Abstract

We demonstrate a technique by which the temporal oscillations in the response of a photorefractive square-law converter, a recently developed high-contrast spatial light modulator, may be removed. This technique uses the translation of an amplitude grating incoherently imaged upon a photorefractive crystal to obtain a moving intensity pattern within the material. We thus obtain running-wave effects similar to those seen by previous investigators writing photorefractive gratings by using the interference of two coherent frequency-shifted beams. We show both theoretically and experimentally that the criteria for removing temporal oscillations simultaneously yields a significant improvement in the diffraction efficiency of the square-law converter.

© 1992 Optical Society of America

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References

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  1. Y. Shi, D. Psaltis, A. Marrakchi, A. R. Tanguay, “Photorefractive incoherent-to-coherent converter,” Appl. Opt. 22, 3665–3667 (1983).
    [CrossRef] [PubMed]
  2. F. Vachss, J. Hong, P. Yeh, “Temporal integration using the photorefractive square-law converter,” in Optical and Digital Gallium Arsenside Technologies for Signal Processing Applications, M. P. Bendett, D. H. Butler, A. Prabhakar, A. Yang, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1291, 68–74 (1990).
  3. F. Vachss, J. Hong, S. Campbell, “Photorefractive square-law converter,” Opt. Lett. 16, 1204–1206 (1991).
    [CrossRef] [PubMed]
  4. G. C. Valley, M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704–711 (1983).
  5. J. Hong, J. Yu, S. Hudson, D. Psaltis, “Photorefractive crystals as adaptive elements in acousto-optic filters,” in Optical Technology for Microwave Applications III, S. Yao, ed., Proc. Soc. Photo-Opt. Instrum. Eng.789, 39–47 (1987).
  6. P. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
    [CrossRef]
  7. H. Rajbenbach, J. P. Huignard, B. Loiseaux, “Spatial frequency dependence of the energy transfer in two-wave mixing experiments in BSO crystals,” Opt. Commun. 48, 247–252 (1983).
    [CrossRef]
  8. N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals, I: steady state,” Ferroelectrics 22, 949–960 (1979).
    [CrossRef]
  9. G. C. Valley, “Short pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
    [CrossRef]
  10. F. Vachss, L. Hesselink, “Selective enhancement of spatial harmonics of a photorefractive grating,” J. Opt. Soc. Am. B 5, 1814–1821 (1988).
    [CrossRef]
  11. J. P. Huignard, J. P. Herriau, “Frequency shifters for photorefractive crystals,” Appl. Opt. 24, 4285–4286 (1985).
    [CrossRef] [PubMed]

1991 (1)

1988 (1)

1985 (2)

J. P. Huignard, J. P. Herriau, “Frequency shifters for photorefractive crystals,” Appl. Opt. 24, 4285–4286 (1985).
[CrossRef] [PubMed]

P. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

1983 (4)

H. Rajbenbach, J. P. Huignard, B. Loiseaux, “Spatial frequency dependence of the energy transfer in two-wave mixing experiments in BSO crystals,” Opt. Commun. 48, 247–252 (1983).
[CrossRef]

G. C. Valley, M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704–711 (1983).

G. C. Valley, “Short pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
[CrossRef]

Y. Shi, D. Psaltis, A. Marrakchi, A. R. Tanguay, “Photorefractive incoherent-to-coherent converter,” Appl. Opt. 22, 3665–3667 (1983).
[CrossRef] [PubMed]

1979 (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals, I: steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Campbell, S.

Herriau, J. P.

Hesselink, L.

Hong, J.

F. Vachss, J. Hong, S. Campbell, “Photorefractive square-law converter,” Opt. Lett. 16, 1204–1206 (1991).
[CrossRef] [PubMed]

F. Vachss, J. Hong, P. Yeh, “Temporal integration using the photorefractive square-law converter,” in Optical and Digital Gallium Arsenside Technologies for Signal Processing Applications, M. P. Bendett, D. H. Butler, A. Prabhakar, A. Yang, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1291, 68–74 (1990).

J. Hong, J. Yu, S. Hudson, D. Psaltis, “Photorefractive crystals as adaptive elements in acousto-optic filters,” in Optical Technology for Microwave Applications III, S. Yao, ed., Proc. Soc. Photo-Opt. Instrum. Eng.789, 39–47 (1987).

Hudson, S.

J. Hong, J. Yu, S. Hudson, D. Psaltis, “Photorefractive crystals as adaptive elements in acousto-optic filters,” in Optical Technology for Microwave Applications III, S. Yao, ed., Proc. Soc. Photo-Opt. Instrum. Eng.789, 39–47 (1987).

Huignard, J. P.

P. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

J. P. Huignard, J. P. Herriau, “Frequency shifters for photorefractive crystals,” Appl. Opt. 24, 4285–4286 (1985).
[CrossRef] [PubMed]

H. Rajbenbach, J. P. Huignard, B. Loiseaux, “Spatial frequency dependence of the energy transfer in two-wave mixing experiments in BSO crystals,” Opt. Commun. 48, 247–252 (1983).
[CrossRef]

Klein, M. B.

G. C. Valley, M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704–711 (1983).

Kukhtarev, N. V.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals, I: steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Loiseaux, B.

H. Rajbenbach, J. P. Huignard, B. Loiseaux, “Spatial frequency dependence of the energy transfer in two-wave mixing experiments in BSO crystals,” Opt. Commun. 48, 247–252 (1983).
[CrossRef]

Markov, V. B.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals, I: steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Marrakchi, A.

Odulov, S. G.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals, I: steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Psaltis, D.

Y. Shi, D. Psaltis, A. Marrakchi, A. R. Tanguay, “Photorefractive incoherent-to-coherent converter,” Appl. Opt. 22, 3665–3667 (1983).
[CrossRef] [PubMed]

J. Hong, J. Yu, S. Hudson, D. Psaltis, “Photorefractive crystals as adaptive elements in acousto-optic filters,” in Optical Technology for Microwave Applications III, S. Yao, ed., Proc. Soc. Photo-Opt. Instrum. Eng.789, 39–47 (1987).

Rajbenbach, H.

P. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

H. Rajbenbach, J. P. Huignard, B. Loiseaux, “Spatial frequency dependence of the energy transfer in two-wave mixing experiments in BSO crystals,” Opt. Commun. 48, 247–252 (1983).
[CrossRef]

Refregier, P.

P. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

Shi, Y.

Solymar, L.

P. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two beam coupling in photorefractive Bi12SiO20 crystals with moving grating: 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, V. L. Vinetskii, “Holographic storage in electro-optic crystals, I: steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Tanguay, A. R.

Vachss, F.

F. Vachss, J. Hong, S. Campbell, “Photorefractive square-law converter,” Opt. Lett. 16, 1204–1206 (1991).
[CrossRef] [PubMed]

F. Vachss, L. Hesselink, “Selective enhancement of spatial harmonics of a photorefractive grating,” J. Opt. Soc. Am. B 5, 1814–1821 (1988).
[CrossRef]

F. Vachss, J. Hong, P. Yeh, “Temporal integration using the photorefractive square-law converter,” in Optical and Digital Gallium Arsenside Technologies for Signal Processing Applications, M. P. Bendett, D. H. Butler, A. Prabhakar, A. Yang, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1291, 68–74 (1990).

Valley, G. C.

G. C. Valley, “Short pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
[CrossRef]

G. C. Valley, M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704–711 (1983).

Vinetskii, V. L.

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals, I: steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

Yeh, P.

F. Vachss, J. Hong, P. Yeh, “Temporal integration using the photorefractive square-law converter,” in Optical and Digital Gallium Arsenside Technologies for Signal Processing Applications, M. P. Bendett, D. H. Butler, A. Prabhakar, A. Yang, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1291, 68–74 (1990).

Yu, J.

J. Hong, J. Yu, S. Hudson, D. Psaltis, “Photorefractive crystals as adaptive elements in acousto-optic filters,” in Optical Technology for Microwave Applications III, S. Yao, ed., Proc. Soc. Photo-Opt. Instrum. Eng.789, 39–47 (1987).

Appl. Opt. (2)

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, V. L. Vinetskii, “Holographic storage in electro-optic crystals, I: steady state,” Ferroelectrics 22, 949–960 (1979).
[CrossRef]

IEEE J. Quantum Electron. (1)

G. C. Valley, “Short pulse grating formation in photorefractive materials,” IEEE J. Quantum Electron. QE-19, 1637–1645 (1983).
[CrossRef]

J. Appl. Phys. (1)

P. Refregier, L. Solymar, H. Rajbenbach, J. P. Huignard, “Two beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
[CrossRef]

J. Opt. Soc. Am. B (1)

Opt. Commun. (1)

H. Rajbenbach, J. P. Huignard, B. Loiseaux, “Spatial frequency dependence of the energy transfer in two-wave mixing experiments in BSO crystals,” Opt. Commun. 48, 247–252 (1983).
[CrossRef]

Opt. Eng. (1)

G. C. Valley, M. B. Klein, “Optimal properties of photorefractive materials for optical data processing,” Opt. Eng. 22, 704–711 (1983).

Opt. Lett. (1)

Other (2)

F. Vachss, J. Hong, P. Yeh, “Temporal integration using the photorefractive square-law converter,” in Optical and Digital Gallium Arsenside Technologies for Signal Processing Applications, M. P. Bendett, D. H. Butler, A. Prabhakar, A. Yang, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1291, 68–74 (1990).

J. Hong, J. Yu, S. Hudson, D. Psaltis, “Photorefractive crystals as adaptive elements in acousto-optic filters,” in Optical Technology for Microwave Applications III, S. Yao, ed., Proc. Soc. Photo-Opt. Instrum. Eng.789, 39–47 (1987).

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Figures (4)

Fig. 1
Fig. 1

(a) Basic configuration of the PICOC. Coherent writing with incoherent erasure is used. (b) Basic configuration of the photorefractive square-law converter. Direct incoherent writing is used. f, Focal length.

Fig. 2
Fig. 2

Moving grating technique applied to the square-law converter. Note that the input is imaged at a fixed location in the crystal while the grating moves.

Fig. 3
Fig. 3

Experimental apparatus.

Fig. 4
Fig. 4

(a) Temporal response with a stationary grating. Note the pronounced overshoot. (b) Temporal response with optimal grating velocity. Note the monotonic response and the change in vertical scale from that in (a).

Equations (7)

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

I ( x , t ) = I 0 [ 1 + m ( t ) cos ( k G x ) ]
A ( t ) - ( t ) m ( t ) exp [ ( t - t ) / τ ] d t ,
( 1 - i μ k G E A t R ) d E s c / d t + [ ( E q - i E A ) / ( E q t di ) ] E s c = E A m ( t ) / ( 2 t di ) ,
I ( x , t ) = I 0 { 1 + m ( t ) cos [ k G ( x - v t ) ] }
( 1 - i μ k G E A t R ) d E s c / d t + [ ( E q - i E A ) / ( E q t di ) + i v k G ( 1 - i μ k G E A t R ) ] E s c = E A m ( t ) / ( 2 t di ) .
v k G = ( E A / t di ) [ ( 1 / E q ) - μ k G t R ] / [ 1 + ( μ k G E A t R ) 2 ]
v k G = - ( t di μ k G E A t R ) - 1 ,

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