Abstract

We present an analytical approximative solution of four-wave mixing in photorefractive crystals with depleted pumps for the case of a negative coupling coefficient and then discuss the solution.

© 1989 Optical Society of America

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References

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  1. M. Cronin-Colomb, J. O. White, B. Fischer, A. Yariv, Opt. Lett. 7, 313 (1982).
    [CrossRef]
  2. A. Hardy, Y. Silberberg, J. Opt. Soc. Am. 73, 594 (1983).
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  3. J. Goltz, C. Denz, H. Klumb, T. Tschudi, J. Albers, Opt. Lett. 13, 321 (1988).
    [CrossRef] [PubMed]
  4. B. Fischer, M. Cronin-Colomb, J. O. White, A. Yariv, Opt. Lett. 6, 519 (1981).
    [CrossRef] [PubMed]
  5. K. R. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
    [CrossRef] [PubMed]

1988

1985

K. R. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
[CrossRef] [PubMed]

1983

1982

1981

Albers, J.

Cronin-Colomb, M.

Denz, C.

Feinberg, J.

K. R. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
[CrossRef] [PubMed]

Fischer, B.

Goltz, J.

Hardy, A.

Klumb, H.

MacDonald, K. R.

K. R. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
[CrossRef] [PubMed]

Silberberg, Y.

Tschudi, T.

White, J. O.

Yariv, A.

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Figures (1)

Fig. 1
Fig. 1

Basic geometry of the four-wave mixing.

Equations (34)

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d s 1 * d z = γ J 0 ( s 1 * p 1 + s 2 p 2 * ) p 1 * ,
d s 2 d z = γ J 0 ( s 1 * p 1 + s 2 p 2 * ) p 2 ,
exp ( γ l ) 1.
s 2 ( z ) 2 + p 2 ( z ) 2 = p 2 , l 2 ,
s 1 ( z ) 2 + p 1 ( z ) 2 = s 1 , 0 2 + p 1 , 0 2 ,
R u ( z ) = s 2 ( z ) 2 s 1 , 0 2 = r | exp ( γ z ) - exp ( γ l ) 1 + r exp ( γ l ) | 2 ,
r 1 = exp ( - γ l ) .
r 1.
0 z z 1 ,
z 1 l .
s 1 * p 1 s 1 , 0 p 1 , 0 and s 2 p 2 * s 1 , 0 p 2 , l .
d s 2 2 d z = 2 γ J 0 s 2 2 ( p 2 , l 2 - s 2 2 ) .
ln s 2 2 s 1 , 0 2 1 - s 2 2 s 1 , 0 2 s 1 , 0 2 p 2 , l 2 = 2 p 2 , l 2 γ z J 0 + b ,
b = - 2 p 2 , l 2 γ z 1 J 0 + ln s 2 ( z 1 ) 2 s 1 , 0 2 1 - s 2 ( z 1 ) 2 s 1 , 0 2 s 1 , 0 2 p 2 , l 2 .
ln R u = 2 p 2 , l 2 J 0 - 1 γ z + b .
ln R u = ln R 0 + 2 ln 1 - exp [ γ ( l - z ) ] 1 - exp ( γ l ) + 2 p 2 , l 2 J 0 + 2 p 1 , 0 2 γ z J 0 ,
R 0 = R u ( 0 ) = r | 1 - exp ( γ l ) 1 + r exp ( γ l ) | 2 .
ln R u = 2 p 2 , l 2 J 0 - 1 γ z + ln R 0 .
b = ln R 0 .
s 2 = s 1 , 0 [ R 0 - 1 exp ( 2 p 2 , l 2 J 0 - 1 γ z ) + ( 1 + r - 1 ) q ] - 1 / 2 ,
R = s 2 ( 0 ) 2 s 1 , 0 2 = R 0 1 + R 0 ( 1 + r - 1 ) q .
s 2 ( p 2 , l 2 - s 2 2 ) 1 / 2 = s 2 ( p 2 , l 2 - s 2 2 ) 1 / 2 + s 1 p 1 ,
s 1 , 0 p 1 , 0 ( p 2 , l 2 - R s 1 , 0 2 ) 1 / 2 ( R s 1 , 0 2 ) 1 / 2 .
ξ 1 + ξ 2 1 ,
ξ 1 = s 1 , 0 2 p 2 , l 2 1 - exp ( γ l ) 1 + r exp ( γ l ) and ξ 2 = r + exp ( γ l ) 1 - exp ( γ l ) .
q 1 + r exp ( γ l ) ( 1 + r - 1 ) [ 1 - exp ( γ l ) ] .
q 1 + r exp ( γ l ) .
r opt = exp ( - γ l ) { 1 + [ 1 - exp ( γ l ) ] q } 1 / 2 .
r opt exp ( - γ l ) 1.
η = s 2 ( 0 ) 2 J 0 = 1 1 + q - 1 R 0 1 + R 0 ( 1 - r - 1 ) q .
q opt = 1 + r exp ( γ l ) [ 1 - exp ( γ l ) ] r + 1 .
q opt = 2 exp ( γ l / 2 ) ,
q opt = 1 + r exp ( γ l ) exp ( - γ l / 2 ) 1 + r exp ( γ l ) .
η max 1 1 + 10 × exp ( γ l ) + 2 × exp ( γ l / 2 ) .

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