Abstract

The cross-talk noise in hologram memory is analyzed with hybrid multiplexing of the Hadamard phase code and wavelength. The minimum wavelength differences required for obtaining a given signal-to-noise ratio are calculated, as well as the optimum angle between the signal and reference beams for this hybrid multiplexing scheme. Hybrid multiplexing with sufficient wavelength difference is a good method for memory extension in the case of limited-pixel-number spatial light modulators.

© 1999 Optical Society of America

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References

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  1. K. Curtis, D. Psaltis, “Cross talk in phase-coded holographic memories,” J. Opt. Soc. Am. A 10, 2547–2550 (1993).
    [CrossRef]
  2. K. Curtis, C. Gu, D. Psaltis, “Cross talk in wavelength-multiplexed holographic memories,” Opt. Lett. 18, 1001–1003 (1993).
    [CrossRef] [PubMed]
  3. M. C. Bashaw, R. C. Singer, J. F. Heanue, L. Hesselink, “Coded-wavelength multiplex volume holography,” Opt. Lett. 20, 1916–1918 (1995).
    [CrossRef] [PubMed]
  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. 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]

1995

1994

1993

1992

Aharoni, A.

Bashaw, M. C.

Curtis, K.

Gu, C.

Heanue, J. F.

Hesselink, L.

Hong, J.

McMichael, I.

Mok, F.

Psaltis, D.

Saxena, R.

Singer, R. C.

Walkup, J. F.

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Figures (4)

Fig. 1
Fig. 1

Schematic diagram of the hybrid hologram memory system that uses a PRC.

Fig. 2
Fig. 2

Worst SNR versus hologram designation number for various kinds of multiplexing. Circles, 32 phase codes with one wavelength; diamonds, four phase codes with ten wavelengths; triangles, one phase code with thirty wavelengths; Δλ =0.5 nm, θ=π/2. (a) Different values of pixel-to-pixel spacing Δy are used for different wavelengths to minimize the cross talk for each recording wavelength. (b) A fixed value of 15 µm is taken as Δy, which is the optimum value for the recording wavelength λ0=500 nm. dB, decibels.

Fig. 3
Fig. 3

SNR for θ and Δλ variation in the hybrid scheme (four phase codes with ten wavelengths, Δy=15 µm). dB, decibels.

Fig. 4
Fig. 4

SNR for Δy and Δλ variation in the hybrid scheme (four phase codes with ten wavelengths, θ=π/2). dB, decibels.

Equations (10)

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Rl,m=i=1NPil,m exp(jkil·r),
Pil,m=exp(jϕil,m),
NSR=1N2llmjiPjl,m(Pil,m)*×sinct2π(ΔKijll)z+λlλlF(ΔKijll)yy2+λl(ΔKijll)y24π+2π1λl-1λl+πF2λlλl2-1λly222+mjij×Pjl,m(Pil,m)*sinct2π(ΔKijll)z+(ΔKijll)yy2F+λl(ΔKijll)y24π2,
Sl,m=expj 2πzλldx0dy0fl,m(x0, y0)×exp-j 2πλlF(xx0+yy0)×exp-j πzλlF2(x02+y02),
Δl,mRl,m*Sl,m+c.c.,
E(r)k024πexp(ikr)rjdrPjl,m×exp(-iK·r)Δ(r),
kdl=2πλlx2F, 2πλly2F, 2πλl1-x222F2-y222F2.
x0=-λlλlx2-Fλl2π(kixl-kjxl),
y0=-λlλly2-Fλl2π(kiyl-kjyl).
El,mijPjl,m(Pil,m)*×fl,m-λlλlx2-Fλl2π(kixl-kjxl),-λlλly2-Fλl2π(kiyl-kjyl)t sinct2π(kizl-kjzl)+λlλlF[(kixl-kjxl)x2+(kiyl-kjyl)y2]+λl4π[(kixl-kjxl)2+(kiyl-kjyl)2]+2π1λl-1λl+πF2λlλl2-1λl(x22+y22).

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