Abstract

A theoretical analysis for the optimization of the selective-erasure process in holographic photorefractive memories is presented. It is based on the solution of the standard material equations under a linear approximation (low modulation depths). Specific expressions for the optimum phase shifts and erasure rates are obtained. The approach includes all transport processes and so applies to photovoltaic materials such as LiNbO3. The different behavior with regard to nonphotovoltaic materials is discussed. Some additional strategies to improve the overall erasure process are proposed.

© 1997 Optical Society of America

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References

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  1. L. Hesselink and M. C. Bashaw, “Optical memories implemented with photorefractive media,” Opt. Quantum Electron. 25, S611–S661 (1993).
    [CrossRef]
  2. J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
    [CrossRef] [PubMed]
  3. D. Psaltis and F. Mok, “Holographic memories,” Sci. Am. 273, 52–58 (1995).
    [CrossRef]
  4. F. H. Mok, “Angle-multiplexed storage of 5000 holograms in lithium niobate,” Opt. Lett. 18, 915–917 (1993).
    [CrossRef] [PubMed]
  5. J.-P. Huignard, J. P. Herriau, and F. Micheron, “Selective erasure and processing in volume holograms superimposed in photosensitive ferroelectrics,” Ferroelectrics 11, 393–396 (1976).
    [CrossRef]
  6. H. Sasaki, J. Ma, Y. Fainman, S. H. Lee, and Y. Taketomi, “Fast update of dynamic photorefractive optical memory,” Opt. Lett. 17, 1468–1470 (1992).
    [CrossRef] [PubMed]
  7. J. H. Hong, S. Campbell, and P. Yeh, “Optical pattern classifier with perceptron learning,” Appl. Opt. 29, 3019–3025 (1990).
    [CrossRef] [PubMed]
  8. H. Sasaki, J. Ma, Y. Fainmann, S. H. Lee, and Y. Taketomi, “Dynamics of a composite grating in photorefractive crystals for memory applications,” J. Opt. Soc. Am. B 11, 2465–2470 (1994).
  9. J. V. Alvarez-Bravo and L. Arizmendi, “Coherent erasure and updating of holograms in LiNbO3,” Opt. Mater. 4, 419–422 (1995).
    [CrossRef]
  10. M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Effect of light phase-shift on photorefractive kinetics: linear regime,” Opt. Mater. 4, 304–307 (1995).
    [CrossRef]
  11. M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Effects of light phase-shift on photorefractive kinetics: computer simulations,” Opt. Mater. 4, 461–465 (1995).
    [CrossRef]
  12. M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Optimization of photorefractive recording by means of light phase-shifts,” Opt. Commun. 116, 398–404 (1995).
    [CrossRef]
  13. F. Jariego and F. Agulló-López, “Monotonic versus oscillatory behavior during holographic writing in photorefractive photovoltaic materials,” Opt. Commun. 76, 169–172 (1990).
    [CrossRef]
  14. Ph. Refregier, L. Solymar, H. R. Rajbenbach, and J.-P. Huignard, “Two-beam coupling in photorefractive Bi12SiO20 crystals with moving grating: theory and experiments,” J. Appl. Phys. 58, 45–57 (1985).
    [CrossRef]

1995 (5)

D. Psaltis and F. Mok, “Holographic memories,” Sci. Am. 273, 52–58 (1995).
[CrossRef]

J. V. Alvarez-Bravo and L. Arizmendi, “Coherent erasure and updating of holograms in LiNbO3,” Opt. Mater. 4, 419–422 (1995).
[CrossRef]

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Effect of light phase-shift on photorefractive kinetics: linear regime,” Opt. Mater. 4, 304–307 (1995).
[CrossRef]

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Effects of light phase-shift on photorefractive kinetics: computer simulations,” Opt. Mater. 4, 461–465 (1995).
[CrossRef]

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Optimization of photorefractive recording by means of light phase-shifts,” Opt. Commun. 116, 398–404 (1995).
[CrossRef]

1994 (2)

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

H. Sasaki, J. Ma, Y. Fainmann, S. H. Lee, and Y. Taketomi, “Dynamics of a composite grating in photorefractive crystals for memory applications,” J. Opt. Soc. Am. B 11, 2465–2470 (1994).

1993 (2)

L. Hesselink and M. C. Bashaw, “Optical memories implemented with photorefractive media,” Opt. Quantum Electron. 25, S611–S661 (1993).
[CrossRef]

F. H. Mok, “Angle-multiplexed storage of 5000 holograms in lithium niobate,” Opt. Lett. 18, 915–917 (1993).
[CrossRef] [PubMed]

1992 (1)

1990 (2)

J. H. Hong, S. Campbell, and P. Yeh, “Optical pattern classifier with perceptron learning,” Appl. Opt. 29, 3019–3025 (1990).
[CrossRef] [PubMed]

F. Jariego and F. Agulló-López, “Monotonic versus oscillatory behavior during holographic writing in photorefractive photovoltaic materials,” Opt. Commun. 76, 169–172 (1990).
[CrossRef]

1985 (1)

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

1976 (1)

J.-P. Huignard, J. P. Herriau, and F. Micheron, “Selective erasure and processing in volume holograms superimposed in photosensitive ferroelectrics,” Ferroelectrics 11, 393–396 (1976).
[CrossRef]

Aguilar, M.

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Effect of light phase-shift on photorefractive kinetics: linear regime,” Opt. Mater. 4, 304–307 (1995).
[CrossRef]

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Effects of light phase-shift on photorefractive kinetics: computer simulations,” Opt. Mater. 4, 461–465 (1995).
[CrossRef]

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Optimization of photorefractive recording by means of light phase-shifts,” Opt. Commun. 116, 398–404 (1995).
[CrossRef]

Agulló-López, F.

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Optimization of photorefractive recording by means of light phase-shifts,” Opt. Commun. 116, 398–404 (1995).
[CrossRef]

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Effect of light phase-shift on photorefractive kinetics: linear regime,” Opt. Mater. 4, 304–307 (1995).
[CrossRef]

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Effects of light phase-shift on photorefractive kinetics: computer simulations,” Opt. Mater. 4, 461–465 (1995).
[CrossRef]

F. Jariego and F. Agulló-López, “Monotonic versus oscillatory behavior during holographic writing in photorefractive photovoltaic materials,” Opt. Commun. 76, 169–172 (1990).
[CrossRef]

Alvarez-Bravo, J. V.

J. V. Alvarez-Bravo and L. Arizmendi, “Coherent erasure and updating of holograms in LiNbO3,” Opt. Mater. 4, 419–422 (1995).
[CrossRef]

Arizmendi, L.

J. V. Alvarez-Bravo and L. Arizmendi, “Coherent erasure and updating of holograms in LiNbO3,” Opt. Mater. 4, 419–422 (1995).
[CrossRef]

Bashaw, M. C.

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

L. Hesselink and M. C. Bashaw, “Optical memories implemented with photorefractive media,” Opt. Quantum Electron. 25, S611–S661 (1993).
[CrossRef]

Campbell, S.

Carrascosa, M.

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Optimization of photorefractive recording by means of light phase-shifts,” Opt. Commun. 116, 398–404 (1995).
[CrossRef]

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Effects of light phase-shift on photorefractive kinetics: computer simulations,” Opt. Mater. 4, 461–465 (1995).
[CrossRef]

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Effect of light phase-shift on photorefractive kinetics: linear regime,” Opt. Mater. 4, 304–307 (1995).
[CrossRef]

Fainman, Y.

Fainmann, Y.

H. Sasaki, J. Ma, Y. Fainmann, S. H. Lee, and Y. Taketomi, “Dynamics of a composite grating in photorefractive crystals for memory applications,” J. Opt. Soc. Am. B 11, 2465–2470 (1994).

Heanue, J. F.

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

Herriau, J. P.

J.-P. Huignard, J. P. Herriau, and F. Micheron, “Selective erasure and processing in volume holograms superimposed in photosensitive ferroelectrics,” Ferroelectrics 11, 393–396 (1976).
[CrossRef]

Hesselink, L.

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

L. Hesselink and M. C. Bashaw, “Optical memories implemented with photorefractive media,” Opt. Quantum Electron. 25, S611–S661 (1993).
[CrossRef]

Hong, J. H.

Huignard, J.-P.

Ph. Refregier, L. Solymar, H. R. Rajbenbach, and 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, and F. Micheron, “Selective erasure and processing in volume holograms superimposed in photosensitive ferroelectrics,” Ferroelectrics 11, 393–396 (1976).
[CrossRef]

Jariego, F.

F. Jariego and F. Agulló-López, “Monotonic versus oscillatory behavior during holographic writing in photorefractive photovoltaic materials,” Opt. Commun. 76, 169–172 (1990).
[CrossRef]

Lee, S. H.

H. Sasaki, J. Ma, Y. Fainmann, S. H. Lee, and Y. Taketomi, “Dynamics of a composite grating in photorefractive crystals for memory applications,” J. Opt. Soc. Am. B 11, 2465–2470 (1994).

H. Sasaki, J. Ma, Y. Fainman, S. H. Lee, and Y. Taketomi, “Fast update of dynamic photorefractive optical memory,” Opt. Lett. 17, 1468–1470 (1992).
[CrossRef] [PubMed]

López, V.

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Optimization of photorefractive recording by means of light phase-shifts,” Opt. Commun. 116, 398–404 (1995).
[CrossRef]

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Effect of light phase-shift on photorefractive kinetics: linear regime,” Opt. Mater. 4, 304–307 (1995).
[CrossRef]

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Effects of light phase-shift on photorefractive kinetics: computer simulations,” Opt. Mater. 4, 461–465 (1995).
[CrossRef]

Ma, J.

H. Sasaki, J. Ma, Y. Fainmann, S. H. Lee, and Y. Taketomi, “Dynamics of a composite grating in photorefractive crystals for memory applications,” J. Opt. Soc. Am. B 11, 2465–2470 (1994).

H. Sasaki, J. Ma, Y. Fainman, S. H. Lee, and Y. Taketomi, “Fast update of dynamic photorefractive optical memory,” Opt. Lett. 17, 1468–1470 (1992).
[CrossRef] [PubMed]

Micheron, F.

J.-P. Huignard, J. P. Herriau, and F. Micheron, “Selective erasure and processing in volume holograms superimposed in photosensitive ferroelectrics,” Ferroelectrics 11, 393–396 (1976).
[CrossRef]

Mok, F.

D. Psaltis and F. Mok, “Holographic memories,” Sci. Am. 273, 52–58 (1995).
[CrossRef]

Mok, F. H.

Psaltis, D.

D. Psaltis and F. Mok, “Holographic memories,” Sci. Am. 273, 52–58 (1995).
[CrossRef]

Rajbenbach, H. R.

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

Refregier, Ph.

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

Sasaki, H.

H. Sasaki, J. Ma, Y. Fainmann, S. H. Lee, and Y. Taketomi, “Dynamics of a composite grating in photorefractive crystals for memory applications,” J. Opt. Soc. Am. B 11, 2465–2470 (1994).

H. Sasaki, J. Ma, Y. Fainman, S. H. Lee, and Y. Taketomi, “Fast update of dynamic photorefractive optical memory,” Opt. Lett. 17, 1468–1470 (1992).
[CrossRef] [PubMed]

Serrano, E.

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Effect of light phase-shift on photorefractive kinetics: linear regime,” Opt. Mater. 4, 304–307 (1995).
[CrossRef]

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Optimization of photorefractive recording by means of light phase-shifts,” Opt. Commun. 116, 398–404 (1995).
[CrossRef]

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Effects of light phase-shift on photorefractive kinetics: computer simulations,” Opt. Mater. 4, 461–465 (1995).
[CrossRef]

Solymar, L.

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

Taketomi, Y.

H. Sasaki, J. Ma, Y. Fainmann, S. H. Lee, and Y. Taketomi, “Dynamics of a composite grating in photorefractive crystals for memory applications,” J. Opt. Soc. Am. B 11, 2465–2470 (1994).

H. Sasaki, J. Ma, Y. Fainman, S. H. Lee, and Y. Taketomi, “Fast update of dynamic photorefractive optical memory,” Opt. Lett. 17, 1468–1470 (1992).
[CrossRef] [PubMed]

Yeh, P.

Appl. Opt. (1)

Ferroelectrics (1)

J.-P. Huignard, J. P. Herriau, and F. Micheron, “Selective erasure and processing in volume holograms superimposed in photosensitive ferroelectrics,” Ferroelectrics 11, 393–396 (1976).
[CrossRef]

J. Appl. Phys. (1)

Ph. Refregier, L. Solymar, H. R. Rajbenbach, and 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)

H. Sasaki, J. Ma, Y. Fainmann, S. H. Lee, and Y. Taketomi, “Dynamics of a composite grating in photorefractive crystals for memory applications,” J. Opt. Soc. Am. B 11, 2465–2470 (1994).

Opt. Commun. (2)

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Optimization of photorefractive recording by means of light phase-shifts,” Opt. Commun. 116, 398–404 (1995).
[CrossRef]

F. Jariego and F. Agulló-López, “Monotonic versus oscillatory behavior during holographic writing in photorefractive photovoltaic materials,” Opt. Commun. 76, 169–172 (1990).
[CrossRef]

Opt. Lett. (2)

Opt. Mater. (3)

J. V. Alvarez-Bravo and L. Arizmendi, “Coherent erasure and updating of holograms in LiNbO3,” Opt. Mater. 4, 419–422 (1995).
[CrossRef]

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Effect of light phase-shift on photorefractive kinetics: linear regime,” Opt. Mater. 4, 304–307 (1995).
[CrossRef]

M. Aguilar, E. Serrano, V. López, M. Carrascosa, and F. Agulló-López, “Effects of light phase-shift on photorefractive kinetics: computer simulations,” Opt. Mater. 4, 461–465 (1995).
[CrossRef]

Opt. Quantum Electron. (1)

L. Hesselink and M. C. Bashaw, “Optical memories implemented with photorefractive media,” Opt. Quantum Electron. 25, S611–S661 (1993).
[CrossRef]

Sci. Am. (1)

D. Psaltis and F. Mok, “Holographic memories,” Sci. Am. 273, 52–58 (1995).
[CrossRef]

Science (1)

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

Time evolution of the two terms of Eq. (4) for a BSO crystal with an applied field of 5 kV/cm. The dotted–dashed curve is the amplitude of the decay term; the dashed curve is the amplitude of the growth term. The solid curve represents the amplitude of the total solution.

Fig. 2
Fig. 2

Phase mismatch of the different gratings with regard to the shifted light intensity pattern used for selective erasure. The initial light pattern (dashed curves) is shifted δm (solid curves). Grating I (dotted–dashed curve) has a phase shift Φ with regard to the initial light pattern and a phase shift Φ+δm with regard to the shifted light pattern. Grating II (dashed curve) starts growing with a phase shift Φin with regard to the shifted light pattern.

Fig. 3
Fig. 3

Optimum erasure phase shift as a function of the previous recording time for BSO with an applied field E0=5 kV/cm and Λ=10 µm.

Fig. 4
Fig. 4

Time evolution after the optimum erasure phase shift of the amplitude of the space-charge field normalized by its saturation value for BSO for different values of the external field: E0=0 kV/cm (solid curves), E0=5 kV/cm (dashed curves), E0=10 kV/cm (dotted curves) for (a) Λ=10 µm and (b) Λ=1 µm.

Fig. 5
Fig. 5

Time evolution after the optimum erasure phase shift of the amplitude of the space-charge field normalized by its saturation value for LiNbO3 for (a) an oxidized sample and (b) a reduced sample. The incoherent erasure (dashed curves) is also shown for comparison.

Fig. 6
Fig. 6

Time evolution after the optimum erasure phase shift of the amplitude of the space-charge field normalized by Es1 with a change in the modulation depth m2=10 m1 (solid curve) and without change (dashed curve). The dotted curve represents the incoherent erasure. A BSO crystal with E0=5 kV/cm and Λ =10 µm was considered.

Fig. 7
Fig. 7

Time evolution after the optimum erasure phase shift of the normalized amplitude of the space-charge field with moving fringes (solid curve) and without moving fringes (dashed curve). The dotted curve represents the incoherent erasure. A BSO crystal with E0=5 kV/cm and Λ=10 µm was considered.

Equations (20)

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

E˜t+g˜E˜=mh˜,
g˜=1D˜τ1+EDEq+iE0Eq+EphEqNrND,
h˜=1D˜τ-E0-Eph+iED,
D˜=1+ED+iE0EM,
ED=KBTeK,EM=γNAμK,Eq=eNr0K,
Eph=-LphγNAμ,τ=0eμn0,n0=sI0NDγNA.
E˜(t)=E˜ exp(iδ)exp(-g˜t)+E˜s[1-exp(-g˜t)],
Ett=0=Remh˜ exp-iΦ+δ-g˜E˜0=mhr cosΦ+δ+hi sinΦ+δ-grE0,
Ett=0=-mh-grE,
δm+Φ=Φin+π,
EtselectiveEtincoherent=mh+grEgrE
v=Φ/t=-gi.
δmπ,
EtselectiveEtincoherent=1+1grt,
δm=Φin-Φs+π=arg g˜+π.
Et=mh+grEs=Esgr1+1cos Φg,
E˜t+gE˜=m2h˜.
E˜(t)=E˜s1 exp(iδ)exp(-g˜t)+E˜s2[1-exp(-g˜t)],
E˜t+g˜E˜=mh˜ exp(iat),
E˜(t)=E˜s exp(iδ)exp[-(g˜+ia)t]+E˜s g˜g˜+ia×exp(iat)[1-exp(-g˜t)].

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