Abstract

An exact solution to photorefractive four-wave mixing equations with complex couplings in reflection geometry is obtained. It is shown that the efficiency of the process of phase conjugation can be enhanced by introduction of a frequency shift between the pumps and the signal, similar to the case of transmission geometry. However, to obtain an improved agreement with experiment, the inclusion of transverse effects is found to be necessary.

© 1996 Optical Society of America

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References

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  1. M. Cronin-Golomb, J. O. White, B. Fischer, A. Yariv, Opt. Lett. 7, 313 (1982).
    [CrossRef] [PubMed]
  2. M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984 ); A. Bledowski, W. Krolikowski, Opt. Lett. 13, 146 (1988).
    [CrossRef] [PubMed]
  3. M. Belić, M. Petrović, J.Opt. Soc. Am. B 11, 481 (1994).
    [CrossRef]
  4. P. Stojkov, M. Belić, Phys. Rev. A 45, 5061 (1992).
    [CrossRef] [PubMed]
  5. M. Belić, Opt. Lett. 12, 105 (1987).
    [CrossRef]
  6. K. R. MacDonald, J. Feinberg, Phys. Rev. Lett. 55, 821 (1985).
    [CrossRef] [PubMed]
  7. M. Cronin-Golomb, A. Yariv, Opt. Lett. 11, 242 (1986);B. Fischer, S. Sternklar, S. Weiss, IEEE J. Quantum Electron. 25550 (1989).
    [CrossRef] [PubMed]
  8. M. Belić, J. Leonardy, D. Timotijević, F. Kaiser, J.Opt. Soc. Am. B 12, 1602 (1995).
    [CrossRef]

1995 (1)

M. Belić, J. Leonardy, D. Timotijević, F. Kaiser, J.Opt. Soc. Am. B 12, 1602 (1995).
[CrossRef]

1994 (1)

M. Belić, M. Petrović, J.Opt. Soc. Am. B 11, 481 (1994).
[CrossRef]

1992 (1)

P. Stojkov, M. Belić, Phys. Rev. A 45, 5061 (1992).
[CrossRef] [PubMed]

1987 (1)

1986 (1)

1985 (1)

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

1984 (1)

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984 ); A. Bledowski, W. Krolikowski, Opt. Lett. 13, 146 (1988).
[CrossRef] [PubMed]

1982 (1)

Belic, M.

M. Belić, J. Leonardy, D. Timotijević, F. Kaiser, J.Opt. Soc. Am. B 12, 1602 (1995).
[CrossRef]

M. Belić, M. Petrović, J.Opt. Soc. Am. B 11, 481 (1994).
[CrossRef]

P. Stojkov, M. Belić, Phys. Rev. A 45, 5061 (1992).
[CrossRef] [PubMed]

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

Cronin-Golomb, M.

Feinberg, J.

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

Fischer, B.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984 ); A. Bledowski, W. Krolikowski, Opt. Lett. 13, 146 (1988).
[CrossRef] [PubMed]

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

Kaiser, F.

M. Belić, J. Leonardy, D. Timotijević, F. Kaiser, J.Opt. Soc. Am. B 12, 1602 (1995).
[CrossRef]

Leonardy, J.

M. Belić, J. Leonardy, D. Timotijević, F. Kaiser, J.Opt. Soc. Am. B 12, 1602 (1995).
[CrossRef]

MacDonald, K. R.

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

Petrovic, M.

M. Belić, M. Petrović, J.Opt. Soc. Am. B 11, 481 (1994).
[CrossRef]

Stojkov, P.

P. Stojkov, M. Belić, Phys. Rev. A 45, 5061 (1992).
[CrossRef] [PubMed]

Timotijevic, D.

M. Belić, J. Leonardy, D. Timotijević, F. Kaiser, J.Opt. Soc. Am. B 12, 1602 (1995).
[CrossRef]

White, J. O.

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984 ); A. Bledowski, W. Krolikowski, Opt. Lett. 13, 146 (1988).
[CrossRef] [PubMed]

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

Yariv, A.

IEEE J. Quantum Electron. (1)

M. Cronin-Golomb, B. Fischer, J. O. White, A. Yariv, IEEE J. Quantum Electron. QE-20, 12 (1984 ); A. Bledowski, W. Krolikowski, Opt. Lett. 13, 146 (1988).
[CrossRef] [PubMed]

J.Opt. Soc. Am. B (2)

M. Belić, M. Petrović, J.Opt. Soc. Am. B 11, 481 (1994).
[CrossRef]

M. Belić, J. Leonardy, D. Timotijević, F. Kaiser, J.Opt. Soc. Am. B 12, 1602 (1995).
[CrossRef]

Opt. Lett. (3)

Phys. Rev. A (1)

P. Stojkov, M. Belić, Phys. Rev. A 45, 5061 (1992).
[CrossRef] [PubMed]

Phys. Rev. Lett. (1)

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

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Figures (3)

Fig. 1
Fig. 1

Reflectivity as a function of the coupling strength, for different arguments of the coupling constant: (a) arg(γ) = 85°, (b) arg(γ) = 89.9°. The other parameters are I10 = I2d = 1 and I40 = 0.4, corresponding to an example considered in Ref. 1.

Fig. 2
Fig. 2

Diffraction efficiency as a function of the frequency detuning δf. Similar curves appear in TG.

Fig. 3
Fig. 3

Diffraction efficiency as a function of the detuning in the transverse case and in TG. The solid curve is for focused Gaussian beams A10 and A40 and almost flat A2d and A3d; the dashed curve is for focused A2d and A3d and flat A10 and A40. Parameters I10 = 1.15, I2d = 0.031, I40 = 1.25, and γ0d = −4.5 are chosen to correspond to an experiment reported by MacDonald and Feinberg.6 The PC beam is seeded with I3d = 0.001.

Equations (15)

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d A 1 d z = γ I Q A 3 , d A 2 d z = γ I Q A 4 ,
d A 3 d z = γ I Q A 1 , d A 4 d z = γ I Q A 2 ,
d d z ( A 1 A 2 ) = γ I [ c + ( d 1 d 2 ) ( A 1 A 2 ) c ( A 1 A 2 ) 2 ] ,
d d z ( A 3 A 4 ) = γ I [ c + ( d 1 d 2 ) A 3 A 4 c ( A 3 A 4 ) 2 ] .
d θ d z = δ 2 I ,
A 1 A 2 = ( Δ δ ) D exp ( γ θ ) ( Δ + δ ) D 1 exp ( γ θ ) 2 c [ D exp ( γ θ ) D 1 exp ( γ θ ) ] ,
A 3 A 4 = ( Δ δ ) E 1 exp ( γ θ ) ( Δ + δ ) E exp ( γ θ ) 2 c [ E exp ( γ θ ) E 1 exp ( γ θ ) ] ,
( | c | 2 | C 1 C 2 | 2 ) | Δ T δ | 2 + 4 | c | 2 | C 2 C 4 | 2 | T | 2 = 0 ,
[ ( | c | 2 + | C 1 C 2 | 2 ) Δ 2 4 | c | 2 | C 2 C 4 | 2 + 2 Δ | c | 2 ε ] × T r | c | 2 ( ε + Δ ) δ = 0 ,
d I 2 / d z = 8 | Q d | 2 γ r exp [ 2 γ r ( z d ) ] ,
exp ( 4 γ r θ d ) = [ exp ( 2 γ r d ) + w 2 ] 1 / 2 + w ( 1 + w 2 ) 1 / 2 w [ exp ( 2 γ r d ) + w 2 ] 1 / 2 w ( 1 + w 2 ) 1 / 2 + w ,
E 2 = exp ( 2 γ θ d ) Δ δ Δ + δ , D 2 = exp ( 2 γ θ d ) 2 | c | 2 + | C 2 | 2 ( Δ + δ ) 2 | c | 2 + | C 2 | 2 ( Δ δ ) .
I 1 d = | c | 2 | C 2 | 2 , I 4 d = | C 2 | 2 Δ | c | 2 | C 2 | 2 .
R = I 30 | C 4 | 2 = 4 | c | 2 | T | 2 | Δ T δ | 2 , D = I 30 | C 2 | 2 = | C 4 | 2 | C 2 | 2 R .
γ = γ 0 1 + 2 π i τ δ f ,

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