16, 1938 (1991).
[CrossRef] [PubMed]

Zel’dovich, B. Ya.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985), Chaps. 2–5.

Zozulya, A. A.

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

Opt. Commun. (1)

M. Segev, Y. Ophir, B. Fischer, Opt. Commun. 77, 265 (1990).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

M. Segev, B. Crosignani, A. Yariv, B. Fischer, Phys. Rev. Lett. 68, 923 (1992); B. Crosignani, M. Segev, D. Engin, P. DiPorto, A. Yariv, G. Salamo, J. Opt. Soc. Am. B 10, 446 (1993).
[CrossRef] [PubMed]

Other (2)

M. C. Escher, J. L. Locher, The World of M. C. Escher (Abrams, New York, 1971), p. 84.

B. Ya. Zel’dovich, N. F. Pilipetsky, V. V. Shkunov, Principles of Phase Conjugation (Springer-Verlag, Berlin, 1985), Chaps. 2–5.

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Figures (4)

Fig. 1
Fig. 1

Steady-state spatial evolution of the plane-wave amplitudes for a DPCM in a photorefractive crystal.

Fig. 2
Fig. 2

Steady-state input and output phases for the interacting beams at angles corresponding to the location of pictorial information.

Fig. 3
Fig. 3

Phase-conjugation fidelity as a function of time for several gain levels (from the top to the bottom curves): γ0L ≈ 4.9, 2.46, 2.05, 1.64, 1.23, 0.98.

Fig. 4
Fig. 4

Phase-conjugation fidelity at steady state as a function of coupling coefficient times length γ0L.

Equations (12)

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E ( x , z , t ) = 1 2 [ A 1 ( x , z , t ) exp ( i k z i ω t ) + A 2 ( x , z , t ) exp ( i k z + i ω t ) + c . c . ] .
A 1 ( x , z , t ) = m a m ( z , t ) exp [ i k m ( x + m z / 2 ) ] ,
A 2 ( x , z , t ) = m b m ( z , t ) exp [ i k m ( x + m z / 2 ) ] ,
A 1 z i 2 k 2 A 1 x 2 = i k n b δ n ( x , z , t ) A 1 ,
A 2 z i 2 k 2 A 2 x 2 = i k n b δ n ( x , z , t ) A 2 ,
δ n t + ( 1 + | A 1 | 2 + | A 2 | 2 ) δ n = i m , n γ m n { a m a n * × exp [ i k ( m n ) x i k 2 ( m 2 n 2 ) z / 2 ] + b m b n * × exp [ i k ( m n ) x i k 2 ( m 2 n 2 ) z / 2 ] }
δ n ( x , z , t ) = m , n n m , n ( z , t ) exp [ i k ( m n ) x i k 2 ( m 2 n 2 ) z / 2 ] .
a p z = i k n b m , n n m n a p + n m exp ( i k 2 Δ 1 z / 2 ) .
b p z = i k n b m , n n m n a p n + m exp ( i k 2 Δ 2 z / 2 ) .
n m n t + I 0 n m n = γ m n ( a m a n * + b m * b n ) ,
a p z = i k n b n n p n a n , b p z = i k n b n n p n b n .
CF = m a m b m / ( m | a m | 2 m | b m | 2 ) 1 / 2 ,

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