Abstract

We present an exact solution of a nonlinear vector analysis of two-beam coupling and forward four-wave mixing in photorefractive media.

© 1986 Optical Society of America

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References

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  1. We note that in many cases of practical importance in BaTiO3 and LiNb2O6, for example, the couplings for the different polarizations are not the same.
  2. A. Khyzniak, V. Kondilenko, Yu. Kucherov, S. Lesnik, S. Odulov, M. Soskin, J. Opt. Soc. Am. A 1, 169 (1984).
    [CrossRef]
  3. A. Yariv, Appl. Phys. Lett. 28, 88 (1976).
    [CrossRef]
  4. D. W. Vahey, J. Appl. Phys. 46, 3510 (1975).
    [CrossRef]
  5. N. V. Khuktarev, V. B. Markov, S. G. Odulov, M. S. Soskin, L. Vinetskii, Ferroelectrics 22, 949 (1979).
    [CrossRef]
  6. B. Fischer, M. Cronin-Golomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
    [CrossRef] [PubMed]
  7. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, Opt. Lett. 7, 313 (1982).
    [CrossRef] [PubMed]
  8. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
    [CrossRef]

1984

A. Khyzniak, V. Kondilenko, Yu. Kucherov, S. Lesnik, S. Odulov, M. Soskin, J. Opt. Soc. Am. A 1, 169 (1984).
[CrossRef]

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

1982

1981

1979

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

1976

A. Yariv, Appl. Phys. Lett. 28, 88 (1976).
[CrossRef]

1975

D. W. Vahey, J. Appl. Phys. 46, 3510 (1975).
[CrossRef]

Cronin-Golomb, M.

Fischer, B.

Khuktarev, N. V.

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

Khyzniak, A.

Kondilenko, V.

Kucherov, Yu.

Lesnik, S.

Markov, V. B.

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

Odulov, S.

Odulov, S. G.

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

Soskin, M.

Soskin, M. S.

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

Vahey, D. W.

D. W. Vahey, J. Appl. Phys. 46, 3510 (1975).
[CrossRef]

Vinetskii, L.

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

White, J. O.

Yariv, A.

Appl. Phys. Lett.

A. Yariv, Appl. Phys. Lett. 28, 88 (1976).
[CrossRef]

Ferroelectrics

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

IEEE J. Quantum Electron.

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

J. Appl. Phys.

D. W. Vahey, J. Appl. Phys. 46, 3510 (1975).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Other

We note that in many cases of practical importance in BaTiO3 and LiNb2O6, for example, the couplings for the different polarizations are not the same.

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Figures (3)

Fig. 1
Fig. 1

Vectorial two-wave mixing geometry analyzed in text.

Fig. 2
Fig. 2

Forward four-wave mixing geometry analyzed in text.

Fig. 3
Fig. 3

Contour plot of log forward phase-conjugate conversion efficiency for coupling constant bIl = 3 versus pump and probe ratio logarithms.

Equations (24)

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d A 1 d z = - b I g A 4 - b II g A 3 ,
d A 2 d z = - b I g A 3 - b II g A 4 ,
d A 3 * d z = b I g A 2 * + b II g A 1 * ,
d A 4 * d z = b I g A 1 * + b II g A 2 * ,
g = A 1 A 4 * + A 2 A 3 * I 0 ,
I 0 = A 1 A 1 * + A 2 A 2 * + A 3 A 3 * + A 4 A 4 * ,
I 1 + I 4 = d 1 ,
I 2 + I 3 = d 2 ,
A 1 A 2 * + A 3 * A 4 = c ,
d d z ( A 1 A 2 ) = - b I [ c + ( d 1 - d 2 ) ( A 1 A 2 ) - c * ( A 1 A 2 ) 2 ] ,
d d z ( A 3 A 4 ) = b I [ c + ( d 2 - d 1 ) ( A 3 A 4 ) - c * ( A 3 A 4 ) 2 ] .
A 1 A 2 = - [ D S - e - μ z - D - 1 S + e μ z 2 c * ( D e - μ z - D - 1 e μ z ) ] ,
A 3 A 4 = - [ E S - e - μ z - E - 1 S + e μ z 2 c * ( E e - μ z - E - 1 e μ z ) ] ,
S ± = Δ ± ( Δ 2 + 4 c 2 ) 1 / 2 ,
μ = b I 2 ( Δ 2 + 4 c 2 ) 1 / 2 ,
Δ = d 2 - d 1 .
D 2 = 2 c * A 12 ( 0 ) + S + 2 c * A 12 ( 0 ) + S - ,
E 2 = 2 c * A 34 ( 0 ) - S + 2 c * A 34 ( 0 ) - S - ,
Δ = I 2 ( 0 ) + I 3 ( 0 ) - I 1 ( 0 ) - I 4 ( 0 ) ,
c = A 1 ( 0 ) A 2 * ( 0 ) + A 3 * ( 0 ) A 4 ( 0 )
I 1 ( z ) = I 12 ( z ) [ d 2 - I 34 ( z ) d 1 1 - I 12 ( z ) I 34 ( z ) ] ,
I 2 ( z ) = [ d 2 - I 34 ( z ) d 1 1 - I 12 ( z ) I 34 ( z ) ] ,
I 3 ( z ) = I 34 ( z ) [ d 1 - I 12 ( z ) d 2 1 - I 12 ( z ) I 34 ( z ) ] ,
I 4 ( z ) = [ d 1 - I 12 ( z ) d 2 1 - I 12 ( z ) I 34 ( z ) ] .

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