Abstract

Unwanted erasure during readout of holographic data can be reduced or eliminated by use of a different wavelength for reading than that which was used for writing. To prevent distortion and Bragg mismatch that would be unacceptable for digital data storage, one can format data to account for the wavelength difference. Techniques to format data and the results of this formatting are presented. Varying the formatting parameters is investigated to optimize diffraction efficiency.

© 1997 Optical Society of America

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References

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  1. P. J. van Heerden, “Theory of optical information storage in solids,” Appl. Opt. 2, 393–400 (1963).
    [CrossRef]
  2. J. J. Amodei and D. L. Staebler, “Holographic pattern fixing in electrooptic crystals,” Appl. Phys. Lett. 18, 540–542 (1971).
    [CrossRef]
  3. D. Brady, K. Hsu, and D. Psaltis, “Periodically refreshed multiply exposed photorefractive holograms,” Opt. Lett. 15, 817–819 (1990).
    [CrossRef] [PubMed]
  4. D. von der Linde and A. M. Glass, “Photorefractive effects for reversible holographic storage of information,” Appl. Phys. 8, 85–100 (1975).
    [CrossRef]
  5. H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  6. E. K. Gulanyan, I. R. Dorosh, V. D. Iskin, A. L. Mikaélyan, and M. A. Maíorchuk, “Nondestructive readout of holograms in iron-doped lithium niobate crystals,” Sov. J. Quantum Electron. 9 (5), 647–649 (1979).
    [CrossRef]
  7. M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Holographic storage of information and peculiarities of light diffraction in birefringent electro-optic crystals,” Opt. Laser Technol. 6, 149–151 (1979).
    [CrossRef]
  8. H. C. Külich, “A new approach to read volume holograms at different wavelengths,” Opt. Commun. 64, 407–411 (1987).
    [CrossRef]
  9. D. Psaltis, F. Mok, and H. S. Li, “Nonvolatile storage in photorefractive crystals,” Opt. Lett. 19, 210–212 (1994).
    [CrossRef] [PubMed]
  10. W. J. Burke and P. Sheng, “Cross talk noise from multiple thick-phase holograms,” J. Appl. Phys. 48, 681–685 (1977).
    [CrossRef]
  11. H. C. Külich and E. Krätzig, “Reconstruction of volume holograms at different wavelengths,” in Nonlinear Optical Materials III, P. Guenter, ed., Proc. SPIE 1273, 60–67 (1990).
    [CrossRef]
  12. H. W. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Tech. J. 48, 2909–2947 (1969).
    [CrossRef]
  13. A. Aharoni, M. C. Bashaw and, L. Hesselink, “Capacity considerations for multiplexed holographic optical data storage,” in Practical Holography VII: Imaging and Materials, S. A. Benton, ed., Proc. SPIE 1914, 56–65 (1993).
  14. M. C. Bashaw, J. F. Heanue, A. Aharoni, J. F. Walkup, and L. Hesselink, “Cross-talk considerations for angular and phase-encoded multiplexing in volume holography,” J. Opt. Soc. Am. B 11, 1820–1836 (1994).
    [CrossRef]

1994 (2)

1990 (1)

1987 (1)

H. C. Külich, “A new approach to read volume holograms at different wavelengths,” Opt. Commun. 64, 407–411 (1987).
[CrossRef]

1979 (1)

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Holographic storage of information and peculiarities of light diffraction in birefringent electro-optic crystals,” Opt. Laser Technol. 6, 149–151 (1979).
[CrossRef]

1977 (1)

W. J. Burke and P. Sheng, “Cross talk noise from multiple thick-phase holograms,” J. Appl. Phys. 48, 681–685 (1977).
[CrossRef]

1975 (1)

D. von der Linde and A. M. Glass, “Photorefractive effects for reversible holographic storage of information,” Appl. Phys. 8, 85–100 (1975).
[CrossRef]

1971 (1)

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

1969 (2)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

H. W. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

1963 (1)

Aharoni, A.

Amodei, J. J.

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

Bashaw, M. C.

Brady, D.

Burke, W. J.

W. J. Burke and P. Sheng, “Cross talk noise from multiple thick-phase holograms,” J. Appl. Phys. 48, 681–685 (1977).
[CrossRef]

Glass, A. M.

D. von der Linde and A. M. Glass, “Photorefractive effects for reversible holographic storage of information,” Appl. Phys. 8, 85–100 (1975).
[CrossRef]

Heanue, J. F.

Hesselink, L.

Hsu, K.

Kamshilin, A. A.

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Holographic storage of information and peculiarities of light diffraction in birefringent electro-optic crystals,” Opt. Laser Technol. 6, 149–151 (1979).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Kogelnik, H. W.

H. W. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

Külich, H. C.

H. C. Külich, “A new approach to read volume holograms at different wavelengths,” Opt. Commun. 64, 407–411 (1987).
[CrossRef]

Li, H. S.

Mok, F.

Petrov, M. P.

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Holographic storage of information and peculiarities of light diffraction in birefringent electro-optic crystals,” Opt. Laser Technol. 6, 149–151 (1979).
[CrossRef]

Psaltis, D.

Sheng, P.

W. J. Burke and P. Sheng, “Cross talk noise from multiple thick-phase holograms,” J. Appl. Phys. 48, 681–685 (1977).
[CrossRef]

Staebler, D. L.

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

Stepanov, S. I.

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Holographic storage of information and peculiarities of light diffraction in birefringent electro-optic crystals,” Opt. Laser Technol. 6, 149–151 (1979).
[CrossRef]

van Heerden, P. J.

von der Linde, D.

D. von der Linde and A. M. Glass, “Photorefractive effects for reversible holographic storage of information,” Appl. Phys. 8, 85–100 (1975).
[CrossRef]

Walkup, J. F.

Appl. Opt. (1)

Appl. Phys. (1)

D. von der Linde and A. M. Glass, “Photorefractive effects for reversible holographic storage of information,” Appl. Phys. 8, 85–100 (1975).
[CrossRef]

Appl. Phys. Lett. (1)

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

Bell Sys. Tech. J. (2)

H. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

H. W. Kogelnik, “Coupled wave theory for thick hologram gratings,” Bell Sys. Tech. J. 48, 2909–2947 (1969).
[CrossRef]

J. Appl. Phys. (1)

W. J. Burke and P. Sheng, “Cross talk noise from multiple thick-phase holograms,” J. Appl. Phys. 48, 681–685 (1977).
[CrossRef]

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

Opt. Commun. (1)

H. C. Külich, “A new approach to read volume holograms at different wavelengths,” Opt. Commun. 64, 407–411 (1987).
[CrossRef]

Opt. Laser Technol. (1)

M. P. Petrov, S. I. Stepanov, and A. A. Kamshilin, “Holographic storage of information and peculiarities of light diffraction in birefringent electro-optic crystals,” Opt. Laser Technol. 6, 149–151 (1979).
[CrossRef]

Opt. Lett. (2)

Other (3)

E. K. Gulanyan, I. R. Dorosh, V. D. Iskin, A. L. Mikaélyan, and M. A. Maíorchuk, “Nondestructive readout of holograms in iron-doped lithium niobate crystals,” Sov. J. Quantum Electron. 9 (5), 647–649 (1979).
[CrossRef]

H. C. Külich and E. Krätzig, “Reconstruction of volume holograms at different wavelengths,” in Nonlinear Optical Materials III, P. Guenter, ed., Proc. SPIE 1273, 60–67 (1990).
[CrossRef]

A. Aharoni, M. C. Bashaw and, L. Hesselink, “Capacity considerations for multiplexed holographic optical data storage,” in Practical Holography VII: Imaging and Materials, S. A. Benton, ed., Proc. SPIE 1914, 56–65 (1993).

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Figures (16)

Fig. 1
Fig. 1

System configuration used to obtain the modeling results. The first lens (left-hand side) Fourier-transforms the SLM data. The second lens (right-hand side) Fourier-transforms the data to be read by the camera. Note that the medium shape is not generally assumed to be cubic.

Fig. 2
Fig. 2

Circle showing the set of all possible grating K vectors that are obtainable in reciprocal space with the shown reference k vector.

Fig. 3
Fig. 3

Use of the writing signals and reference beams as shown permits the grating desired to be read to be formed by the writing beams.

Fig. 4
Fig. 4

Single reading page written with four writing pages: Only the four reading-signal vectors shown can be written with no mismatch. All other points being written will have a mismatch proportional to the separation between the reading and writing circles. Thus, writing with multiple pages that are closely spaced decreases the mismatch.

Fig. 5
Fig. 5

When multiple pages of data are to be read, multiple reading pages intersect a single writing page. Thus, a single writing page may write data for several reading pages.

Fig. 6
Fig. 6

Five reading pages and the range of writing reference angles to which each page corresponds. This range allows the required set of writing pages to be determined. Overlap of data from multiple reading pages onto a single writing page is also shown.

Fig. 7
Fig. 7

Diagram showing the linear relation between the number of writing and reading pages: Mapping the reading points to the writing points allows the number of writing pages needed for a given number of reading pages to be calculated (Δ k ρ W is equal to Δ k ρR ).

Fig. 8
Fig. 8

Reading and writing vectors used to form the same grating: After drawing a dividing line, symmetry causes right triangles to result; thus the reading and writing signals can easily be related.

Fig. 9
Fig. 9

Determination from a given reading signal and reference angle of the corresponding writing signal and reference angle: The boldface line segment shows gratings within a single page of reading data. The parallelogram shows gratings within a range of reading pages. The horizontal (vertical) dashed lines allow one to map a point to its corresponding writing reference (writing signal) numerical aperture (NA).

Fig. 10
Fig. 10

Example of a page of data to be written to allow five pages of checkered data to be read. Each strip being written with this page is part of one of the pages to be read. A value of 2 was chosen for Δ k R k W , as well as a sample length of 0.4 mm, so that the separation between strips and the widths of the strips can clearly be seen.

Fig. 11
Fig. 11

Factor by which the diffraction efficiency of a point is reduced plotted versus the z component of the point’s ideal writing reference angle: Four pages are shown that could be used to write the point. The solid curve shows the maximized diffraction-efficiency factor. The dashed curves indicate the diffraction-efficiency factor obtainable when a page other than the page with the closest writing reference angle is used for writing.

Fig. 12
Fig. 12

Minimum number of pages that needs to be written to read a single page plotted as a function of the ratio of the wavelengths while the writing wavelength remains fixed at 514 nm. The graph verifies the theoretical result as calculated by means of Eq. (23).

Fig. 13
Fig. 13

Ratio of writing pages to reading pages as a function of the ratio of the wavelengths.

Fig. 14
Fig. 14

Two spheres representing possible reading and writing gratings as viewed from along the x axis. The dashed curves indicate reading and writing grating vectors corresponding to vertical displacements on the camera and SLM, respectively.

Fig. 15
Fig. 15

Infinitesimal displacements about the intersection of the reading and writing spheres where x = 0. Projection of the reading displacements to the writing displacements allows the derivative d Rz /d Wz to be calculated.

Fig. 16
Fig. 16

Sphere of writing gratings as viewed from the x axis: Considering the displacement of a point originally at x = 0 allows the curvature of the divisions between pages to be calculated.

Equations (82)

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K=kσ-kρ,
PW=N+RPR-1,
ηRW=η0N+RPR-12,
θρW=θmid+sin-1sinθhalf RkR/kW,
θσW=θmid-sin-1sinθhalf RkR/kW,
θmid=θρR+θσR/2,
θhalfR=θρR-θσR/2,
Kx=kσRx=kR sin θσR cos ϕσR, Ky=kσRy-kρRy=kR sin θσR sin ϕσR-kR sin θρR,Kz=kσRz-kρRz=kR cos θσR-kR cos θρR,
Kx=kxσWx=kW sin θσW cos ϕσW, Ky=kσWy-kρWy=kW sin θσW sin ϕσW-kW sin ρϕW, Kz=kσWz-kρWz=kW cos θσW-kW cos θρW.
Kz+kW cos θρW2+Ky+kW sin θρW2=kW2-Kx2,
-K2/2kW=Ky sin θρW+Kz cos θρW.
A sin ϕ+B cos ϕ=A2+B2 sinϕ+tan-1B/A.
θρW=-sin-1K22kWKy2+Kz21/2-tan-1KzKy.
ξ=LkWΔθρWkˆρW×kˆσW·xˆ2kˆσR·kˆσW cosθσR,
ΔθσWΔθρW=cosθhalfR+θhalfWcosθhalfR-θhalfW=cosθhalfR+sin-1kRkwsinθhalfRcosθhalfR-sin-1kRkwsinθhalfR.
ξ  ΔθWkWL2<ΔkρWzL4 sinθρW.
ΔkρWz=4 ξmax sinθρW/L.
N=kWNAminΔkρWz=NAminLkWξmax cosθρW.
dθρW=1-kR/kWcosθhalfR1-kR/kW2 sin2θhalfRdθσR2.
NAρW=1-kR/kWcosθhalfR1-kR/kW2 sin2θhalfR×sinθρWsinθρRNAσR2.
NAρR=2xmaxf2+xmax22xmaxf.
NAρW=1-2 kR/kW2-1-1/2sinθρWxmaxf.
N=1-2kR/kW2-1-1/2LkWxmax4fξmax.
dθρW=1+2kR/kW2-1-1/2dθρR2.
RdPW/dPR=kWNAρWΔkρWzkRNAρRΔkρRz=kWΔkρRzdθρW sin θρWkRΔkρWzdθρR sin θρR.
R=ΔkρRzΔkρWzkW2kR1+2kR/kW2-1-1/2sin θρW.
drWdrR=zWzRzWxRxWzRxWxR=kRkWD001,
D=1kˆRρ·kˆWρ.
R=nftanθhalfWsinθσW-θmW.
PW=SΔkρWz,
ηRW=η0PW2sinc2 ξ=η0ΔkρW2S2sinc2ΔkρWzL4 sin θρW.
ΔkρWz=j2πL sin θρW, for integers j.
ξ<π,
ΔkρWz<4πL sin θρW.
ξ=π2,
ΔkρWz=2πL sin θρW.
ξcjo-ξcjRW<ξmax.
ΔkρRz=2πL s, for any positive integer s.
PWRPR=PR sin θρW1+2kR/kW2-1-1/2/2.
ηRW=η0/V,
Vπ sin θρW1+2 kR/kW2-1-1/2/42.
kρRθσR, ϕσR-kρRθρR=K=kσWθσW, ϕσW-kρWθρW,
kσR=kσW-kρW+kρR.
kσR=KσWθσW,ϕσW-kρWθρW+kρRθρR.
MkˆσR=ΔkσW-ΔkρW,
ΔkσWkσW-kσW, ΔkρWkρW-kρW.
M=-ΔkρW·kˆσWkˆσR·kˆσW-θρW-θρWkWkˆρW×xˆ·kˆσWkˆσR·kˆσW=ΔθρWkWkˆρW×kˆσW·xˆkˆσR·kˆσW.
ξ=kR2-kσR24kσRzL
ξkR-kσR2 cosθσRL.
ξ=LkWΔθρWkˆρW×kˆσW·xˆ2kˆσR·kˆσW cosθσR.
ΔθσW cosθhalfR-θhalfW-ΔθρW cosθhalfR+θhalfW=0.
sinθhalfW=kRkWsinθhalfR.
ΔθσWΔθσW=cosθhalfR+θhalfWcosθhalfR-θhalfW=cosθhalfR+sin-1kRkW sin θhalfRcosθhalfR-sin-1kRkW sin θhalfR.
zR, xR  kzR, kxR  kzW, kxW  zW, xW.
rR  kR  kW  rW.
kR,W=kR,WnrR,WlR,W,
lR,W2=f2+rR,W2,
kR,WrR,W=kR,WzzR,WkR,WzxR,WkR,WxzR,WkR,WxxR,W=kR,WnlR,W3lR,W2-zR,W2-zR,WxR,W-zR,WxR,WlR,W2-xR,W2.
kRrR=kRnlR3lR2-zR2-zRxR-zRxRlR2-xR2.
rWkW=nlWkWf2lW2-xW2-zWxW-zWxWlW2-zW2.
dkR=dkRy1-zR2n2f2+zR21/2,dkW=dkWy1-zW2n2f2+zW21/2.
dkR=dkW cosθW-θR.
dkR=dkWkˆRρ·kˆWρ.
dkWzdkRz=n-zW2f2+zW21/2n-zR2f2+zR21/21kˆRρ·kˆWρ.
dkWdkR=D001.
drWdrR=kRkWlWlR3DlW200lR2.
drWdrR=kRkWD001,
D=1kˆRρ·kˆWρ.
k=kσ-kρ.
KW-kρW=kW, KR-kρR=kR.
K·kρW-kρR=0,
dz=dx2/2R,
kcent=kW cosθhalfW.
kzy=kcentcosθhalfW-Δθ=kWcosθhalfWcosθhalfW-ΔθkW1-ΔθtanθhalfW.
kx2+kzy2=kW2 kx2=2kW2Δθ tanθhalfW.
kxkWXxf,
kzkWXzf.
kz=-kW cosθσW-θmW.
-kW cosθσW-θm=kWXzf.
kW sinθσW-θmΔθ=kWXdzf
dz=kWXkWsinθσW-θmW2 tanθhalfW1fdx2.
R=nf tanθhalfWsinθσW-θmW,

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