Abstract

We investigate contradirectional two-wave mixing with partially coherent waves in photorefractive crystals in the nondepleted pump regime. Equations governing the propagation of the self-coherence function and the mutual-coherence function of the signal wave and the pump wave are derived and simulated numerically. Numerical solutions of these equations are in excellent agreement with the experimental measurements.

© 1996 Optical Society of America

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References

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  1. N. V. Bogodaev, L. I. Ivleva, A. S. Korshunov, N. M. Polozkov, V. V. Shkunov, J. Opt. Soc. Am. B 10, 2287 (1993).
    [CrossRef]
  2. M. Cronin-Golomb, H. Z. Kong, W. Krolikowski, J. Opt. Soc. Am. B 9, 1698 (1992).
    [CrossRef]
  3. H. Z. Kong, C. K. Wu, M. Cronin-Golomb, Opt. Lett. 16, 1183 (1991).
    [CrossRef] [PubMed]
  4. P. Yeh, Appl. Opt. 26, 602 (1987).
    [CrossRef] [PubMed]
  5. See, for example, J. W. Goodman, Statistical Optics (Wiley, New York, 1985), Chap. 5.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the two-wave-mixing configuration used in our calculations and experiments. The distances Li and L2 are the optical path lengths of the signal wave and the pump wave from the laser source to the signal-wave incident plane z = 0, respectively. L2ref is the optical path length of reference wave E2ref from the laser source to the signal output plane z = d.

Fig. 2
Fig. 2

Mutual-coherence function Γ12(z, 0) and the self-coherence function of the signal wave Γ11(z, 0) as a function of z for coupling constants γ = 3 (solid curves) and γ = 7 (dashed curves).

Fig. 3
Fig. 3

Interference patterns of the signal wave and the reference wave at the output plane P1 (a) without and (b) with coupling. Note the increase of fringe visibility owing to the coupling.

Fig. 4
Fig. 4

Mutual coherence Γ12(d, 0) as a function of the optical path difference ΔL.

Fig. 5
Fig. 5

Intensity gain of the signal wave at z = d plane as a function of the path difference ΔL.

Equations (10)

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E 1 z + 1 υ E 1 t = γ 2 Q · E 2 I 1 + I 2 α 2 E 1 ,
E 2 z 1 υ E 2 t = γ 2 Q * · E 1 I 1 + I 2 + α 2 E 2 ,
τ Q t + Q = E 1 E 2 * ,
Γ 12 ( z , Δ t ) z = 2 υ Γ 12 ( z , Δ t ) Δ t + γ 2 Γ 12 ( z , 0 ) I 1 + I 2 × [ Γ 11 ( z , Δ t ) + Γ 22 ( z , Δ t ) ] ,
Γ 11 ( z , Δ t ) z = γ 2 Γ 12 ( z , 0 ) I 1 + I 2 Γ 12 * ( z Δ t ) + Γ 12 * ( z , 0 ) I 1 + I 2 × [ Γ 12 ( z , Δ t ) α Γ 11 ( z , Δ t ) ] ,
Γ 22 ( z , Δ t ) z = γ 2 Γ 12 ( z , 0 ) I 1 + I 2 Γ 12 * ( z , Δ t ) + γ 2 Γ 12 * ( z , 0 ) I 1 + I 2 × Γ 12 ( z , Δ t ) α Γ 22 ( z , Δ t ) .
Γ s ( δ t ) = exp [ ( π Δ υ δ t 2 ln 2 ) 2 ] .
Γ 12 ( z = 0 , Δ t ) β Γ s ( Δ t + δ t ) ,
Γ 11 ( z = 0 , Δ t ) β Γ s ( Δ t ) ,
Γ 22 ( z = 0 , Δ t ) Γ s ( Δ t ) ,

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