Abstract

We focus on the investigation of multilayer recording in microholographic data storage. We have developed a numerical model for calculating the electromagnetic scattering from thick microholographic gratings using the Born approximation and the direct volume integral. The signal-to-noise ratio and bit error rate were calculated to estimate the noise arising from interlayer and interhologram cross talk. Measurements were done to prove the validity of the model. The results of our calculations and the measurements show good agreement. We present the application of the model to the investigation of confocal filtering at the image plane and to the evaluation of positioning and wavelength tolerances.

© 2007 Optical Society of America

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  1. H. J. Eichler, P. Kuemmel, S. Orlic, and A. Wappelt, "High-density disk storage by multiplexed microholograms," IEEE J. Sel. Top. Quantum Electron. 4, 840-848 (1998).
    [CrossRef]
  2. S. Orlic, E. Dietz, S. Frohmann, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "High-density multilayer recording of microgratings for optical data storage," in Proc. SPIE 5521, 161-173 (2004).
  3. S. Orlic, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "Optical storage in photopolymers using 3D microgratings," in Proc. SPIE 4459, 323-333 (2002).
  4. R. R. McLeod, A. J. Daiber, M. E. McDonald, T. L. Robertson, T. Slage, S. L. Sochava, and L. Hesselink, "Microholographic multilayer optical disk data storage," Appl. Opt. 44, 3197-3207 (2005).
    [CrossRef] [PubMed]
  5. S. Orlic, S. Ulm, and H. J. Eichler, "3D bit-oriented optical storage in photopolymers," J. Opt. A , Pure Appl. Opt. 3, 72-81 (2001).
    [CrossRef]
  6. J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).
  7. G. Barbastathis, M. Levene, and D. Psaltis, "Shift multiplexing with spherical reference waves," Appl. Opt. 35, 2403-2417 (1996).
    [CrossRef] [PubMed]
  8. H. J. Coufal, D. Psaltis, and G. T. Sincerbox, Holographic Data Storage (Springer, 2000).
  9. G. Gao and C. Torres-Verdín, "High-order generalized extended Born approximation for electromagnetic scattering," IEEE Trans. Antennas Propag. 54, 1243-1256 (2006).
    [CrossRef]
  10. B. Gombkötő, P. Koppa, P. Maák, and E. Lőrincz, "Application of the fast-Fourier-transform-based volume integral equation method to model volume diffraction in shift multiplexed holographic data storage," J. Opt. Soc. Am. A 23, 2954-2960 (2006).
    [CrossRef]

2006 (2)

2005 (1)

2004 (1)

S. Orlic, E. Dietz, S. Frohmann, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "High-density multilayer recording of microgratings for optical data storage," in Proc. SPIE 5521, 161-173 (2004).

2002 (1)

S. Orlic, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "Optical storage in photopolymers using 3D microgratings," in Proc. SPIE 4459, 323-333 (2002).

2001 (1)

S. Orlic, S. Ulm, and H. J. Eichler, "3D bit-oriented optical storage in photopolymers," J. Opt. A , Pure Appl. Opt. 3, 72-81 (2001).
[CrossRef]

1998 (1)

H. J. Eichler, P. Kuemmel, S. Orlic, and A. Wappelt, "High-density disk storage by multiplexed microholograms," IEEE J. Sel. Top. Quantum Electron. 4, 840-848 (1998).
[CrossRef]

1996 (1)

Barbastathis, G.

Coufal, H. J.

H. J. Coufal, D. Psaltis, and G. T. Sincerbox, Holographic Data Storage (Springer, 2000).

Daiber, A. J.

Dietz, E.

S. Orlic, E. Dietz, S. Frohmann, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "High-density multilayer recording of microgratings for optical data storage," in Proc. SPIE 5521, 161-173 (2004).

Eichler, H. J.

S. Orlic, E. Dietz, S. Frohmann, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "High-density multilayer recording of microgratings for optical data storage," in Proc. SPIE 5521, 161-173 (2004).

S. Orlic, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "Optical storage in photopolymers using 3D microgratings," in Proc. SPIE 4459, 323-333 (2002).

S. Orlic, S. Ulm, and H. J. Eichler, "3D bit-oriented optical storage in photopolymers," J. Opt. A , Pure Appl. Opt. 3, 72-81 (2001).
[CrossRef]

H. J. Eichler, P. Kuemmel, S. Orlic, and A. Wappelt, "High-density disk storage by multiplexed microholograms," IEEE J. Sel. Top. Quantum Electron. 4, 840-848 (1998).
[CrossRef]

Frohmann, S.

S. Orlic, E. Dietz, S. Frohmann, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "High-density multilayer recording of microgratings for optical data storage," in Proc. SPIE 5521, 161-173 (2004).

Gao, G.

G. Gao and C. Torres-Verdín, "High-order generalized extended Born approximation for electromagnetic scattering," IEEE Trans. Antennas Propag. 54, 1243-1256 (2006).
[CrossRef]

Gombköto, B.

Hesselink, L.

Jackson, J. D.

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

Koppa, P.

Kuemmel, P.

H. J. Eichler, P. Kuemmel, S. Orlic, and A. Wappelt, "High-density disk storage by multiplexed microholograms," IEEE J. Sel. Top. Quantum Electron. 4, 840-848 (1998).
[CrossRef]

Levene, M.

Lorincz, E.

Maák, P.

McDonald, M. E.

McLeod, R. R.

Mueller, C.

S. Orlic, E. Dietz, S. Frohmann, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "High-density multilayer recording of microgratings for optical data storage," in Proc. SPIE 5521, 161-173 (2004).

S. Orlic, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "Optical storage in photopolymers using 3D microgratings," in Proc. SPIE 4459, 323-333 (2002).

Orlic, S.

S. Orlic, E. Dietz, S. Frohmann, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "High-density multilayer recording of microgratings for optical data storage," in Proc. SPIE 5521, 161-173 (2004).

S. Orlic, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "Optical storage in photopolymers using 3D microgratings," in Proc. SPIE 4459, 323-333 (2002).

S. Orlic, S. Ulm, and H. J. Eichler, "3D bit-oriented optical storage in photopolymers," J. Opt. A , Pure Appl. Opt. 3, 72-81 (2001).
[CrossRef]

H. J. Eichler, P. Kuemmel, S. Orlic, and A. Wappelt, "High-density disk storage by multiplexed microholograms," IEEE J. Sel. Top. Quantum Electron. 4, 840-848 (1998).
[CrossRef]

Psaltis, D.

Robertson, T. L.

Schoen, R.

S. Orlic, E. Dietz, S. Frohmann, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "High-density multilayer recording of microgratings for optical data storage," in Proc. SPIE 5521, 161-173 (2004).

S. Orlic, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "Optical storage in photopolymers using 3D microgratings," in Proc. SPIE 4459, 323-333 (2002).

Sincerbox, G. T.

H. J. Coufal, D. Psaltis, and G. T. Sincerbox, Holographic Data Storage (Springer, 2000).

Slage, T.

Sochava, S. L.

Torres-Verdín, C.

G. Gao and C. Torres-Verdín, "High-order generalized extended Born approximation for electromagnetic scattering," IEEE Trans. Antennas Propag. 54, 1243-1256 (2006).
[CrossRef]

Trefzer, M.

S. Orlic, E. Dietz, S. Frohmann, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "High-density multilayer recording of microgratings for optical data storage," in Proc. SPIE 5521, 161-173 (2004).

S. Orlic, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "Optical storage in photopolymers using 3D microgratings," in Proc. SPIE 4459, 323-333 (2002).

Ulm, S.

S. Orlic, S. Ulm, and H. J. Eichler, "3D bit-oriented optical storage in photopolymers," J. Opt. A , Pure Appl. Opt. 3, 72-81 (2001).
[CrossRef]

Wappelt, A.

H. J. Eichler, P. Kuemmel, S. Orlic, and A. Wappelt, "High-density disk storage by multiplexed microholograms," IEEE J. Sel. Top. Quantum Electron. 4, 840-848 (1998).
[CrossRef]

Appl. Opt. (2)

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

H. J. Eichler, P. Kuemmel, S. Orlic, and A. Wappelt, "High-density disk storage by multiplexed microholograms," IEEE J. Sel. Top. Quantum Electron. 4, 840-848 (1998).
[CrossRef]

IEEE Trans. Antennas Propag. (1)

G. Gao and C. Torres-Verdín, "High-order generalized extended Born approximation for electromagnetic scattering," IEEE Trans. Antennas Propag. 54, 1243-1256 (2006).
[CrossRef]

J. Opt. A (1)

S. Orlic, S. Ulm, and H. J. Eichler, "3D bit-oriented optical storage in photopolymers," J. Opt. A , Pure Appl. Opt. 3, 72-81 (2001).
[CrossRef]

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

Other (4)

J. D. Jackson, Classical Electrodynamics, 3rd ed. (Wiley, 1999).

H. J. Coufal, D. Psaltis, and G. T. Sincerbox, Holographic Data Storage (Springer, 2000).

S. Orlic, E. Dietz, S. Frohmann, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "High-density multilayer recording of microgratings for optical data storage," in Proc. SPIE 5521, 161-173 (2004).

S. Orlic, C. Mueller, R. Schoen, M. Trefzer, and H. J. Eichler, "Optical storage in photopolymers using 3D microgratings," in Proc. SPIE 4459, 323-333 (2002).

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Figures (15)

Fig. 1
Fig. 1

Calculated refractive index modulation of a microhologram, proportional to the local intensity of the interference between the signal and reference beams ( E r + E s ) 2 . The black is the unchanged background refractive index, and the gray scale shows the increase of the refractive index attributable to the exposure.

Fig. 2
Fig. 2

(Color online) Calculated intensity distribution of the diffracted beam before the objective lens at z = 5   mm from the hologram.

Fig. 3
Fig. 3

(Color online) Normalized diffraction efficiency as the function of dz beam displacement along the optical axis.

Fig. 4
Fig. 4

Model of the readout process in the microholographic data storage system: (1) laser diode, (2) collimator lens, (3) objective lens, (4) disk, (5) microholograms in the disk, (6) confocal filter. The solid line indicates the probe beam and the dotted line indicates the beam reflected from the microhologram.

Fig. 5
Fig. 5

(Color online) Calculated beam intensity (a), (c) before the objective lens and (b), (d) in the output plane. (a) and (b) show the intensity distribution created by the currently read hologram; (c) and (d) are created by a hologram in the first layer with d z = 6 μ m and d y = 0.5 μ m position. In (b) and (d) the intensity distribution is shown at the plane of the confocal filter. The white circle represents the confocal filter. We can see that the confocal filter blocks the major part of the noise.

Fig. 6
Fig. 6

Sample histogram. The histogram shows the probability distribution of the zero (plotted as 0) and one bits (plotted as X) as a function of their energy at the output.

Fig. 7
Fig. 7

Projected histogram showing how the sample histogram from Fig. 6 fits into a projected histogram.

Fig. 8
Fig. 8

Calculated distribution of the readout signal for single-layer configuration.

Fig. 9
Fig. 9

Calculated distribution of the read energy for multilayer configuration setup with 18 μ m layer separation.

Fig. 10
Fig. 10

Distribution of the readout energy for multilayer configuration with 6 μ m layer separation.

Fig. 11
Fig. 11

Probability distribution of zeros and ones with fitted Gaussian functions for the case of (a) no confocal filter, BER = 3.6 × 10 - 2 ; (b) 10 μ m confocal filter, BER = 1.5 × 10 - 7 ; and (c) 20 μ m confocal filter, BER = 1.2 × 10 - 3 .

Fig. 12
Fig. 12

Probability distribution of zeros and ones with fitted Gaussian functions for the case of 0.2 μ m track error with 12 μ m confocal filter size, BER = 2.5 × 10 - 4 .

Fig. 13
Fig. 13

Bit error rate during readout as the function of track error. Tracks are 0.7 μ m from each other. BER increases exponentially up to half the track distance.

Fig. 14
Fig. 14

Probability distribution of zeros and ones with fitted Gaussian functions for the case of a focus error of 0.3 μm with a confocal filter size of 12 μ m , BER = 6.2 × 10 6 .

Fig. 15
Fig. 15

Wavelength selectivity curve—diffracted energy in the function of the probe beam wavelength. The hologram was written into the media with a 405   nm blue wavelength and readout at different wavelengths up to 445   nm .

Equations (6)

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E d ( x 1 , y 1 , z 1 , Δ x , Δ y , Δ z )
= k 2 4 π E p ( x + Δ x , y + Δ y , z + Δ z ) × δ n E r * ( x , y , z ) E s ( x , y , z ) × exp ( i k ( x 1 x ) 2 + ( y 1 y ) 2 + ( z 1 z ) 2 ) ( x 1 x ) 2 + ( y 1 y ) 2 + ( z 1 z ) 2  d x d y d z ,
E ( x , y , z ) = 2 π w ( z )  exp ( - x 2 + y 2 w ( z ) 2 ) × exp ( i k x 2 + y 2 2 R ( z ) + i k z i Φ ( z ) ) ,
E ( N ) = E b + G ( Δ ε ε E ( N 1 ) ) ,
S N R = μ 1 μ 0 σ 1 2 + σ 0 2 ,
B E R = 1 N ( 0 E c W 1 ( E ) d E + E c W 0 ( E ) d E ) ,

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