Abstract

A novel method to selectively erase and update speckle-multiplexed holograms in photorefractive crystals by use of a double Mach-Zehnder (DMZ) interferometric arrangement is presented. The DMZ arrangement automatically produces a pair of π-phase-shifted interference patterns used for holographic recording, erasure, and update operations with a fairly simple optical configuration that consists of a commonly used dielectric multilayer beam splitter and two mirrors. The recording and the erasure conditions required for erasing a photorefractive hologram quickly and completely are discussed by calculating the temporal property of the hologram buildup and decay using the time-dependent coupled-wave equations. An experiment is also performed, in which arbitrary holograms in speckle-multiplexed holograms are selectively erased and updated with the simple DMZ optical configuration.

© 2006 Optical Society of America

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2005 (1)

2004 (2)

1999 (1)

1998 (1)

D. Psaltis and G. W. Burr, "Holographic data storage," Computer 31(2),52-60 (1998).
[CrossRef]

1997 (2)

1996 (1)

1994 (2)

1993 (1)

1992 (3)

1991 (2)

M. Horowitz, D. Kligler, and B. Fischer, "Time-dependent behavior of photorefractive two- and four-wave mixing," J. Opt. Soc. Am. B 8, 2204-2217 (1991).
[CrossRef]

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase coding method," Opt. Commun. 85, 171-176 (1991).
[CrossRef]

1990 (1)

J. H. Hong, S. Campbell, and P. Yeh, "Optical pattern classifier with Perceptron learning," Appl. Opt. 29, 3020-3025 (1990).
[CrossRef]

1988 (1)

A. M. Darskii and V. B. Markov, "Shift selectivity of holograms with a reference speckle wave," Opt. Spectrosc. (USSR) 65, 392-394 (1988).

1978 (1)

1976 (1)

J. P. Huignard, J. P. Herriau, and F. Micheron, "Selective erasure and processing in volume holograms superimposed in photosensitive ferroelectrics," Ferroelectrics 11, 393-396 (1976).
[CrossRef]

Aguilar, M.

Agullo-Lopez, F.

Anderson, K.

Barbastathis, G.

Bjornson, E.

Burr, G. W.

D. Psaltis and G. W. Burr, "Holographic data storage," Computer 31(2),52-60 (1998).
[CrossRef]

Campbell, S.

J. H. Hong, S. Campbell, and P. Yeh, "Optical pattern classifier with Perceptron learning," Appl. Opt. 29, 3020-3025 (1990).
[CrossRef]

Carrascosa, M.

Coufal, H. J.

H. J. Coufal, D. Psaltis, and G. T. Sincerbox, Holographic Data Storage, Springer Series in Optical Sciences (Springer-Verlag, 2000).

Curtis, K.

Darskii, A. M.

A. M. Darskii and V. B. Markov, "Shift selectivity of holograms with a reference speckle wave," Opt. Spectrosc. (USSR) 65, 392-394 (1988).

Denz, C.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase coding method," Opt. Commun. 85, 171-176 (1991).
[CrossRef]

Fainman, Y.

Fischer, B.

Herriau, J. P.

J. P. Huignard, J. P. Herriau, and F. Micheron, "Selective erasure and processing in volume holograms superimposed in photosensitive ferroelectrics," Ferroelectrics 11, 393-396 (1976).
[CrossRef]

Hesselink, L.

Hong, J. H.

J. H. Hong, S. Campbell, and P. Yeh, "Optical pattern classifier with Perceptron learning," Appl. Opt. 29, 3020-3025 (1990).
[CrossRef]

Horimai, H.

Horowitz, M.

Huignard, J. P.

J. P. Huignard, J. P. Herriau, and F. Micheron, "Selective erasure and processing in volume holograms superimposed in photosensitive ferroelectrics," Ferroelectrics 11, 393-396 (1976).
[CrossRef]

Kang, Y. H.

Kim, K. H.

Kligler, D.

Kwan, D.

Lee, B.

Lee, S. H.

Levene, M.

Levya, V.

Li, J.

Ma, J.

Markov, V.

Markov, V. B.

A. M. Darskii and V. B. Markov, "Shift selectivity of holograms with a reference speckle wave," Opt. Spectrosc. (USSR) 65, 392-394 (1988).

Micheron, F.

J. P. Huignard, J. P. Herriau, and F. Micheron, "Selective erasure and processing in volume holograms superimposed in photosensitive ferroelectrics," Ferroelectrics 11, 393-396 (1976).
[CrossRef]

Millerd, J.

Moharam, M. G.

Mok, F. H.

Norrie, M.

Okas, R.

Orlov, S. S.

Pauliat, G.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase coding method," Opt. Commun. 85, 171-176 (1991).
[CrossRef]

Phillips, W.

Psaltis, D.

Pu, A.

Qiao, Y.

Rakuljic, G. A.

Roosen, G.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase coding method," Opt. Commun. 85, 171-176 (1991).
[CrossRef]

Sasaki, H.

Serrano, E.

Sincerbox, G. T.

H. J. Coufal, D. Psaltis, and G. T. Sincerbox, Holographic Data Storage, Springer Series in Optical Sciences (Springer-Verlag, 2000).

Snyder, R.

Sundaram, P.

Takashima, Y.

Taketomi, Y.

Tan, X.

Trolinge, J.

Tschudi, T.

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase coding method," Opt. Commun. 85, 171-176 (1991).
[CrossRef]

Yariv, A.

Yeh, P.

J. H. Hong, S. Campbell, and P. Yeh, "Optical pattern classifier with Perceptron learning," Appl. Opt. 29, 3020-3025 (1990).
[CrossRef]

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, 1993).

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

Young, L.

Appl. Opt. (5)

Computer (1)

D. Psaltis and G. W. Burr, "Holographic data storage," Computer 31(2),52-60 (1998).
[CrossRef]

Ferroelectrics (1)

J. P. Huignard, J. P. Herriau, and F. Micheron, "Selective erasure and processing in volume holograms superimposed in photosensitive ferroelectrics," Ferroelectrics 11, 393-396 (1976).
[CrossRef]

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

J. Opt. Soc. Am. B (2)

Opt. Commun. (1)

C. Denz, G. Pauliat, G. Roosen, and T. Tschudi, "Volume hologram multiplexing using a deterministic phase coding method," Opt. Commun. 85, 171-176 (1991).
[CrossRef]

Opt. Lett. (8)

Opt. Spectrosc. (1)

A. M. Darskii and V. B. Markov, "Shift selectivity of holograms with a reference speckle wave," Opt. Spectrosc. (USSR) 65, 392-394 (1988).

Other (3)

P. Yeh, Introduction to Photorefractive Nonlinear Optics (Wiley, 1993).

P. Yeh, Optical Waves in Layered Media (Wiley, 1988).

H. J. Coufal, D. Psaltis, and G. T. Sincerbox, Holographic Data Storage, Springer Series in Optical Sciences (Springer-Verlag, 2000).

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Figures (9)

Fig. 1
Fig. 1

Double Mach–Zehnder interferometric arrangement. BS denotes the beam splitter. The solid and the dashed sinusoidal curves correspond to the interference patterns induced by the beams from port 1 and port 2, respectively. There is the mutual phase difference of π rad between these interference patterns.

Fig. 2
Fig. 2

Observation of mutual π-phase difference between interference patterns produced by the DMZ interferometric arrangement:(a) Experimental setup:M, mirrors; L, lens; HWP, half-wave plates; PBS, polarizing beam splitters; BS, beam splitters; S, shutters. DMZ is composed of M 3 , M 4 , and BS 1 . (b) Interference pattern formed by the beams from port 1. (c) Interference pattern formed by the beams from port 2. (d) Theoretical sum of images (b) and (c) with computer processing. (e) Brightness curves on the horizontal center lines of (b)–(d).

Fig. 3
Fig. 3

Conceptual diagrams of hologram recording and selective erasure with speckle-multiplexing technique and DMZ interferometric arrangement:(a) recording, (b) retrieving, and (c) selective erasure. We can also use split laser beams originating from a laser source, while separate laser sources are employed for port 1 and port 2 in these figures.

Fig. 4
Fig. 4

Temporal property of U for various values of ϕ:(a) t w / τ = 3.0 , (b) t w / τ = 0.1 .

Fig. 5
Fig. 5

Temporal property of U for various values of γ L ( t w / τ = 3.0 , ϕ = 180 ° ) .

Fig. 6
Fig. 6

Experimental setup for selective erasure with DMZ interferometric arrangement:M, mirrors; HWP, half-wave plates; L, lenses; PBS, polarizing beam splitters; BS, beam splitter; S, shutters. DMZ is composed of M 3 , M 4 , and BS.

Fig. 7
Fig. 7

Experimentally measured temporal characteristics of diffraction efficiency for selective and incoherent erasures.

Fig. 8
Fig. 8

Reconstructed images from holograms recorded in LiNbO 3 : Fe crystal:(a) Primarily recorded circular image by beams from port 1. (b) Secondly recorded image “F” by beams from port 2. (c) Diffracted image from composite hologram.

Fig. 9
Fig. 9

Experimental result of selective erasure and update of speckle-multiplexed holograms. Reconstructed images from the multiplexed holograms after (a) recording, (b) erasure, and (c) update are presented.

Equations (11)

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Δ n ( r ) = Δ n REC ( r ) cos ( K g r ) ,
Δ n ( r ) = Δ n REC ( r ) cos ( K g r ) + Δ n ERA ( r ) cos ( K g r + π ) .
E port 1 = r A exp ( - i k 1 r ) + t A exp ( - i k 2 r ) ,
E port 2 = t B exp ( - i k 1 r ) + r B exp ( - i k 2 r ) ,
t t * + r r * = 1 ,
t r * + r t * = 0.
I port 1 = | E port 1 | 2 = ( | r | 2 + | t | 2 + r t * e i K r + r * te - i K r ) | A | 2 ,
I port 2 = | E port 2 | 2 = ( | r | 2 + | t | 2 + r t * e - i K r + r * t e i K r ) | B | 2 = { | r | 2 + | t | 2 + ( r t * e i K r + r * t e - i K r ) e } | B | 2 ,
A O ( z , t ) / z = Q ( z , t ) A R ( z , t ) ,
A R ( z , t ) / z = Q * ( z , t ) A O ( z , t ) ,
τ Q ( z , t ) / t + Q ( z , t ) = γ A O ( z , t ) A R * ( z , t ) / I 0 ,

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