Abstract

Coherent amplification of images by two-wave mixing in photorefractive crystals is examined with attention given to processing in the Fourier domain. It is shown that the gain that is experienced as the probe image traverses the crystal is approximately uniform across the image. The gain can be expressed as a function of the average probe to pump intensity ratio. Experimental verification is given to support the theory.

© 1990 Optical Society of America

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References

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  1. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, “Holographic Storage in Electro-Optic Crystals II. Self Amplification,” Ferroelectrics 22, 961–964 (1979).
    [CrossRef]
  2. J. P. Huignard, A. Marrakchi, “Coherent Signal Beam Amplification in Two-Wave Mixing Experiments with Photorefractive Bi12SiO20 Crystals,” Opt. Commun. 38, 249–254 (1981).
    [CrossRef]
  3. Y. Fainman, E. Klancnik, S. H. Lee, “Optimal Coherent Image Amplification by Two-Wave Coupling in Photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
    [CrossRef]
  4. D. Z. Anderson, R. Saxena, “Theory of Multimode Operation of a Unidirectional Ring Oscillator Having Photorefractive Gain: Weak Field Limit,” J. Opt. Soc. Am. B 4, 164–176 (1987).
    [CrossRef]
  5. E. Ochoa, F. Vachss, L. Hesselink, “Higher-order Analysis of the Photorefractive Effect for Large Modulation Depths,” J. Opt. Soc. Am. A 3, 181–187 (1986).
    [CrossRef]
  6. Ph. Refrigier, L. Solymar, H. Rajenbach, J. P. Huignard, “Two Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Gratings: Theory and Experiments,” J. Appl. Phys. 58, 45–57 (1985).
    [CrossRef]
  7. F. Vachss, L. Hesselink, “Nonlinear Photorefractive Response at High Modulation Depths,” J. Opt. Soc. Am. A 5, 690–701 (1988).
    [CrossRef]
  8. G. C. Gilbreath, F. M. Davidson, “Spatial light modulation using two-wave mixing properties of photorefractive materials,” in Technical Digest, OSA Annual MeetingTechnical Digest Series, Vol. 11, (Optical Society of America, Washington, DC, 1988), p. 144.
  9. J. Ma, L. Liu, S. Wu, Z. Wang, L. Xu, B. Shu, “Multibeam Coupling in Photorefractive SBN:Ce,” Opt. lett. 13, 1020–1022 (1988).
    [CrossRef] [PubMed]
  10. F. Vachss, P. Yeh, “Image degradation mechanisms in photorefractive amplifiers,” J. Opt. Soc. Am. B 6, 1834–1844 (1989).
    [CrossRef]

1989 (1)

1988 (2)

1987 (1)

1986 (2)

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal Coherent Image Amplification by Two-Wave Coupling in Photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
[CrossRef]

E. Ochoa, F. Vachss, L. Hesselink, “Higher-order Analysis of the Photorefractive Effect for Large Modulation Depths,” J. Opt. Soc. Am. A 3, 181–187 (1986).
[CrossRef]

1985 (1)

Ph. Refrigier, L. Solymar, H. Rajenbach, J. P. Huignard, “Two Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Gratings: Theory and Experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

1981 (1)

J. P. Huignard, A. Marrakchi, “Coherent Signal Beam Amplification in Two-Wave Mixing Experiments with Photorefractive Bi12SiO20 Crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, “Holographic Storage in Electro-Optic Crystals II. Self Amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Anderson, D. Z.

Davidson, F. M.

G. C. Gilbreath, F. M. Davidson, “Spatial light modulation using two-wave mixing properties of photorefractive materials,” in Technical Digest, OSA Annual MeetingTechnical Digest Series, Vol. 11, (Optical Society of America, Washington, DC, 1988), p. 144.

Fainman, Y.

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal Coherent Image Amplification by Two-Wave Coupling in Photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
[CrossRef]

Gilbreath, G. C.

G. C. Gilbreath, F. M. Davidson, “Spatial light modulation using two-wave mixing properties of photorefractive materials,” in Technical Digest, OSA Annual MeetingTechnical Digest Series, Vol. 11, (Optical Society of America, Washington, DC, 1988), p. 144.

Hesselink, L.

Huignard, J. P.

Ph. Refrigier, L. Solymar, H. Rajenbach, J. P. Huignard, “Two Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Gratings: Theory and Experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

J. P. Huignard, A. Marrakchi, “Coherent Signal Beam Amplification in Two-Wave Mixing Experiments with Photorefractive Bi12SiO20 Crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

Klancnik, E.

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal Coherent Image Amplification by Two-Wave Coupling in Photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
[CrossRef]

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, “Holographic Storage in Electro-Optic Crystals II. Self Amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Lee, S. H.

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal Coherent Image Amplification by Two-Wave Coupling in Photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
[CrossRef]

Liu, L.

Ma, J.

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, “Holographic Storage in Electro-Optic Crystals II. Self Amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Marrakchi, A.

J. P. Huignard, A. Marrakchi, “Coherent Signal Beam Amplification in Two-Wave Mixing Experiments with Photorefractive Bi12SiO20 Crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

Ochoa, E.

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, “Holographic Storage in Electro-Optic Crystals II. Self Amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Rajenbach, H.

Ph. Refrigier, L. Solymar, H. Rajenbach, J. P. Huignard, “Two Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Gratings: Theory and Experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Refrigier, Ph.

Ph. Refrigier, L. Solymar, H. Rajenbach, J. P. Huignard, “Two Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Gratings: Theory and Experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Saxena, R.

Shu, B.

Solymar, L.

Ph. Refrigier, L. Solymar, H. Rajenbach, J. P. Huignard, “Two Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Gratings: Theory and Experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Soskin, M. S.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, “Holographic Storage in Electro-Optic Crystals II. Self Amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

Vachss, F.

Wang, Z.

Wu, S.

Xu, L.

Yeh, P.

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, “Holographic Storage in Electro-Optic Crystals II. Self Amplification,” Ferroelectrics 22, 961–964 (1979).
[CrossRef]

J. Appl. Phys. (1)

Ph. Refrigier, L. Solymar, H. Rajenbach, J. P. Huignard, “Two Beam Coupling in Photorefractive Bi12SiO20 Crystals with Moving Gratings: Theory and Experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

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

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

Opt. Commun. (1)

J. P. Huignard, A. Marrakchi, “Coherent Signal Beam Amplification in Two-Wave Mixing Experiments with Photorefractive Bi12SiO20 Crystals,” Opt. Commun. 38, 249–254 (1981).
[CrossRef]

Opt. Eng. (1)

Y. Fainman, E. Klancnik, S. H. Lee, “Optimal Coherent Image Amplification by Two-Wave Coupling in Photorefractive BaTiO3,” Opt. Eng. 25, 228–234 (1986).
[CrossRef]

Opt. lett. (1)

Other (1)

G. C. Gilbreath, F. M. Davidson, “Spatial light modulation using two-wave mixing properties of photorefractive materials,” in Technical Digest, OSA Annual MeetingTechnical Digest Series, Vol. 11, (Optical Society of America, Washington, DC, 1988), p. 144.

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Figures (6)

Fig. 1
Fig. 1

Typical image amplification experiment using two-wave mixing in photorefractive crystals.

Fig. 2
Fig. 2

Two-wave mixing with the crystal at the Fourier plane of the input image. The pump Ep is a plane wave and the image effectively consists of a set of point sources.

Fig. 3
Fig. 3

Experimental setup used to verify approximately uniform gain. Mask MA1 consists of five identical apertures and comprises the probe image to be amplified. Because of the Gaussian illumination, the intensity pattern at MA1 is not uniform. Mask MA2 is the pump image aperture.

Fig. 4
Fig. 4

Input (lower amplitude) and amplified (higher amplitude) intensity distributions. Each portion of the overall input distribution receives roughly the same gain.

Fig. 5
Fig. 5

Experimental setup used to record the dynamics of multiple grating buildup.

Fig. 6
Fig. 6

Dynamics of two gratings in the same volume: (a) input probe intensities (upper corresponds to no. 1 and lower no. 2 in reference to Fig. 5; note, that these are given to only indicate relative intensity levels of the two probes and do not correspond temporally to the amplified output traces shown in (b); (b) output amplified intensities (history: no. 1 turned on, no 1 turned off, no 2 turned on, no 2 turned off, no 1 turned on, no 2 turned on, no 1 turned off,…).

Equations (7)

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I ( r ) = I 0 { 1 + 1 I 0 Re [ E p m = 1 N E m * exp [ i ( k p - k m ) r ] + q m N m = 1 N E q E m * exp [ i ( k q - k m ) r ] ] } ,
k p = 2 π λ ( - x ^ sin θ p + z ^ cos π p ) , k m = 2 π λ ( x ^ sin θ m + z ^ cos θ m ) ,
n = n 0 - Re { i n 1 I 0 m = 1 N E p E m * exp [ - i ( k p - k m ) r ] } ,
d E p d z = - γ p I 0 m = 1 N E m 2 E p , γ p = n 1 λ 4 cos θ d E m d z = γ m I 0 E p 2 E m , m = 1 , 2 , , N , γ m = n 1 λ 4 cos θ m ,
d I p d z = - Γ p I 0 m = 1 N I m I p , Γ p = 2 γ p d I m d z = Γ m I 0 I p I m , m = 1 , 2 , , N , Γ m = 2 γ m .
d I p d z = - Γ I 0 m = 1 N I m I p , d I m d z = Γ I 0 I p I m , m = 1 , 2 , , N
I p ( z ) = β I 0 exp ( - Γ z ) 1 + β exp ( - Γ z ) , I m ( z ) I m ( 0 ) = 1 + β 1 + β exp ( - Γ z ) ,             β = I p ( 0 ) m = 1 N I m ( 0 )

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