Abstract

The exposure schedule for partially coherent hologram multiplexing, in which data pages are multiplexed by multiple signal beams and a single reference beam, is investigated in detail for the case of a π/2 phase-shifted photorefractive medium. We found that the optimum recording schedule for partially coherent multiplexing cannot be determined by the classical recording schedule theory because of time-constant errors induced by partially coherent interaction between a reference beam and self-diffraction signal beams. To overcome the issue, we derive a modified recursion equation that accounts for the time-constant errors, and we also propose a novel iterative recording-schedule correction algorism for finding the optimum solution. In the calculation with hologram multiplicity of 30 and photorefractive coupling strength of 3.0, we could successfully obtain a flat diffraction-efficiency profile after the second recursion.

© 2007 Optical Society of America

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References

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    [CrossRef]
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2006 (2)

T. Ito and A. Okamoto, "Volume holographic recording using spatial spread-spectrum multiplexing," Jpn. J. Appl. Phys. 45, 1270-1276 (2006).
[CrossRef]

T. Ito and A. Okamoto, "Coherent parallel copying of holograms recorded by spatial spread-spectrum multiplexing," Jpn. J. Appl. Phys. 45, 1270-1276 (2006).
[CrossRef]

2005 (2)

T. Ito, A. Okamoto, and M. Bunsen, "Shift selectivity of spatial spread-spectrum holographic recording system," Proc. SPIE 6050, 66-73 (2005).

H. Horimai, X. Tan, and J. Li, "Collinear holography," Appl. Opt. 44, 2575-2579 (2005).
[CrossRef] [PubMed]

2004 (2)

K. Anderson and K. Curtis, "Polytopic multiplexing," Opt. Lett. 29, 1402-1404 (2004).
[CrossRef] [PubMed]

L. Hesselink, S. S. Orlov, and M. C. Bashaw, "Holographic data storage systems," Proc. IEEE 92, 1231-1280 (2004).
[CrossRef]

2001 (1)

C. C. Sun, W. C. Su, B. Wang, and A. E. T. Chiou, "Lateral shifting sensitivity of a ground glass for holographic encryption and multiplexing using phase-conjugate readout algorithm," Opt. Commun. 191, 209-224 (2001).
[CrossRef]

1998 (3)

1996 (4)

1993 (1)

1991 (2)

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

E. S. Maniloff and K. M. Johnson, "Maximized photorefractive holographic storage," J. Appl. Phys. 70, 4702-4707 (1991).
[CrossRef]

1988 (2)

A. M. Darskii and V. B. Markov, "Shift selectivity of holograms with a reference speckle wave," Opt. Spectrosc. 65, 392-395 (1988).

D. Psaltis, D. Brady, and K. Wagner, "Adaptive optical networks using photorefractive crystals," Appl. Opt. 27, 1752-1759 (1988).
[CrossRef]

1984 (1)

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. QE-20, 12-30 (1984).
[CrossRef]

1979 (2)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals. I. Steady state," Ferroelectrics 22, 949-960 (1979).
[CrossRef]

K. Bloetekjaer, "Limitations on holographic storage capacity of photochromic and photorefractive media," Appl. Opt. 18, 55-67 (1979).

1978 (1)

Appl. Opt. (7)

Computer (1)

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

Ferroelectrics (1)

N. V. Kukhtarev, V. B. Markov, S. G. Odulov, M. S. Soskin, and V. L. Vinetskii, "Holographic storage in electrooptic crystals. I. Steady state," Ferroelectrics 22, 949-960 (1979).
[CrossRef]

IEEE J. Quantum Electron. (1)

M. Cronin-Golomb, B. Fischer, J. O. White, and A. Yariv, "Theory and applications of four-wave mixing in photorefractive media," IEEE J. Quantum Electron. QE-20, 12-30 (1984).
[CrossRef]

J. Appl. Phys. (1)

E. S. Maniloff and K. M. Johnson, "Maximized photorefractive holographic storage," J. Appl. Phys. 70, 4702-4707 (1991).
[CrossRef]

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

Jpn. J. Appl. Phys. (2)

T. Ito and A. Okamoto, "Volume holographic recording using spatial spread-spectrum multiplexing," Jpn. J. Appl. Phys. 45, 1270-1276 (2006).
[CrossRef]

T. Ito and A. Okamoto, "Coherent parallel copying of holograms recorded by spatial spread-spectrum multiplexing," Jpn. J. Appl. Phys. 45, 1270-1276 (2006).
[CrossRef]

Opt. Commun. (2)

C. C. Sun, W. C. Su, B. Wang, and A. E. T. Chiou, "Lateral shifting sensitivity of a ground glass for holographic encryption and multiplexing using phase-conjugate readout algorithm," Opt. Commun. 191, 209-224 (2001).
[CrossRef]

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

Opt. Eng. (1)

A. Pu, K. Curtis, and D. Psaltis, "Exposure schedule for multiplexing holograms in photopolymer films," Opt. Eng. 35, 2824-2829 (1996).
[CrossRef]

Opt. Lett. (3)

Opt. Spectrosc. (1)

A. M. Darskii and V. B. Markov, "Shift selectivity of holograms with a reference speckle wave," Opt. Spectrosc. 65, 392-395 (1988).

Proc. IEEE (1)

L. Hesselink, S. S. Orlov, and M. C. Bashaw, "Holographic data storage systems," Proc. IEEE 92, 1231-1280 (2004).
[CrossRef]

Proc. SPIE (1)

T. Ito, A. Okamoto, and M. Bunsen, "Shift selectivity of spatial spread-spectrum holographic recording system," Proc. SPIE 6050, 66-73 (2005).

Other (1)

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

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Figures (11)

Fig. 1
Fig. 1

Hologram enhancement via self-diffraction in a photorefractive medium. The graph below the model shows the local distribution of beam intensities.

Fig. 2
Fig. 2

(Color online) Optical geometry of spatial spread-spectrum multiplexing: (a) Multiplexing process and (b) reading process. The same reference is used to record all holograms, and holograms can be addressed by spatial phase modulation and demodulation onto signal beams using a random diffuser.

Fig. 3
Fig. 3

Analysis model. Photorefractive beam coupling between multiple signals A j and a single reference A ref is numerically calculated. In the calculation, the direction of energy transfer (i.e., crystalline c axis) is set so that signal beams are amplified.

Fig. 4
Fig. 4

(Color online) Calculation results in the case of the sequential decision algorism:(a) The growth and decay of diffraction efficiency of multiplexed holograms. (Solid curves) Dynamic behaviors of 30 multiplexed holograms. (Dashed curve) Normal incoherent erasure curve. (Dotted curve) Partially coherent erasure curve (illumination by an incoherent erasure beam and a coherent reference beam with a 1:1 intensity ratio). (b) Corresponding recording time. (c) Diffraction-efficiency profile of 30 multiplexed holograms. Parameters used in the calculation are as follows: t 1 = 100   s , γ L = 3.0 , τ 0 = 0.1 J / cm 2 , I sig = 1.0 mW / cm 2 , I ref = 1.0 mW / cm 2 ( τ = 50   s ) .

Fig. 5
Fig. 5

(Color online) Calculation results in the case of the backward recursion algorism: (a) Growth and decay of diffraction efficiency of multiplexed holograms, (b) corresponding recording time, and (c) calculated diffraction efficiency profile of 30 multiplexed holograms. Parameters used in the calculation are the same as those in Fig. 4.

Fig. 6
Fig. 6

Calculated time-constant errors of each hologram, where γ L = 3.0 , τ = 50   s , and M = 30 .

Fig. 7
Fig. 7

Local hologram strength profiles of recorded holograms, where γ = 30 cm 1 , L = 1   mm , and M = 50 .

Fig. 8
Fig. 8

(Color online) Model for describing the relationship between the local hologram strength distribution Q ( z ) and the local self-diffraction beam distribution I dif ( z ) . Because latterly recorded holograms have a “flat” hologram strength profile (left), a large self-diffraction signal intensity can be induced throughout the medium, and therefore the hologram can be efficiently enhanced. In the case of initially recorded holograms with an “upward” profile (right), however, the hologram enhancement becomes weak due to the small self-diffraction signal intensity in the vicinity of z = 0 .

Fig. 9
Fig. 9

(Color online) Flow diagram of iterative recording schedule correction algorism.

Fig. 10
Fig. 10

(Color online) Diffraction-efficiency profiles after iterative recording schedule correction, (a) after the first correction and (b) after the second correction [compare with the results before correction shown in Figs. 4(c) and 5(c)].

Fig. 11
Fig. 11

(Color online) Temporal response of diffraction efficiency of 30 multiplexed holograms after the second iterative recording schedule correction.

Equations (24)

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1 exp ( t m + 1 τ w ) = [ 1 exp ( t m τ w ) ] exp ( t m + 1 τ e ) .
M # = U max τ w τ e ,
η ( f U max τ w τ e M ) 2 = f 2 ( M # M ) 2 ,
A j z = Q j * A ref ,
A ref z = j = 1 M ( Q j A j ) ,
τ Q j t + Q j = γ A j A ref * I 0 ,
A j ( 0 , t ) = { I sig ( j = k ) 0 ( j k ) ,
A ref ( 0 , t ) = I ref .
τ = τ 0 I 0 ,
U j = 0 L Q j d z ,
U all = j = 1 M U j 2 .
η j = U j 2 U all 2 sin 2 U all .
t M = f τ e M .
U av = U max [ 1 exp ( t m τ w ) ] exp [ 1 τ e ( m ) ( t m + 1 + t m + 2 + + t M ) ] ,
U av = U max [ 1 exp ( t M τ w ) ] U max t M τ w ,
t m = τ w ln { 1 U av U max exp [ 1 τ e ( m ) ( t m + 1 + t m + 2 + + t M ) ] } .
τ e ( m ) = t m + 1 + t m + 2 + + t M ln [ U max { 1 exp ( t m / τ w ) } | U m t = T M ] .
U av < U max 1 + τ w τ e ( M 1 ) .
1 U av U max exp [ 1 τ e ( m ) ( t m + 1 + t m + 2 + + t M ) ] ] > 0
U av U max < exp [ 1 τ e ( 1 ) ( t 2 + t 3 + + t M ) ] .
exp [ 1 τ e ( 1 ) ( t 2 + t 3 + + t M ) ] < exp [ ( M 1 ) t M τ e ( 1 ) ]
< 1 ( M 1 ) t M τ e ( 1 ) .
U av < U max 1 + τ w τ e ( 1 ) ( M 1 ) .
U av < U max 1 + τ w τ e ( M 1 ) .

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