Abstract

Recently holographic memory with lensless phase-conjugate holograms has attracted much attention because it opens up the possibility of compact holographic memories. We investigate cross-talk noise in compact holographic memories with angular multiplexing. It turns out that the optimum angular separation is the same as that for the Fourier plane hologram in the leading order and that the noise-to-signal ratio is independent of the positions in the output plane, similar to the case of the image plane hologram.

© 2000 Optical Society of America

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References

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  1. P. J. van Heerden, “Theory of optical information storage in solids,” Appl. Opt. 2, 393–400 (1963).
    [CrossRef]
  2. W. J. Burke, P. Sheng, “Crosstalk noise from multiple thick-phase holograms,” J. Appl. Phys. 48, 681–685 (1977).
    [CrossRef]
  3. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  4. C. Gu, J. Hong, I. McMichael, R. Saxena, F. Mok, “Cross-talk limited storage capacity of volume holographic memory,” J. Opt. Soc. Am. A 9, 1978–1983 (1992).
    [CrossRef]
  5. A. Yariv, “Interpage and interpixel cross talk in orthogonal (wavelength-multiplexed) holograms,” Opt. Lett. 18, 652–654 (1993).
    [CrossRef]
  6. K. Curtis, C. Gu, D. Psaltis, “Cross talk in wavelength-multiplexed holographic memories,” Opt. Lett. 18, 1001–1003 (1993).
    [CrossRef] [PubMed]
  7. K. Curtis, D. Psaltis, “Cross talk in phase-coded holographic memories,” J. Opt. Soc. Am. A 10, 2547–2550 (1993).
    [CrossRef]
  8. K. Curtis, D. Psaltis, “Cross talk for angle- and wavelength-multiplexed image plane holograms,” Opt. Lett. 19, 1774–1776 (1994).
    [CrossRef] [PubMed]
  9. X. Yi, S. Campbell, P. Yeh, C. Gu, “Statistical analysis of cross-talk noise and storage capacity in volume holographic memory: image plane holograms,” Opt. Lett. 20, 779–781 (1995).
    [CrossRef] [PubMed]
  10. X. Yi, P. Yeh, C. Gu, “Cross-talk noise in volume holographic memory with spherical reference beams,” Opt. Lett. 20, 1812–1814 (1995).
    [CrossRef] [PubMed]
  11. M. C. Bashaw, J. F. Heanue, A. Aharoni, J. F. Walkup, L. Hesselink, “Cross-talk considerations for angular and phase-encoded multiplexing in volume holography,” J. Opt. Soc. Am. B 11, 1820–1836 (1994).
    [CrossRef]
  12. H.-S. Lee, Y. H. Kim, D. K. Han, B. Lee, “Cross-talk noise analysis in hologram memory with hybrid multiplexing of the Hadamard phase code and wavelength,” J. Opt. Soc. Am. A 16, 563–567 (1999).
    [CrossRef]
  13. C. Gu, F. Dai, “Cross-talk noise reduction in volume holographic storage with an extended recording reference,” Opt. Lett. 20, 2336–2338 (1995).
    [CrossRef] [PubMed]
  14. M. Neifeld, M. McDonald, “Technique for controlling cross-talk noise in volume holography,” Opt. Lett. 21, 1298–1300 (1996).
    [CrossRef] [PubMed]
  15. F. Dai, C. Gu, “Effect of Gaussian references on cross-talk noise reduction in volume holographic memory,” Opt. Lett. 22, 1802–1804 (1997).
    [CrossRef]
  16. F. Zhao, K. Sayano, “Compact read-only memory with lensless phase-conjugate holograms,” Opt. Lett. 21, 1295–1297 (1996).
    [CrossRef] [PubMed]
  17. J. J. P. Drolet, E. Chuang, G. Barbastathis, D. Psaltis, “Compact, integrated dynamic holographic memory with refreshed holograms,” Opt. Lett. 22, 552–554 (1997).
    [CrossRef] [PubMed]
  18. J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), pp. 63–89.
  19. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 427–432.

1999 (1)

1997 (2)

1996 (2)

1995 (3)

1994 (2)

1993 (3)

1992 (1)

1977 (1)

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

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

1963 (1)

Aharoni, A.

Barbastathis, G.

Bashaw, M. C.

Burke, W. J.

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

Campbell, S.

Chuang, E.

Curtis, K.

Dai, F.

Drolet, J. J. P.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), pp. 63–89.

Gu, C.

Han, D. K.

Heanue, J. F.

Hesselink, L.

Hong, J.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 427–432.

Kim, Y. H.

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Lee, B.

Lee, H.-S.

McDonald, M.

McMichael, I.

Mok, F.

Neifeld, M.

Psaltis, D.

Saxena, R.

Sayano, K.

Sheng, P.

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

van Heerden, P. J.

Walkup, J. F.

Yariv, A.

Yeh, P.

Yi, X.

Zhao, F.

Appl. Opt. (1)

Bell Syst. Tech. J. (1)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Syst. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

J. Appl. Phys. (1)

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

J. Opt. Soc. Am. A (3)

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

Opt. Lett. (10)

X. Yi, S. Campbell, P. Yeh, C. Gu, “Statistical analysis of cross-talk noise and storage capacity in volume holographic memory: image plane holograms,” Opt. Lett. 20, 779–781 (1995).
[CrossRef] [PubMed]

A. Yariv, “Interpage and interpixel cross talk in orthogonal (wavelength-multiplexed) holograms,” Opt. Lett. 18, 652–654 (1993).
[CrossRef]

K. Curtis, C. Gu, D. Psaltis, “Cross talk in wavelength-multiplexed holographic memories,” Opt. Lett. 18, 1001–1003 (1993).
[CrossRef] [PubMed]

K. Curtis, D. Psaltis, “Cross talk for angle- and wavelength-multiplexed image plane holograms,” Opt. Lett. 19, 1774–1776 (1994).
[CrossRef] [PubMed]

X. Yi, P. Yeh, C. Gu, “Cross-talk noise in volume holographic memory with spherical reference beams,” Opt. Lett. 20, 1812–1814 (1995).
[CrossRef] [PubMed]

C. Gu, F. Dai, “Cross-talk noise reduction in volume holographic storage with an extended recording reference,” Opt. Lett. 20, 2336–2338 (1995).
[CrossRef] [PubMed]

J. J. P. Drolet, E. Chuang, G. Barbastathis, D. Psaltis, “Compact, integrated dynamic holographic memory with refreshed holograms,” Opt. Lett. 22, 552–554 (1997).
[CrossRef] [PubMed]

F. Dai, C. Gu, “Effect of Gaussian references on cross-talk noise reduction in volume holographic memory,” Opt. Lett. 22, 1802–1804 (1997).
[CrossRef]

F. Zhao, K. Sayano, “Compact read-only memory with lensless phase-conjugate holograms,” Opt. Lett. 21, 1295–1297 (1996).
[CrossRef] [PubMed]

M. Neifeld, M. McDonald, “Technique for controlling cross-talk noise in volume holography,” Opt. Lett. 21, 1298–1300 (1996).
[CrossRef] [PubMed]

Other (2)

J. W. Goodman, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, New York, 1996), pp. 63–89.

J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 427–432.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of an angle-multiplexed compact holographic memory.

Fig. 2
Fig. 2

Selectivity curve.

Fig. 3
Fig. 3

NSR versus reading point i when M=1000.

Fig. 4
Fig. 4

Worst NSR versus M.

Fig. 5
Fig. 5

NSR versus reading point i when M=1000 and y0/F=1/10 in the case of Fourier plane holograms.

Fig. 6
Fig. 6

Worst NSR versus M when y0/F=1/10 in the case of Fourier plane holograms.

Equations (21)

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Sm(x, y, z)=exp[ik(l+z)]iλ(l+z)expi k2(l+z) (x2+y2)×dx0dy0fm(x0, y0)×exp-i k(l+z) (xx0+yy0)×expi k2(l+z) (x02+y02),
Rm(x, y, z)=exp[i(kmxx+kmyy+kmzz)],
kmx=-k xmf=0,
kmy=-k ymfcos θ-k1-12ymf2sin θ,
kmz=-k ymfsin θ+k1-12ymf2cos θ,
Δm=-MM(SmRm*+Sm*Rm),
Ei(x0, y0)dxdydz exp[ik(l+z)]iλ(l+z)
×expi k2(l+z) (x02+y02)Ii(x, y, z)×exp-i k(l+z) (xx0+yy0)×expi k2(l+z) (x2+y2),
Ii(x, y, z)=m=-MMSm*RmRi*.
Eim=-MMdzdx0dy01[λ(l+z)]2×expik x02+y02-x02-y022(l+z)×fm*(x0, y0)exp(ikmzz)exp(-ikizz)×a sinca2kx0l+z-kx0l+z+kmx-kix×b sincb2ky0l+z-ky0l+z+kmy-kiy,
Eim=-MMdz expik x02+y02-x02-y022(l+z)×fm*(x0, y0)exp(iΔKmizz),
x0=x0,y0=y0-ΔKmiyl+zk,
k x02+y02-x02-y022(l+z)+ΔKmizz
=y0ΔKmiy-l2k ΔKmiy2
+ΔKmiz-12k ΔKmiy2z.
noise=mit2sinc2t2 (ΔKmiz-12k ΔKmiy2),
NSR=misinc2t2 (ΔKmiz-12k ΔKmiy2).
NSR=misinc2t2ΔKmiz+ΔKmiyy0F+ΔKmiy22k,
ym=mΔ,Δ=λft sin θ.
SNR<2tfλdN,
Nmax2tfλdSNRre,

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