Abstract

A novel method for the exact solution of four-wave mixing in photorefractive media is presented. This method allows us to treat exactly the effects of nonequal angles of incidence, different refractive-index modulation of interacting waves, and external incoherent illumination of the photorefractive crystal.

© 1988 Optical Society of America

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References

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  1. See, for example, P. Günter, Phys. Rep. 93, 199 (1982).
    [CrossRef]
  2. M. Crohin-Golomb, J. O. White, B. Fischer, A. Yariv, Opt. Lett. 7, 313 (1982).
    [CrossRef]
  3. M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984).
    [CrossRef]
  4. M. R. Belić, Phys. Rev. A 31, 3169 (1985).
    [CrossRef]
  5. M. R. Belić, M. Lax, Opt. Commun. 56, 197 (1985).
    [CrossRef]
  6. M. R. Belić, Opt. Lett. 12, 105 (1987).
    [CrossRef]
  7. N. V. Kukhtarev, T. I. Semenets, K. H. Ringhofer, G. Tomberger, Appl. Phys. B 41, 259 (1986).
    [CrossRef]
  8. A. Bledowski, W. Krolikowski, “Anisotropic four-wave mixing in cubic photorefractive crystals,” IEEE J. Quantum Electron, (to be published).
  9. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetski, Ferroelectrics 22, 949 (1979).
    [CrossRef]
  10. S. L Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
    [CrossRef]
  11. S. I. Stepanov, V. V. Kulikov, M. P. Petrov, Opt Commun. 44, 19 (1982).
    [CrossRef]

1987 (1)

1986 (1)

N. V. Kukhtarev, T. I. Semenets, K. H. Ringhofer, G. Tomberger, Appl. Phys. B 41, 259 (1986).
[CrossRef]

1985 (3)

S. L Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
[CrossRef]

M. R. Belić, Phys. Rev. A 31, 3169 (1985).
[CrossRef]

M. R. Belić, M. Lax, Opt. Commun. 56, 197 (1985).
[CrossRef]

1984 (1)

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

1982 (3)

See, for example, P. Günter, Phys. Rep. 93, 199 (1982).
[CrossRef]

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

S. I. Stepanov, V. V. Kulikov, M. P. Petrov, Opt Commun. 44, 19 (1982).
[CrossRef]

1979 (1)

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

Belic, M. R.

M. R. Belić, Opt. Lett. 12, 105 (1987).
[CrossRef]

M. R. Belić, Phys. Rev. A 31, 3169 (1985).
[CrossRef]

M. R. Belić, M. Lax, Opt. Commun. 56, 197 (1985).
[CrossRef]

Bledowski, A.

A. Bledowski, W. Krolikowski, “Anisotropic four-wave mixing in cubic photorefractive crystals,” IEEE J. Quantum Electron, (to be published).

Crohin-Golomb, M.

Cronin-Golomb, M.

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

Fischer, B.

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

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

Günter, P.

See, for example, P. Günter, Phys. Rep. 93, 199 (1982).
[CrossRef]

Krolikowski, W.

A. Bledowski, W. Krolikowski, “Anisotropic four-wave mixing in cubic photorefractive crystals,” IEEE J. Quantum Electron, (to be published).

Kukhtarev, N. V.

N. V. Kukhtarev, T. I. Semenets, K. H. Ringhofer, G. Tomberger, Appl. Phys. B 41, 259 (1986).
[CrossRef]

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

Kulikov, V. V.

S. I. Stepanov, V. V. Kulikov, M. P. Petrov, Opt Commun. 44, 19 (1982).
[CrossRef]

Lax, M.

M. R. Belić, M. Lax, Opt. Commun. 56, 197 (1985).
[CrossRef]

Markov, V. B.

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

Odulov, S. G.

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

Petrov, M. P.

S. L Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
[CrossRef]

S. I. Stepanov, V. V. Kulikov, M. P. Petrov, Opt Commun. 44, 19 (1982).
[CrossRef]

Ringhofer, K. H.

N. V. Kukhtarev, T. I. Semenets, K. H. Ringhofer, G. Tomberger, Appl. Phys. B 41, 259 (1986).
[CrossRef]

Semenets, T. I.

N. V. Kukhtarev, T. I. Semenets, K. H. Ringhofer, G. Tomberger, Appl. Phys. B 41, 259 (1986).
[CrossRef]

Soskin, M. S.

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

Stepanov, S. I.

S. I. Stepanov, V. V. Kulikov, M. P. Petrov, Opt Commun. 44, 19 (1982).
[CrossRef]

Stepanov, S. L

S. L Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
[CrossRef]

Tomberger, G.

N. V. Kukhtarev, T. I. Semenets, K. H. Ringhofer, G. Tomberger, Appl. Phys. B 41, 259 (1986).
[CrossRef]

Vinetski, V. L.

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

White, J. O.

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

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

Yariv, A.

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

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

Appl. Phys. B (1)

N. V. Kukhtarev, T. I. Semenets, K. H. Ringhofer, G. Tomberger, Appl. Phys. B 41, 259 (1986).
[CrossRef]

Ferroelectrics (1)

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

IEEE J. Quantum Electron. (1)

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

Opt Commun. (1)

S. I. Stepanov, V. V. Kulikov, M. P. Petrov, Opt Commun. 44, 19 (1982).
[CrossRef]

Opt. Commun. (2)

S. L Stepanov, M. P. Petrov, Opt. Commun. 53, 292 (1985).
[CrossRef]

M. R. Belić, M. Lax, Opt. Commun. 56, 197 (1985).
[CrossRef]

Opt. Lett. (2)

Phys. Rep. (1)

See, for example, P. Günter, Phys. Rep. 93, 199 (1982).
[CrossRef]

Phys. Rev. A (1)

M. R. Belić, Phys. Rev. A 31, 3169 (1985).
[CrossRef]

Other (1)

A. Bledowski, W. Krolikowski, “Anisotropic four-wave mixing in cubic photorefractive crystals,” IEEE J. Quantum Electron, (to be published).

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Figures (2)

Fig. 1
Fig. 1

Geometry of reflection 4WM.

Fig. 2
Fig. 2

Intensity of the phase-conjugate wave as a function of the intensity of the input probe wave for several values of angle of incidence ϑ3; in each case ϑ1 + ϑ3 = 60°. Intensities are normalized to the total pump intensity I10 + I2L The pump ratio I1/I2 is assumed to be 1

Equations (26)

Equations on this page are rendered with MathJax. Learn more.

A ˙ 1 = γ 1 g / I 0 A 3 ,
A ˙ 2 * = γ 2 g / I 0 A 4 * ,
A ˙ 3 * = γ 3 g / I 0 A 1 * ,
A ˙ 4 = γ 4 g / I 0 A 2 ,
g = ( A 1 A 3 * + A 2 * A 4 ) .
γ j = i n j ω exp ( i φ ) 2 c cos ϑ j ,
g = g ( γ 1 I 3 + γ 2 I 4 + γ 3 I 1 + γ 4 I 2 ) / I 0 = g F .
g ˙ = g ( 0 ) exp [ 0 z F ( z ) d z ] .
g = | g | exp ( i ) .
x = 0 z | g ( z ) | / I 0 d z ,
A ˙ 1 = γ 1 exp ( i ) A 3 ,
A ˙ 3 = γ 3 exp ( i ) A 1 ,
A ˙ 2 = γ 2 exp ( i ) A 4 ,
A ˙ 4 = γ 4 exp ( i ) A 2 ,
A 1 = [ A 10 cosh ( ϕ 13 L ϕ 13 ) + exp ( i ) η 13 A 3 L × sinh ϕ 13 ] / cosh ϕ 13 L ,
A 3 = [ exp ( i ) η 31 A 10 sinh ( ϕ 13 L ϕ 13 ) + A 3 L cosh ϕ 13 ] / cosh ϕ 13 L ,
A 2 = [ exp ( i ) η 24 A 40 sinh ( ϕ 24 L ϕ 24 ) + A 2 L cosh ϕ 24 ] / cosh ϕ 24 L ,
A 4 = [ A 40 cosh ( ϕ 24 L ϕ 24 ) + exp ( i ) η 42 A 2 L × sinh ϕ 24 ] / cosh ϕ 24 L ,
ϕ i j = γ i γ j x , ϕ i j L = γ i γ j x L , x L = x ( z = L ) , η i j = γ i / γ j ,
d x d z = A 1 A 3 * + A 2 * A 4 I 0 ,
γ 1 γ 3 / γ 2 γ 4 = integer .
γ 1 = γ 2 = γ / cos ϑ 1 , γ 3 = γ 4 = γ / cos ϑ 3 .
I 3 ( 0 ) = I 1 tanh 2 ϕ L ,
[ ( ρ + 1 ρ ) + α 0 ( α 1 2 α 2 2 ) 1 / 2 ] ln [ sinh ( ln q 2 ϕ L ) sinh ( ln q ) ] + α 0 ( α 1 2 α 2 2 ) 1 / 2 ln [ 1 + cosh ( ln q ) 1 + cosh ( ln q 2 ϕ L ) ] 2 γ ˜ z = 0 ,
α 0 = 1 2 ( 1 ρ 2 ) [ I 10 I 40 / ρ 2 + I 2 L 2 ( I 2 L I 40 ) 1 / 2 × sinh ϕ L / ρ ] , α 1 = ρ 2 [ ( I 10 + I 40 / ρ 2 ) cosh 2 ϕ L + I 2 L 2 ( I 2 L I 40 ) 1 / 2 × sinh ϕ L / ρ ] , α 2 = 1 2 [ ( I 10 + I 40 / ρ 2 ) sinh 2 ϕ L + 2 ( I 2 L I 40 ) 1 / 2 × cosh ϕ L / ρ ] , ρ = cos ϑ 1 / cos ϑ 3 , q = ( α 1 α 2 α 1 + α 2 ) 1 / 2 ,
I 3 = I 10 I 2 L I 40 [ exp ( γ L ) 1 ] 2 I 2 L I 40 [ exp ( γ L ) 1 ] 2 + [ ( I 10 + I 40 ) exp ( γ L ) + I 2 L ] 2 ,

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