Abstract

We analyze cross talk in resonant holographic memories and derive the conditions under which resonance improves storage quality. We also carry out the analysis for both plane-wave and apodized Gaussian reference beams.

© 2004 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  7. W. Liu, D. Psaltis, G. Barbastathis, “Real-time spectral imaging in three spatial dimensions,” Opt. Lett. 27, 854–856 (2002).
    [CrossRef]
  8. G. Barbastathis, D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE 87, 2098–2120 (1999).
    [CrossRef]
  9. Rayleigh, “Investigation in optics, with special reference to the spectroscope,” Philos. Mag. 8, 261–274 (1879).
    [CrossRef]
  10. H. Kogelnik, T. Li, “Laser beams and resonators,” Proc. IEEE 5, 1550–1567 (1966).
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    [CrossRef]
  12. C. Gu, F. Dai, J. Hong, “Statistics of both optical and electrical noise in digital volume holographic data storage,” Electron. Lett. 32, 1400–1402 (1996).
    [CrossRef]
  13. G. Barbastathis, M. Levene, D. Psaltis, “Shift multiplexing with spherical reference waves,” Appl. Opt. 35, 2403–2417 (1996).
    [CrossRef] [PubMed]
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    [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. H. Coufal, D. Psaltis, G. Sincerbox, eds., Holographic Data Storage (Springer, New York, 2000).
  17. K. Tian, G. Barbastathis, “Resonant holographic imaging in confocal cavites,” presented at the Conference on Lasers and Electro-Optics (CLEO) ’03, Baltimore, Maryland, June 1–6, 2003, Paper CFE2.

2002

1999

G. Barbastathis, D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE 87, 2098–2120 (1999).
[CrossRef]

L. Menez, I. Zaquine, A. Maruani, “Intracavity bragg grating,” J. Opt. Soc. Am. B 16, 1849–1855 (1999).
[CrossRef]

1997

1996

1992

1989

1988

1986

1985

1966

H. Kogelnik, T. Li, “Laser beams and resonators,” Proc. IEEE 5, 1550–1567 (1966).

1879

Rayleigh, “Investigation in optics, with special reference to the spectroscope,” Philos. Mag. 8, 261–274 (1879).
[CrossRef]

Anderson, D. Z.

Barbastathis, G.

A. Sinha, G. Barbastathis, “Resonant holography,” Opt. Lett. 27, 385–387 (2002).
[CrossRef]

W. Liu, D. Psaltis, G. Barbastathis, “Real-time spectral imaging in three spatial dimensions,” Opt. Lett. 27, 854–856 (2002).
[CrossRef]

G. Barbastathis, D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE 87, 2098–2120 (1999).
[CrossRef]

G. Barbastathis, M. Levene, D. Psaltis, “Shift multiplexing with spherical reference waves,” Appl. Opt. 35, 2403–2417 (1996).
[CrossRef] [PubMed]

K. Tian, G. Barbastathis, “Resonant holographic imaging in confocal cavites,” presented at the Conference on Lasers and Electro-Optics (CLEO) ’03, Baltimore, Maryland, June 1–6, 2003, Paper CFE2.

Brady, D. J.

G. Barbastathis, D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE 87, 2098–2120 (1999).
[CrossRef]

Caulfield, H. J.

Collins, S. A.

Dai, F.

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

C. Gu, F. Dai, J. Hong, “Statistics of both optical and electrical noise in digital volume holographic data storage,” Electron. Lett. 32, 1400–1402 (1996).
[CrossRef]

Farhat, N.

Gu, C.

Hong, J.

C. Gu, F. Dai, J. Hong, “Statistics of both optical and electrical noise in digital volume holographic data storage,” Electron. Lett. 32, 1400–1402 (1996).
[CrossRef]

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]

Kavounas, G. T.

Kogelnik, H.

H. Kogelnik, T. Li, “Laser beams and resonators,” Proc. IEEE 5, 1550–1567 (1966).

Kumar, J.

Levene, M.

Li, T.

H. Kogelnik, T. Li, “Laser beams and resonators,” Proc. IEEE 5, 1550–1567 (1966).

Liu, W.

Maruani, A.

McDonald, M.

McMichael, I.

Menez, L.

Mok, F.

Neifeld, M. A.

Psaltis, D.

Rayleigh,

Rayleigh, “Investigation in optics, with special reference to the spectroscope,” Philos. Mag. 8, 261–274 (1879).
[CrossRef]

Sahara, R. T.

Saxena, R.

Sinha, A.

Steier, W. H.

Tian, K.

K. Tian, G. Barbastathis, “Resonant holographic imaging in confocal cavites,” presented at the Conference on Lasers and Electro-Optics (CLEO) ’03, Baltimore, Maryland, June 1–6, 2003, Paper CFE2.

Zaquine, I.

Appl. Opt.

Electron. Lett.

C. Gu, F. Dai, J. Hong, “Statistics of both optical and electrical noise in digital volume holographic data storage,” Electron. Lett. 32, 1400–1402 (1996).
[CrossRef]

J. Opt. Soc. Am. A

J. Opt. Soc. Am. B

Opt. Lett.

Philos. Mag.

Rayleigh, “Investigation in optics, with special reference to the spectroscope,” Philos. Mag. 8, 261–274 (1879).
[CrossRef]

Proc. IEEE

H. Kogelnik, T. Li, “Laser beams and resonators,” Proc. IEEE 5, 1550–1567 (1966).

G. Barbastathis, D. J. Brady, “Multidimensional tomographic imaging using volume holography,” Proc. IEEE 87, 2098–2120 (1999).
[CrossRef]

Other

H. Coufal, D. Psaltis, G. Sincerbox, eds., Holographic Data Storage (Springer, New York, 2000).

K. Tian, G. Barbastathis, “Resonant holographic imaging in confocal cavites,” presented at the Conference on Lasers and Electro-Optics (CLEO) ’03, Baltimore, Maryland, June 1–6, 2003, Paper CFE2.

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Figures (8)

Fig. 1
Fig. 1

Geometry for resonant holography.

Fig. 2
Fig. 2

(a) Geometry for resonant holography with angle multiplexing, (b) geometry for resonant holography with shift multiplexing.

Fig. 3
Fig. 3

Figure of merit with plane reference. Parameters are hologram thickness L = 10   mm , wavelength λ = 488   nm , focal length F = 50   mm , and angle of incidence of the signal θ S = 20 ° .

Fig. 4
Fig. 4

Geometry for apodization with angle multiplexing.

Fig. 5
Fig. 5

Apodization with Gaussian references. Parameters are hologram thickness L = 10   mm , angle of incidence of the signal θ S = 20 ° , angle of the reference beam θ = 20 ° , wavelength λ = 488   nm , and width of the Gaussian beam w = 1.6   mm .

Fig. 6
Fig. 6

Cross-talk noise with Gaussian references. Parameters are the same as in Fig. 5. (Note that here the logarithm coordinate is used.)

Fig. 7
Fig. 7

Figure of merit with Gaussian reference. Parameters are the same as in Fig. 5. (Note that here the logarithm coordinate is used.)

Fig. 8
Fig. 8

Single-pass cross-talk noise in angle multiplexing and shift multiplexing. Parameters are hologram thickness L = 10 mm, wavelength λ = 488   nm , focal length F = 50   mm , angle of incidence of the signal θ S = 20 ° , angle of the initial reference beam θ i = 0 ° , and m i = 501 .

Equations (24)

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SNR = P S P X + P N ,
η 1 X η 1 m = 1 M sinc 2 p ( m - m ) 1 - x cos   θ   cos   θ S F   sin ( θ + θ S ) ,
η 1 X η 1 m = 1 M sinc 2 p ( m - m ) 1 - x θ S F ,
r = 1 - η 1 - b ,
l = ( 2 m + 1 )   λ 4 .
η = η 1 η 1 + b .
η fw X = η 1 X ( 1 - r 2 ) 1 + r 2 ( 1 - η 1 X - b ) 2 + 2 r ( 1 - η 1 X - b ) ,
η pc X = η fw X ( 1 - η 1 X - b ) ,
η X = η fw X + η pc X .
( SNR ) = η η X + η N .
Fm = ( SNR ) ( SNR ) 1 ,
I ( Δ θ ) - rect z L E ˜ f ( z ) E ˜ p ( z ) exp ( i ξ z ) d z 2 ,
I ( Δ θ ) - rect z L E ˜ f ( z ) 2   exp ( i ξ z ) d z 2 .
I ( Δ θ ) - rect z L exp - sin 2   θ w 2   z 2 × exp - sin 2 ( θ + Δ θ ) w 2   z 2 exp ( i ξ z ) d z 2 .
I ( Δ θ ) sinc L 2 π   ξ exp - w 2 8   sin 2   θ   ξ 2 2 | ( sinc Gauss ) ( ξ ) | 2 .
η 1 X η 1 m = 1 M ( sinc Gauss ) 2 π L   p ( m - m ) × 1 - x cos   θ   cos   θ S F   sin ( θ + θ S )   2 .
η = η 1 sinc 2 L λ   sin ( θ + θ S ) cos   θ S   Δ θ .
( Δ θ ) B = cos   θ S sin ( θ + θ S ) λ L ,
δ θ S = arctan ( x / F ) .
η 1 X m ( x ) = η 1 sinc 2 L λ   sin ( θ m + θ S - δ θ S ) cos ( θ S - δ θ S )   p ( m - m ) × ( Δ θ ) B .
sin ( θ m + θ S - δ θ S ) cos ( θ S - δ θ S ) sin ( θ m + θ S ) cos   θ S - cos   θ m x F ,
η 1 X m ( x ) = η 1 sinc 2 p ( m - m ) sin ( θ m + θ S ) sin ( θ i + θ S ) - cos   θ m cos   θ S sin ( θ i + θ S ) x F .
η 1 X η 1 m = 1 M sinc 2 p ( m - m ) sin ( θ m + θ S ) sin ( θ i + θ S ) - cos   θ m cos   θ S sin ( θ i + θ S ) x F .
η 1 X η 1 m = 1 M sinc 2 p ( m - m ) 1 - x cos   θ i cos   θ S F   sin ( θ i + θ S ) .

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