Abstract

We show that when a dynamic hologram is read out by illumination at the Bragg nulls of a previously recorded grating the diffracted beam inside the medium can result in the recording of two secondary gratings that alter the final selectivity curve. This is confirmed experimentally. This effect can cause cross talk in hologram multiplexing that is stronger than interpage cross talk when a small number of holograms with high diffraction efficiencies are multiplexed.

© 1999 Optical Society of America

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References

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  1. H.-Y. S. Li, “Photorefractive 3-D disks for optical data storage and artificial neural networks,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1993).
  2. A. M. Glass, D. von der Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
    [CrossRef]
  3. J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885–901 (1984).
    [CrossRef]
  4. S. Tao, Z. H. Song, D. R. Selviah, “Bragg-shift of holographic recording in photorefractive Fe:LiNbO3 crystals,” Opt. Commun. 108, 144–152 (1994).
    [CrossRef]
  5. C. Gu, J. Hong, “Noise gratings formed during the multiple exposure schedule in photorefractive media,” Opt. Commun. 93, 213–218 (1992).
    [CrossRef]
  6. W. J. Burke, P. Sheng, “Crosstalk noise from multiple thick-phase holograms,” J. Appl. Phys. 48, 681–685 (1977).
    [CrossRef]
  7. P. Varga, G. Kiss, “Crosstalk and loss of information in holography,” Kvant. Elektron. (Moscow) 10, 111–119 (1983).
  8. D. Psaltis, D. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1759 (1988).
    [CrossRef]

1994

S. Tao, Z. H. Song, D. R. Selviah, “Bragg-shift of holographic recording in photorefractive Fe:LiNbO3 crystals,” Opt. Commun. 108, 144–152 (1994).
[CrossRef]

1992

C. Gu, J. Hong, “Noise gratings formed during the multiple exposure schedule in photorefractive media,” Opt. Commun. 93, 213–218 (1992).
[CrossRef]

1988

1984

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885–901 (1984).
[CrossRef]

1983

P. Varga, G. Kiss, “Crosstalk and loss of information in holography,” Kvant. Elektron. (Moscow) 10, 111–119 (1983).

1977

W. J. Burke, P. Sheng, “Crosstalk noise from multiple thick-phase holograms,” J. Appl. Phys. 48, 681–685 (1977).
[CrossRef]

1974

A. M. Glass, D. von der Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

Brady, D.

Burke, W. J.

W. J. Burke, P. Sheng, “Crosstalk noise from multiple thick-phase holograms,” J. Appl. Phys. 48, 681–685 (1977).
[CrossRef]

Glass, A. M.

A. M. Glass, D. von der Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

Gu, C.

C. Gu, J. Hong, “Noise gratings formed during the multiple exposure schedule in photorefractive media,” Opt. Commun. 93, 213–218 (1992).
[CrossRef]

Heaton, J. M.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885–901 (1984).
[CrossRef]

Hong, J.

C. Gu, J. Hong, “Noise gratings formed during the multiple exposure schedule in photorefractive media,” Opt. Commun. 93, 213–218 (1992).
[CrossRef]

Kiss, G.

P. Varga, G. Kiss, “Crosstalk and loss of information in holography,” Kvant. Elektron. (Moscow) 10, 111–119 (1983).

Li, H.-Y. S.

H.-Y. S. Li, “Photorefractive 3-D disks for optical data storage and artificial neural networks,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1993).

Mills, P. A.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885–901 (1984).
[CrossRef]

Negran, T. J.

A. M. Glass, D. von der Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

Paige, E. G. S.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885–901 (1984).
[CrossRef]

Psaltis, D.

Selviah, D. R.

S. Tao, Z. H. Song, D. R. Selviah, “Bragg-shift of holographic recording in photorefractive Fe:LiNbO3 crystals,” Opt. Commun. 108, 144–152 (1994).
[CrossRef]

Sheng, P.

W. J. Burke, P. Sheng, “Crosstalk noise from multiple thick-phase holograms,” J. Appl. Phys. 48, 681–685 (1977).
[CrossRef]

Solymar, L.

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885–901 (1984).
[CrossRef]

Song, Z. H.

S. Tao, Z. H. Song, D. R. Selviah, “Bragg-shift of holographic recording in photorefractive Fe:LiNbO3 crystals,” Opt. Commun. 108, 144–152 (1994).
[CrossRef]

Tao, S.

S. Tao, Z. H. Song, D. R. Selviah, “Bragg-shift of holographic recording in photorefractive Fe:LiNbO3 crystals,” Opt. Commun. 108, 144–152 (1994).
[CrossRef]

Varga, P.

P. Varga, G. Kiss, “Crosstalk and loss of information in holography,” Kvant. Elektron. (Moscow) 10, 111–119 (1983).

von der Linde, D.

A. M. Glass, D. von der Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

Wagner, K.

Appl. Opt.

Appl. Phys. Lett.

A. M. Glass, D. von der Linde, T. J. Negran, “High-voltage bulk photovoltaic effect and photorefractive process in LiNbO3,” Appl. Phys. Lett. 25, 233–235 (1974).
[CrossRef]

J. Appl. Phys.

W. J. Burke, P. Sheng, “Crosstalk noise from multiple thick-phase holograms,” J. Appl. Phys. 48, 681–685 (1977).
[CrossRef]

Kvant. Elektron. (Moscow)

P. Varga, G. Kiss, “Crosstalk and loss of information in holography,” Kvant. Elektron. (Moscow) 10, 111–119 (1983).

Opt. Acta

J. M. Heaton, P. A. Mills, E. G. S. Paige, L. Solymar, “Diffraction efficiency and angular selectivity of volume phase holograms recorded in photorefractive materials,” Opt. Acta 31, 885–901 (1984).
[CrossRef]

Opt. Commun.

S. Tao, Z. H. Song, D. R. Selviah, “Bragg-shift of holographic recording in photorefractive Fe:LiNbO3 crystals,” Opt. Commun. 108, 144–152 (1994).
[CrossRef]

C. Gu, J. Hong, “Noise gratings formed during the multiple exposure schedule in photorefractive media,” Opt. Commun. 93, 213–218 (1992).
[CrossRef]

Other

H.-Y. S. Li, “Photorefractive 3-D disks for optical data storage and artificial neural networks,” Ph.D. dissertation (California Institute of Technology, Pasadena, Calif., 1993).

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Figures (9)

Fig. 1
Fig. 1

Geometry of a typical grating recorded in a photorefractive crystal in a symmetric transmission geometry. The c axis of the crystal is parallel to the x axis.

Fig. 2
Fig. 2

Readout of the original and the secondary gratings. k i and k d represent the wave vectors of the incident and the diffracted beams, respectively. K g and K gs are the original and the secondary grating vectors, respectively. The Bragg mismatch for the original and the secondary gratings are shown by Δk zo and Δk zs , respectively. The mismatch is nonzero only in the z direction, since we assumed infinite dimensions in the other directions for the grating. It is clear from this figure that the Bragg-matched angles for these two gratings are different.

Fig. 3
Fig. 3

Variation of the normalized diffracted field amplitude with the position inside the grating medium for the Bragg-matched and the first two null exposures. The curves are normalized to the Bragg-matched diffracted beam amplitude and not to the input beam amplitude.

Fig. 4
Fig. 4

Normalized theoretical selectivity curves for the grating: (a) after exposures at the first right null, (b) after exposures at the second nulls for both right- and left-hand sides. The selectivity curve of the original grating (before exposure) is also shown for comparison. All curves are normalized to have the same maximum value as that of the original grating. The reference for 0° is the Bragg-matched angle.

Fig. 5
Fig. 5

Normalized theoretical and experimental selectivity curves for the grating after 50 min of exposure at one of its Bragg nulls for (a) the first three right nulls and (b) the first three left nulls. The original grating was recorded to 10% diffraction efficiency. Solid curves represent theoretical fits. All curves are normalized to have the same maximum value and position as that of the original grating. The reference for 0° is the Bragg-matched angle.

Fig. 6
Fig. 6

Recording curves for the secondary gratings recorded by reading of the original grating at its first two left nulls.

Fig. 7
Fig. 7

Strength of the secondary gratings for the first three right nulls. Curve, 1/n fit as theoretically expected.

Fig. 8
Fig. 8

Typical 4-f system for multiplexing holograms with angle-multiplexed 90° geometry.

Fig. 9
Fig. 9

Comparison of secondary and interpage cross talk. Theoretical NSR when M = 101 holograms are recorded with the system of Fig. 8. (a) NSR for different holograms. (b) NSR versus location in the output plane for hologram number 76.

Equations (5)

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Δ=Δ0 expjKgxrectz-L/2L,
Edx, z=αAijexpjkd·r×exp-jΔkzz/2sinΔkzz/2ΔkzL/2,
Edp=αAijexpjkdp·rexp-j pπL z sinpπ/LZpπ=αAi2pπexpjkdp·rexp-j 2pπL z-1,
I=|Edp+Ei|2Ii1+αpπcosKgx-cosKgx+2pπL z,
Ed1+βpsincΔkzL2π+-1pβp×sincΔkzL2π-pexpjkd·r,

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