Abstract

We consider the storage density limited by the cross talk between stored pages during readout. We review some earlier work done in this area and present new theoretical work that characterizes the storage capacity limitations due to the cross talk. The results show that because of the presence of degeneracy noise, storage capacity does not benefit from expanding the reference points from one dimension to two dimensions. An optimum configuration that fully utilizes storage capacity and completely eliminates degeneracy noise is given for an angularly multiplexed volume holographic memory system.

© 1992 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Mok, M. C. Tackitt, H. M. Stoll, “Storage of 500 high-resolution holograms in a LiNbO3crystal,” Opt. Lett. 16, 605–607 (1991).
    [CrossRef] [PubMed]
  2. P. J. V. Heerden, “Theory of optical information storage in solid,” Appl. Opt. 2, 393–400 (1963).
    [CrossRef]
  3. D. L. Staebler, J. J. Amodei, W. Phillips, “Multiple storage of thick phase holograms in LiNbO3,” IEEE J. Quantum Electron. QE-8, 611 (1972).
    [CrossRef]
  4. J. J. Amodei, D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
    [CrossRef]
  5. E. G. Ramberg, “Holographic information storage,”RCA Rev. 33, 5–53 (1972).
  6. D. Psaltis, D. Brady, K. Wagner, “Adaptive optical networks using photorefractive crystals,” Appl. Opt. 27, 1752–1759 (1988).
    [CrossRef]
  7. J. Hong, P. Yeh, D. Psaltis, D. Brady, “Diffraction efficiency of strong volume holograms,” Opt. Lett. 15, 344–346 (1990).
    [CrossRef] [PubMed]
  8. H. Lee, X.-G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2193 (1989).
    [CrossRef]
  9. J. D. Jackson, Classical Electrodynamics (Wiley, New York, 1975), pp. 427–432.
  10. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 57–96.
  11. C. X.-G. Gu, “Optical neural networks using volume holograms,” Ph.D. thesis (California Institute of Technology, Pasadena, Calif., 1990), pp. 39–116.

1991 (1)

1990 (1)

1989 (1)

H. Lee, X.-G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2193 (1989).
[CrossRef]

1988 (1)

1972 (2)

E. G. Ramberg, “Holographic information storage,”RCA Rev. 33, 5–53 (1972).

D. L. Staebler, J. J. Amodei, W. Phillips, “Multiple storage of thick phase holograms in LiNbO3,” IEEE J. Quantum Electron. QE-8, 611 (1972).
[CrossRef]

1971 (1)

J. J. Amodei, D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

1963 (1)

Amodei, J. J.

D. L. Staebler, J. J. Amodei, W. Phillips, “Multiple storage of thick phase holograms in LiNbO3,” IEEE J. Quantum Electron. QE-8, 611 (1972).
[CrossRef]

J. J. Amodei, D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

Brady, D.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 57–96.

Gu, C. X.-G.

C. X.-G. Gu, “Optical neural networks using volume holograms,” Ph.D. thesis (California Institute of Technology, Pasadena, Calif., 1990), pp. 39–116.

Gu, X.-G.

H. Lee, X.-G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2193 (1989).
[CrossRef]

Heerden, P. J. V.

Hong, J.

Jackson, J. D.

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

Lee, H.

H. Lee, X.-G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2193 (1989).
[CrossRef]

Mok, F.

Phillips, W.

D. L. Staebler, J. J. Amodei, W. Phillips, “Multiple storage of thick phase holograms in LiNbO3,” IEEE J. Quantum Electron. QE-8, 611 (1972).
[CrossRef]

Psaltis, D.

Ramberg, E. G.

E. G. Ramberg, “Holographic information storage,”RCA Rev. 33, 5–53 (1972).

Staebler, D. L.

D. L. Staebler, J. J. Amodei, W. Phillips, “Multiple storage of thick phase holograms in LiNbO3,” IEEE J. Quantum Electron. QE-8, 611 (1972).
[CrossRef]

J. J. Amodei, D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

Stoll, H. M.

Tackitt, M. C.

Wagner, K.

Yeh, P.

Appl. Opt. (2)

Appl. Phys. Lett. (1)

J. J. Amodei, D. L. Staebler, “Holographic pattern fixing in electro-optic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
[CrossRef]

IEEE J. Quantum Electron. (1)

D. L. Staebler, J. J. Amodei, W. Phillips, “Multiple storage of thick phase holograms in LiNbO3,” IEEE J. Quantum Electron. QE-8, 611 (1972).
[CrossRef]

J. Appl. Phys. (1)

H. Lee, X.-G. Gu, D. Psaltis, “Volume holographic interconnections with maximal capacity and minimal cross talk,” J. Appl. Phys. 65, 2191–2193 (1989).
[CrossRef]

Opt. Lett. (2)

RCA Rev. (1)

E. G. Ramberg, “Holographic information storage,”RCA Rev. 33, 5–53 (1972).

Other (3)

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

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968), pp. 57–96.

C. X.-G. Gu, “Optical neural networks using volume holograms,” Ph.D. thesis (California Institute of Technology, Pasadena, Calif., 1990), pp. 39–116.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Optical memory system in which multiple holograms are stored in a thick recording medium located in the Fourier domain.

Fig. 2
Fig. 2

Relative cross-talk noise noise/signal as a function of both the location of the output plane y2/f and the location of the reading point i, according to relation (23).

Fig. 3
Fig. 3

Relative cross-talk noise Noise/Signal as a function of M, according to relation (23), (solid curve) and fitting curve obtained by using polynomial expansions (dotted curve).

Equations (32)

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

N max = t 4 λ ( SNR ) R 2 ,
Δ m = - M M R m * S m + c . c . ,
E ( r ) exp ( i k i · r ) + k 0 2 4 π exp ( i k r ) r d r exp ( - i K · r ) Δ ( r ) ,
K = k d - k i
R m = exp ( i k m · r ) .
S m ( r ) = exp ( 2 i k f + i k n Δ 0 ) i λ f exp ( i k z ) × d x 0 d y 0 f m ( x 0 , y 0 ) exp [ - i 2 π λ f ( x x 0 + y y 0 ) ] × exp [ - i π λ f z f ( x 0 2 + y 0 2 ) ] ,
k d = [ 2 π λ x 2 f , 2 π λ y 2 f , 2 π λ ( 1 - x 2 2 2 f 2 - y 2 2 2 f 2 ) ] .
g ( x 2 , y 2 ) m = - M M d x 0 d y 0 f m ( x 0 , y 0 ) × V sinc [ a 2 π ( k m x - k i x + 2 π λ x 0 + x 2 f ) ] × sinc [ b 2 π ( k m y - k i y + 2 π λ y 0 + y 2 f ) ] × sinc [ t 2 π ( k m z - k i z + π λ x 2 2 - x 0 2 + y 2 2 - y 0 2 f 2 ) ] ,
g ( x 2 , y 2 ) m = - M M d x 0 d y 0 f m ( x 0 , y 0 ) × exp [ - i π ( z 0 - f ) λ x 0 2 + y 0 2 + x 2 2 + y 2 2 f 2 ] × V sinc [ a 2 π ( k m x - k i x + 2 π λ x 0 + x 2 f ) ] × sinc [ b 2 π ( k m y - k i y + 2 π λ y 0 + y 2 f ) ] × sinc [ t 2 π ( k m z - k i z + π λ x 2 2 - x 0 2 + y 2 2 - y 0 2 f 2 ) ] .
g ( x 2 , y 2 ) m = - M M f m ( - x 2 - λ f 2 π Δ K m i x , - y 2 - λ f 2 π Δ K m i y ) × t sinc [ t 2 π ( Δ K m i z + Δ K m i x x 2 + Δ K m i y y 2 f + Δ K m i x 2 + Δ K m i y 2 4 π ) ] ,
Δ K m i = k m - k i
g m ( x 2 , y 2 ) f m ( - x 2 , - y 2 ) ,
k x = - 2 π λ x i f = 0 , k y = - 2 π λ y i f cos θ - 2 π λ [ 1 - 1 2 ( y i f ) 2 ] sin θ , k z = 2 π λ y i f sin θ + 2 π λ [ 1 - 1 2 ( y i f ) 2 ] cos θ ,
Δ K m i x = 0 , Δ K m i y = 2 π λ y m - y i f ( - cos θ + 1 2 sin θ y m + y i f ) , Δ K m i z = 2 π λ y m - y i f ( - sin θ - 1 2 cos θ y m + y i f ) .
g noise ( x 2 , y 2 ) m i f m ( - x 2 - λ f 2 π Δ K m i x , - y 2 - λ f 2 π Δ K m i y ) × t sinc [ t 2 π ( Δ K m i z + Δ K m i x x 2 + Δ K m i y y 2 f + Δ K m i x 2 + Δ K m i y 2 4 π ) ] .
noise = m i t 2 sinc 2 [ t 2 π ( Δ K m i z + Δ K m i x x 2 + Δ K m i y y 2 f + Δ K m i x 2 + Δ K m i y 2 4 π ) ] .
signal = t 2 f i ( - x 2 , - y 2 ) 2 .
noise signal = m i sinc 2 [ t 2 π ( Δ K m i z + Δ K m i x x 2 + Δ K m i y y 2 f + Δ K m i x 2 + Δ K m i y 2 4 π ) ] .
noise signal = m i sinc 2 { t λ y m - y i f × sin θ [ 1 + cot θ ( y 2 f + y m + y i 2 f - cos θ y m - y i 2 f ) + cos θ y m - y i f y m + y i 2 f - y 2 f y m + y i 2 f - sin θ y m - y i 2 f ( y m + y i ) 2 4 f 2 ] } .
noise signal = m i sinc 2 ( t λ y m - y i f sin θ ) .
Δ = λ f t sin θ .
y m = m Δ = m λ f t sin θ .
noise signal m i sinc 2 [ t λ y m - y i f ( 1 - y 2 f y m + y i 2 f ) ] ,
noise signal m i sinc 2 [ ( m - i ) ( 1 - β m + i 2 ) ] ,
β = λ y 2 max t f .
noise signal m = - M M - 1 sinc 2 [ ( m - M ) ( 1 - β m + M 2 ) ] n = 1 n 0 sinc 2 [ n ( 1 - β 2 M - n 2 ) ] ,
n 0 β 2 M - n 0 2 1.
n 0 1 β M
noise signal < n 0 sinc 2 ( 1 - β 2 M - 1 2 ) n 0 ( β M ) 2 = β M .
noise signal max < 2 β M .
SNR = signal noise > t f λ d M 2 t f λ d N ,
N max 2 t f λ d ( SNR ) re ,

Metrics