Abstract

We propose a novel type of unitary matrix for phase-code multiplexed holographic memories, which could be quickly generated from geometric sequences. Our analysis shows that the phase-code matrices are unitary rather than orthogonal. The new matrices have complex elements. The order of unitary matrices can be any positive integer, so that we can accommodate the available spatial light modulators to obtain the maximum possible storage capacity. The cross-talk noises in phase-encoded memories with unitary matrices and with Hadamard matrices are of the same order of magnitude, which are much lower than those in holographic memories with wavelength multiplexing or angle multiplexing.

© 2006 Optical Society of America

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    [CrossRef]

2005 (1)

G. Berger, M. Stumpe, M. Hoehne, and C. Denz, J. Opt. A Pure Appl. Opt. 7, 567 (2005).
[CrossRef]

2001 (1)

G. Berger, C. Denz, S. S. Orlov, B. Phillips, and L. Hesselink, Appl. Phys. B 73, 839 (2001).
[CrossRef]

1998 (2)

C. Denz, K.-O. Mueller, T. Heimann, and T. Tschudi, IEEE J. Sel. Top. Quantum Electron. 4, 832 (1998).
[CrossRef]

Z. Wen and Y. Tao, Opt. Commun. 148, 11 (1998).
[CrossRef]

1996 (3)

1995 (1)

1994 (2)

1993 (1)

1992 (2)

1991 (1)

C. Denz, G. Pauliat, and G. Roosen, Opt. Commun. 85, 171 (1991).
[CrossRef]

1973 (1)

L. d'Auria, J.-P. Huignard, and E. Spitz, IEEE Trans. Magn. 9, 83 (1973).
[CrossRef]

1968 (1)

Alves, C.

Barbastathis, G.

Berger, G.

G. Berger, M. Stumpe, M. Hoehne, and C. Denz, J. Opt. A Pure Appl. Opt. 7, 567 (2005).
[CrossRef]

G. Berger, C. Denz, S. S. Orlov, B. Phillips, and L. Hesselink, Appl. Phys. B 73, 839 (2001).
[CrossRef]

Curtis, K.

d'Auria, L.

L. d'Auria, J.-P. Huignard, and E. Spitz, IEEE Trans. Magn. 9, 83 (1973).
[CrossRef]

Dellwig, T.

Denz, C.

G. Berger, M. Stumpe, M. Hoehne, and C. Denz, J. Opt. A Pure Appl. Opt. 7, 567 (2005).
[CrossRef]

G. Berger, C. Denz, S. S. Orlov, B. Phillips, and L. Hesselink, Appl. Phys. B 73, 839 (2001).
[CrossRef]

C. Denz, K.-O. Mueller, T. Heimann, and T. Tschudi, IEEE J. Sel. Top. Quantum Electron. 4, 832 (1998).
[CrossRef]

C. Denz, T. Dellwig, J. Lembcke, and T. Tschudi, Opt. Lett. 21, 278 (1996).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, Appl. Opt. 31, 5700 (1992).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, and G. Roosen, Opt. Commun. 85, 171 (1991).
[CrossRef]

C. Denz, K.-O. Mueller, F. Visinka, and T. Tschudi, in Holographic Data Storage, H.J.Coufal, D.Psaltis, and G.T.Sincerbox, eds. (Springer-Verlag, 2000).

Heimann, T.

C. Denz, K.-O. Mueller, T. Heimann, and T. Tschudi, IEEE J. Sel. Top. Quantum Electron. 4, 832 (1998).
[CrossRef]

Hesselink, L.

G. Berger, C. Denz, S. S. Orlov, B. Phillips, and L. Hesselink, Appl. Phys. B 73, 839 (2001).
[CrossRef]

Hoehne, M.

G. Berger, M. Stumpe, M. Hoehne, and C. Denz, J. Opt. A Pure Appl. Opt. 7, 567 (2005).
[CrossRef]

Huignard, J.-P.

L. d'Auria, J.-P. Huignard, and E. Spitz, IEEE Trans. Magn. 9, 83 (1973).
[CrossRef]

LaMacchia, J. T.

Lembcke, J.

Levene, M.

Leyva, V.

Mueller, K.-O.

C. Denz, K.-O. Mueller, T. Heimann, and T. Tschudi, IEEE J. Sel. Top. Quantum Electron. 4, 832 (1998).
[CrossRef]

C. Denz, K.-O. Mueller, F. Visinka, and T. Tschudi, in Holographic Data Storage, H.J.Coufal, D.Psaltis, and G.T.Sincerbox, eds. (Springer-Verlag, 2000).

Orlov, S. S.

G. Berger, C. Denz, S. S. Orlov, B. Phillips, and L. Hesselink, Appl. Phys. B 73, 839 (2001).
[CrossRef]

Pauliat, G.

Phillips, B.

G. Berger, C. Denz, S. S. Orlov, B. Phillips, and L. Hesselink, Appl. Phys. B 73, 839 (2001).
[CrossRef]

Psaltis, D.

Pu, A.

Rakuljic, G. A.

Roosen, G.

Spitz, E.

L. d'Auria, J.-P. Huignard, and E. Spitz, IEEE Trans. Magn. 9, 83 (1973).
[CrossRef]

Stumpe, M.

G. Berger, M. Stumpe, M. Hoehne, and C. Denz, J. Opt. A Pure Appl. Opt. 7, 567 (2005).
[CrossRef]

Tao, Y.

Z. Wen and Y. Tao, Opt. Commun. 148, 11 (1998).
[CrossRef]

Tschudi, T.

C. Denz, K.-O. Mueller, T. Heimann, and T. Tschudi, IEEE J. Sel. Top. Quantum Electron. 4, 832 (1998).
[CrossRef]

C. Denz, T. Dellwig, J. Lembcke, and T. Tschudi, Opt. Lett. 21, 278 (1996).
[CrossRef] [PubMed]

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, Appl. Opt. 31, 5700 (1992).
[CrossRef] [PubMed]

C. Denz, K.-O. Mueller, F. Visinka, and T. Tschudi, in Holographic Data Storage, H.J.Coufal, D.Psaltis, and G.T.Sincerbox, eds. (Springer-Verlag, 2000).

Visinka, F.

C. Denz, K.-O. Mueller, F. Visinka, and T. Tschudi, in Holographic Data Storage, H.J.Coufal, D.Psaltis, and G.T.Sincerbox, eds. (Springer-Verlag, 2000).

Wen, Z.

Z. Wen and Y. Tao, Opt. Commun. 148, 11 (1998).
[CrossRef]

X. Yang, Y. Xu, and Z. Wen, Opt. Lett. 21, 1067 (1996).
[CrossRef] [PubMed]

X. Yang, Z. Wen, and Yu Xu, in Proc. SPIE 2849, 217 (1996).
[CrossRef]

White, D. L.

Wilson, W. L.

K. Curtis and W. L. Wilson, U.S. Patent 5,719,691 (February 12, 1998).

Xu, Y.

Xu, Yu

X. Yang, Z. Wen, and Yu Xu, in Proc. SPIE 2849, 217 (1996).
[CrossRef]

Yang, X.

X. Yang, Z. Wen, and Yu Xu, in Proc. SPIE 2849, 217 (1996).
[CrossRef]

X. Yang, Y. Xu, and Z. Wen, Opt. Lett. 21, 1067 (1996).
[CrossRef] [PubMed]

Yariv, A.

Appl. Opt. (2)

Appl. Phys. B (1)

G. Berger, C. Denz, S. S. Orlov, B. Phillips, and L. Hesselink, Appl. Phys. B 73, 839 (2001).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

C. Denz, K.-O. Mueller, T. Heimann, and T. Tschudi, IEEE J. Sel. Top. Quantum Electron. 4, 832 (1998).
[CrossRef]

IEEE Trans. Magn. (1)

L. d'Auria, J.-P. Huignard, and E. Spitz, IEEE Trans. Magn. 9, 83 (1973).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

G. Berger, M. Stumpe, M. Hoehne, and C. Denz, J. Opt. A Pure Appl. Opt. 7, 567 (2005).
[CrossRef]

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

Opt. Commun. (2)

Z. Wen and Y. Tao, Opt. Commun. 148, 11 (1998).
[CrossRef]

C. Denz, G. Pauliat, and G. Roosen, Opt. Commun. 85, 171 (1991).
[CrossRef]

Opt. Lett. (6)

Proc. SPIE (1)

X. Yang, Z. Wen, and Yu Xu, in Proc. SPIE 2849, 217 (1996).
[CrossRef]

Other (2)

C. Denz, K.-O. Mueller, F. Visinka, and T. Tschudi, in Holographic Data Storage, H.J.Coufal, D.Psaltis, and G.T.Sincerbox, eds. (Springer-Verlag, 2000).

K. Curtis and W. L. Wilson, U.S. Patent 5,719,691 (February 12, 1998).

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Figures (3)

Fig. 1
Fig. 1

Recording and readout geometry for phase-code multiplexing.

Fig. 2
Fig. 2

Log(SNR) versus hologram code number.

Fig. 3
Fig. 3

Log(SNR) versus hologram code number without bad codes. U 63 without codes 31, 32; U 64 without code 32; H 64 without code 1.

Equations (7)

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

R m = l = 0 N 1 P m l exp ( j k l r ) .
E n ( l = 0 N 1 P n l P m l * ) S m ,
P P ̃ * = N I ,
U m l N = exp ( j 2 π m l N ) ,
l = 0 n 1 U n l U m l * = 1 exp [ j 2 π ( n m ) l ] 1 exp [ j 2 π ( n m ) l N ] = { N n = m 0 n m } .
U 4 = [ 1 1 1 1 1 j 1 j 1 1 1 1 1 j 1 j ] .
NSR = 1 N 2 m = q q k = q q l k , l = q q U n , k + q U m + q , l + q * sinc [ k l + y λ 2 F t ( l 2 k 2 ) + λ 3 8 t 3 ( l 2 k 2 ) 2 ] 2 ,

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