Abstract

Various multilayer optical data storage methods have been proposed in which bits are written in an initially homogeneous material. To varying degrees, all of these methods will be constrained by phase aberrations that decrease the Strehl ratio as the number of layers and index perturbation of each bit are increased. Although the exact problem is theoretically and numerically intractable, statistical derivations of the impact are possible. These analytic expressions are derived and validated with simulations of low-capacity disks, and then are used to establish limits in the interesting high-capacity case. The resulting approximate expressions are shown to be remarkably simple and also potentially serious in limiting multilayer data storage capacities.

© 2009 Optical Society of America

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2008 (2)

2007 (4)

2005 (2)

2004 (1)

M. S. Akselrod, S. S. Orlov, and G. M. Akselrod, “Bit-wise volumetric optical memory utilizing two-photon absorption in aluminum oxide medium,” Jpn. J. Appl. Phys., Part 1 43, 4908-4911 (2004).
[CrossRef]

2003 (1)

G. W. Burr, “Three-dimensional optical storage,” Proc. SPIE 5225, 78-92 (2003).
[CrossRef]

2001 (2)

R. Hagen and T. Bieringer, “Photoaddressable polymers for optical data storage,” Adv. Mater. (Weinheim, Ger.) 13, 1805-1810 (2001).
[CrossRef]

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]

2000 (4)

H. Zhang, A. S. Dvornikov, E. P. Walker, N. H. Kim, and F. B. McCormick, “Single-beam two-photon-recorded monolithic multi-layer optical disks,” Proc. SPIE 4090, 174-178 (2000).
[CrossRef]

Y. Kawata and S. Kawata, “Three-dimensional optical data storage using photochromic materials,” Chem. Rev. (Washington, D.C.) 100, 1777-1788 (2000).
[CrossRef]

B. M. King and M. A. Neifeld, “Sparse modulation coding for increased capacity in volume holographic storage,” Appl. Opt. 39, 6681-6688 (2000).
[CrossRef]

M. M. Wang and S. C. Esener, “Three-dimensional optical data storage in a fluorescent dye-doped photopolymer,” Appl. Opt. 39, 1826-1834 (2000).
[CrossRef]

1999 (3)

D. Day, M. Gu, and A. Smallridge, “Use of two-photon excitation for erasable-rewritable three-dimensional bit optical data storage in a photorefractive polymer,” Opt. Lett. 24, 948-950 (1999).
[CrossRef]

L. Dhar, A. Hale, H. E. Katz, M. L. Schilling, M. G. Schnoes, and F. C. Schilling, “Recording media that exhibit high dynamic range for digital holographic data storage,” Opt. Lett. 24, 487-489 (1999).
[CrossRef]

A. Partovi, D. Peale, M. Wuttig, C. A. Murray, G. Zydzik, L. Hopkins, K. Baldwin, W. S. Hobson, J. Wynn, J. Lopata, L. Dhar, R. Chichester, and J. H.-J. Yeh, “High-power laser light source for near-field optics and its application to high-density optical data storage,” Appl. Phys. Lett. 75, 1515-1520 (1999).
[CrossRef]

1998 (2)

A. Toriumi, S. Kawata, and M. Gu, “Reflection confocal microscope readout system for three-dimensional photochromic optical data storage,” Opt. Lett. 23, 1924-1926 (1998).
[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]

1997 (1)

1996 (5)

1995 (2)

S. Homan and A. E. Wilner, “High-capacity optical storage using multiple wavelengths, multiple layers and volume holograms,” Electron. Lett. 31, 621-623 (1995).
[CrossRef]

Y. Kawata, H. Ueki, Y. Hashimoto, and S. Kawata, “Three-dimensional optical memory with a photorefractive crystal,” Appl. Opt. 34, 4105-4110 (1995).
[CrossRef] [PubMed]

1994 (1)

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388-390 (1994).
[CrossRef]

1993 (1)

W. J. Gambogi, A. M. Weber, and T. J. Trout, “Advances and applications of DuPont holographic photopolymers,” Proc. SPIE 2043, 2-13 (1993).

1991 (2)

1989 (1)

D. A. Parthenopoulos and P. M. Rentzepis, “Three-dimensional optical storage memory,” Science 245, 843-845 (1989).
[CrossRef] [PubMed]

1966 (1)

1963 (1)

Akselrod, G. M.

M. S. Akselrod, S. S. Orlov, and G. M. Akselrod, “Bit-wise volumetric optical memory utilizing two-photon absorption in aluminum oxide medium,” Jpn. J. Appl. Phys., Part 1 43, 4908-4911 (2004).
[CrossRef]

Akselrod, M. S.

M. S. Akselrod, S. S. Orlov, and G. M. Akselrod, “Bit-wise volumetric optical memory utilizing two-photon absorption in aluminum oxide medium,” Jpn. J. Appl. Phys., Part 1 43, 4908-4911 (2004).
[CrossRef]

Arnaud, C.

Baldwin, K.

A. Partovi, D. Peale, M. Wuttig, C. A. Murray, G. Zydzik, L. Hopkins, K. Baldwin, W. S. Hobson, J. Wynn, J. Lopata, L. Dhar, R. Chichester, and J. H.-J. Yeh, “High-power laser light source for near-field optics and its application to high-density optical data storage,” Appl. Phys. Lett. 75, 1515-1520 (1999).
[CrossRef]

Bieringer, T.

R. Hagen and T. Bieringer, “Photoaddressable polymers for optical data storage,” Adv. Mater. (Weinheim, Ger.) 13, 1805-1810 (2001).
[CrossRef]

Bletcher, W.

Y. Zhang, T. D. Milster, J. Butz, W. Bletcher, K. J. Erwin, and E. Walker, “Signal, cross talk and signal to noise ratio in bit-wise volumetric optical data storage,” in 2002 International Symposium on Optical Memory and Optical Data Storage Topical Meeting (IEEE, 2002), pp. 246-248.
[CrossRef]

Boden, E.-P.

Burr, G. W.

G. W. Burr, “Three-dimensional optical storage,” Proc. SPIE 5225, 78-92 (2003).
[CrossRef]

Butz, J.

Y. Zhang, T. D. Milster, J. Butz, W. Bletcher, K. J. Erwin, and E. Walker, “Signal, cross talk and signal to noise ratio in bit-wise volumetric optical data storage,” in 2002 International Symposium on Optical Memory and Optical Data Storage Topical Meeting (IEEE, 2002), pp. 246-248.
[CrossRef]

Callan, J. P.

Carré, C.

Chichester, R.

A. Partovi, D. Peale, M. Wuttig, C. A. Murray, G. Zydzik, L. Hopkins, K. Baldwin, W. S. Hobson, J. Wynn, J. Lopata, L. Dhar, R. Chichester, and J. H.-J. Yeh, “High-power laser light source for near-field optics and its application to high-density optical data storage,” Appl. Phys. Lett. 75, 1515-1520 (1999).
[CrossRef]

Coblentz, K.

Contreras, K.

Coufal, H. J.

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

Daiber, A.

A. Daiber, R. McLeod, and R. Snyder, U.S. patent 6,549,664, “Sparse modulation codes for holographic data storage,” (15 April 2003).

Daiber, A. J.

Day, D.

Dhal, P. K.

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerimization methods for volume hologram recording,” Proc. SPIE 2689, 127-141 (1996).
[CrossRef]

Dhar, L.

A. Partovi, D. Peale, M. Wuttig, C. A. Murray, G. Zydzik, L. Hopkins, K. Baldwin, W. S. Hobson, J. Wynn, J. Lopata, L. Dhar, R. Chichester, and J. H.-J. Yeh, “High-power laser light source for near-field optics and its application to high-density optical data storage,” Appl. Phys. Lett. 75, 1515-1520 (1999).
[CrossRef]

L. Dhar, A. Hale, H. E. Katz, M. L. Schilling, M. G. Schnoes, and F. C. Schilling, “Recording media that exhibit high dynamic range for digital holographic data storage,” Opt. Lett. 24, 487-489 (1999).
[CrossRef]

Dietz, E.

Dubois, M.

Dvornikov, A.

Dvornikov, A. S.

H. Zhang, A. S. Dvornikov, E. P. Walker, N. H. Kim, and F. B. McCormick, “Single-beam two-photon-recorded monolithic multi-layer optical disks,” Proc. SPIE 4090, 174-178 (2000).
[CrossRef]

Eichler, H. J.

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]

Erben, C.

Erwin, K. J.

Y. Zhang, T. D. Milster, J. Butz, W. Bletcher, K. J. Erwin, and E. Walker, “Signal, cross talk and signal to noise ratio in bit-wise volumetric optical data storage,” in 2002 International Symposium on Optical Memory and Optical Data Storage Topical Meeting (IEEE, 2002), pp. 246-248.
[CrossRef]

Esener, S. C.

Finlay, R. J.

Frohmann, S.

Fujita, G.

K. Saito, T. Horigome, H. Miyamoto, H. Yamatsu, N. Tanabe, K. Hayashi, G. Fujita, S. Kobayashi, T. Kudo, and H. Uchiyama, “Drive system and readout characteristics of micro-reflector optical disc,” in Int. Soc. Opt. Eng., Proc. SPIE 6620, 66200B (2007).
[CrossRef]

Gambogi, W. J.

W. J. Gambogi, A. M. Weber, and T. J. Trout, “Advances and applications of DuPont holographic photopolymers,” Proc. SPIE 2043, 2-13 (1993).

Glezer, E. N.

Grabowski, M. W.

Gu, M.

Guattari, F.

Hagen, R.

R. Hagen and T. Bieringer, “Photoaddressable polymers for optical data storage,” Adv. Mater. (Weinheim, Ger.) 13, 1805-1810 (2001).
[CrossRef]

Hale, A.

Hashimoto, Y.

Hashizume, J.

H. Mikami, T. Shimano, H. Kudo, J. Hashizume, and H. Miyamoto, “Readout-signal amplification by homodyne detection scheme,” Proc. SPIE 6620, 662005 (2007).
[CrossRef]

Hayashi, K.

K. Saito, T. Horigome, H. Miyamoto, H. Yamatsu, N. Tanabe, K. Hayashi, G. Fujita, S. Kobayashi, T. Kudo, and H. Uchiyama, “Drive system and readout characteristics of micro-reflector optical disc,” in Int. Soc. Opt. Eng., Proc. SPIE 6620, 66200B (2007).
[CrossRef]

Her, T.-H.

Hesselink, L.

Hobson, W. S.

A. Partovi, D. Peale, M. Wuttig, C. A. Murray, G. Zydzik, L. Hopkins, K. Baldwin, W. S. Hobson, J. Wynn, J. Lopata, L. Dhar, R. Chichester, and J. H.-J. Yeh, “High-power laser light source for near-field optics and its application to high-density optical data storage,” Appl. Phys. Lett. 75, 1515-1520 (1999).
[CrossRef]

Homan, S.

S. Homan and A. E. Wilner, “High-capacity optical storage using multiple wavelengths, multiple layers and volume holograms,” Electron. Lett. 31, 621-623 (1995).
[CrossRef]

Hopkins, L.

A. Partovi, D. Peale, M. Wuttig, C. A. Murray, G. Zydzik, L. Hopkins, K. Baldwin, W. S. Hobson, J. Wynn, J. Lopata, L. Dhar, R. Chichester, and J. H.-J. Yeh, “High-power laser light source for near-field optics and its application to high-density optical data storage,” Appl. Phys. Lett. 75, 1515-1520 (1999).
[CrossRef]

Horigome, T.

K. Saito, T. Horigome, H. Miyamoto, H. Yamatsu, N. Tanabe, K. Hayashi, G. Fujita, S. Kobayashi, T. Kudo, and H. Uchiyama, “Drive system and readout characteristics of micro-reflector optical disc,” in Int. Soc. Opt. Eng., Proc. SPIE 6620, 66200B (2007).
[CrossRef]

Horner, M. G.

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerimization methods for volume hologram recording,” Proc. SPIE 2689, 127-141 (1996).
[CrossRef]

Huang, L.

Imaino, W.

K. A. Rubin, H. J. Rosen, W. W. Tang, W. Imaino, and T. C. Strand, “Multilevel volumetric optical disk storage,” in Optical Data Storage, Proc. SPIE 2338, 247-250 (1994).

Imaino, W. I.

H. J. Rosen, K. A. Rubin, W. C. Tang, and W. I. Imaino, “Multilayer optical recording (MORE),” in Optical Data Storage 1995, Proc. SPIE 2514, 14-19 (1995).

W. I. Imaino, H. J. Rosen, K. A. Rubin, and T. S. Strand, “Extending the compact disk format to high capacity for video applications,” in Optical Data Storage, Proc. SPIE 2338, 254-258 (1994).

Ingwall, R. T.

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerimization methods for volume hologram recording,” Proc. SPIE 2689, 127-141 (1996).
[CrossRef]

Jradi, S.

Jusiexclkaitis, R.

Katz, H. E.

Kawata, S.

Kawata, Y.

Kim, N. H.

H. Zhang, A. S. Dvornikov, E. P. Walker, N. H. Kim, and F. B. McCormick, “Single-beam two-photon-recorded monolithic multi-layer optical disks,” Proc. SPIE 4090, 174-178 (2000).
[CrossRef]

King, B. M.

Kino, G. S.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388-390 (1994).
[CrossRef]

Kobayashi, S.

K. Saito, T. Horigome, H. Miyamoto, H. Yamatsu, N. Tanabe, K. Hayashi, G. Fujita, S. Kobayashi, T. Kudo, and H. Uchiyama, “Drive system and readout characteristics of micro-reflector optical disc,” in Int. Soc. Opt. Eng., Proc. SPIE 6620, 66200B (2007).
[CrossRef]

Kolb, E. S.

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerimization methods for volume hologram recording,” Proc. SPIE 2689, 127-141 (1996).
[CrossRef]

Koppa, P.

Kozma, A.

Kudo, H.

H. Mikami, T. Shimano, H. Kudo, J. Hashizume, and H. Miyamoto, “Readout-signal amplification by homodyne detection scheme,” Proc. SPIE 6620, 662005 (2007).
[CrossRef]

Kudo, T.

K. Saito, T. Horigome, H. Miyamoto, H. Yamatsu, N. Tanabe, K. Hayashi, G. Fujita, S. Kobayashi, T. Kudo, and H. Uchiyama, “Drive system and readout characteristics of micro-reflector optical disc,” in Int. Soc. Opt. Eng., Proc. SPIE 6620, 66200B (2007).
[CrossRef]

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).
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Lawrence, B.-L.

Leith, E. N.

Li, H.-Y. S.

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerimization methods for volume hologram recording,” Proc. SPIE 2689, 127-141 (1996).
[CrossRef]

Longley, K.-L.

Lopata, J.

A. Partovi, D. Peale, M. Wuttig, C. A. Murray, G. Zydzik, L. Hopkins, K. Baldwin, W. S. Hobson, J. Wynn, J. Lopata, L. Dhar, R. Chichester, and J. H.-J. Yeh, “High-power laser light source for near-field optics and its application to high-density optical data storage,” Appl. Phys. Lett. 75, 1515-1520 (1999).
[CrossRef]

Lorincz, E.

Maire, G.

Mamin, H. J.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388-390 (1994).
[CrossRef]

Mansuripur, M.

M. Mansuripur, The Physical Principles of Magneto-optical Recording (Cambridge U. Press, 1995), pp. 675-676.

Marks, J.

Massey, N.

Mazur, E.

McCormick, F. B.

H. Zhang, A. S. Dvornikov, E. P. Walker, N. H. Kim, and F. B. McCormick, “Single-beam two-photon-recorded monolithic multi-layer optical disks,” Proc. SPIE 4090, 174-178 (2000).
[CrossRef]

McDonald, M. E.

McLeod, R.

A. Daiber, R. McLeod, and R. Snyder, U.S. patent 6,549,664, “Sparse modulation codes for holographic data storage,” (15 April 2003).

McLeod, R. R.

Mikami, H.

H. Mikami, T. Shimano, H. Kudo, J. Hashizume, and H. Miyamoto, “Readout-signal amplification by homodyne detection scheme,” Proc. SPIE 6620, 662005 (2007).
[CrossRef]

Milosavljevic, M.

Milster, T. D.

Y. Zhang, T. D. Milster, J. Butz, W. Bletcher, K. J. Erwin, and E. Walker, “Signal, cross talk and signal to noise ratio in bit-wise volumetric optical data storage,” in 2002 International Symposium on Optical Memory and Optical Data Storage Topical Meeting (IEEE, 2002), pp. 246-248.
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Minns, R. A.

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerimization methods for volume hologram recording,” Proc. SPIE 2689, 127-141 (1996).
[CrossRef]

Miyamoto, H.

H. Mikami, T. Shimano, H. Kudo, J. Hashizume, and H. Miyamoto, “Readout-signal amplification by homodyne detection scheme,” Proc. SPIE 6620, 662005 (2007).
[CrossRef]

K. Saito, T. Horigome, H. Miyamoto, H. Yamatsu, N. Tanabe, K. Hayashi, G. Fujita, S. Kobayashi, T. Kudo, and H. Uchiyama, “Drive system and readout characteristics of micro-reflector optical disc,” in Int. Soc. Opt. Eng., Proc. SPIE 6620, 66200B (2007).
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Morris, G. M.

Murray, C. A.

A. Partovi, D. Peale, M. Wuttig, C. A. Murray, G. Zydzik, L. Hopkins, K. Baldwin, W. S. Hobson, J. Wynn, J. Lopata, L. Dhar, R. Chichester, and J. H.-J. Yeh, “High-power laser light source for near-field optics and its application to high-density optical data storage,” Appl. Phys. Lett. 75, 1515-1520 (1999).
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Neifeld, M. A.

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Z. Nagy, P. Koppa, E. Dietz, S. Frohmann, S. Orlic, and E. Lorincz, “Modeling of multilayer microholographic data storage,” Appl. Opt. 46, 753-761 (2007).
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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]

Orlov, S. S.

M. S. Akselrod, S. S. Orlov, and G. M. Akselrod, “Bit-wise volumetric optical memory utilizing two-photon absorption in aluminum oxide medium,” Jpn. J. Appl. Phys., Part 1 43, 4908-4911 (2004).
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D. A. Parthenopoulos and P. M. Rentzepis, “Three-dimensional optical storage memory,” Science 245, 843-845 (1989).
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Partovi, A.

A. Partovi, D. Peale, M. Wuttig, C. A. Murray, G. Zydzik, L. Hopkins, K. Baldwin, W. S. Hobson, J. Wynn, J. Lopata, L. Dhar, R. Chichester, and J. H.-J. Yeh, “High-power laser light source for near-field optics and its application to high-density optical data storage,” Appl. Phys. Lett. 75, 1515-1520 (1999).
[CrossRef]

Pauliat, G.

Peale, D.

A. Partovi, D. Peale, M. Wuttig, C. A. Murray, G. Zydzik, L. Hopkins, K. Baldwin, W. S. Hobson, J. Wynn, J. Lopata, L. Dhar, R. Chichester, and J. H.-J. Yeh, “High-power laser light source for near-field optics and its application to high-density optical data storage,” Appl. Phys. Lett. 75, 1515-1520 (1999).
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D. H. Pontius, “Confocal optical microscopy system for multi-level data storage and retrieval,” U.S. patent 5619371 (8 April 1997).

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

Rentzepis, P.

Rentzepis, P. M.

D. A. Parthenopoulos and P. M. Rentzepis, “Three-dimensional optical storage memory,” Science 245, 843-845 (1989).
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Roosen, G.

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W. I. Imaino, H. J. Rosen, K. A. Rubin, and T. S. Strand, “Extending the compact disk format to high capacity for video applications,” in Optical Data Storage, Proc. SPIE 2338, 254-258 (1994).

K. A. Rubin, H. J. Rosen, W. W. Tang, W. Imaino, and T. C. Strand, “Multilevel volumetric optical disk storage,” in Optical Data Storage, Proc. SPIE 2338, 247-250 (1994).

H. J. Rosen, K. A. Rubin, W. C. Tang, and W. I. Imaino, “Multilayer optical recording (MORE),” in Optical Data Storage 1995, Proc. SPIE 2514, 14-19 (1995).

Rubin, K. A.

H. J. Rosen, K. A. Rubin, W. C. Tang, and W. I. Imaino, “Multilayer optical recording (MORE),” in Optical Data Storage 1995, Proc. SPIE 2514, 14-19 (1995).

K. A. Rubin, H. J. Rosen, W. W. Tang, W. Imaino, and T. C. Strand, “Multilevel volumetric optical disk storage,” in Optical Data Storage, Proc. SPIE 2338, 247-250 (1994).

W. I. Imaino, H. J. Rosen, K. A. Rubin, and T. S. Strand, “Extending the compact disk format to high capacity for video applications,” in Optical Data Storage, Proc. SPIE 2338, 254-258 (1994).

Rugar, D.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388-390 (1994).
[CrossRef]

Saito, K.

K. Saito, T. Horigome, H. Miyamoto, H. Yamatsu, N. Tanabe, K. Hayashi, G. Fujita, S. Kobayashi, T. Kudo, and H. Uchiyama, “Drive system and readout characteristics of micro-reflector optical disc,” in Int. Soc. Opt. Eng., Proc. SPIE 6620, 66200B (2007).
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B. E. A. Saleh and M. C. Teich, “Fundamentals of Photonics,” in Wiley Series in Pure and Applied Optics (2009), Ch. 3.

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Schild, H. G.

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerimization methods for volume hologram recording,” Proc. SPIE 2689, 127-141 (1996).
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Schilling, M. L.

Schnoes, M. G.

Shi, X.

Shimano, T.

H. Mikami, T. Shimano, H. Kudo, J. Hashizume, and H. Miyamoto, “Readout-signal amplification by homodyne detection scheme,” Proc. SPIE 6620, 662005 (2007).
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H. J. Coufal, D. Psaltis, and G. T. Sincerbox, Holographic Data Storage (Springer, Berlin, 2000).

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Smallridge, A.

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W. J. Smith, Modern Optical Engineering, Second Ed. (McGraw Hill, 1990), p. 336.

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A. Daiber, R. McLeod, and R. Snyder, U.S. patent 6,549,664, “Sparse modulation codes for holographic data storage,” (15 April 2003).

Sochava, S. L.

Steinberg, I. S.

I. S. Steinberg, “Multilayer recording of the microholograms in lithium niobate,” in Photorefractive Effects, Materials and Devices, OSA Trends in Optics and Photonics Series, Vol. 99 (Optical Society of America, 2005), pp. 610-615.

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K. A. Rubin, H. J. Rosen, W. W. Tang, W. Imaino, and T. C. Strand, “Multilevel volumetric optical disk storage,” in Optical Data Storage, Proc. SPIE 2338, 247-250 (1994).

Strand, T. S.

W. I. Imaino, H. J. Rosen, K. A. Rubin, and T. S. Strand, “Extending the compact disk format to high capacity for video applications,” in Optical Data Storage, Proc. SPIE 2338, 254-258 (1994).

Strickler, J. H.

Studenmund, W. R.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388-390 (1994).
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Sullivan, A. C.

Tanabe, N.

K. Saito, T. Horigome, H. Miyamoto, H. Yamatsu, N. Tanabe, K. Hayashi, G. Fujita, S. Kobayashi, T. Kudo, and H. Uchiyama, “Drive system and readout characteristics of micro-reflector optical disc,” in Int. Soc. Opt. Eng., Proc. SPIE 6620, 66200B (2007).
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Tanaka, T.

Tang, W. C.

H. J. Rosen, K. A. Rubin, W. C. Tang, and W. I. Imaino, “Multilayer optical recording (MORE),” in Optical Data Storage 1995, Proc. SPIE 2514, 14-19 (1995).

Tang, W. W.

K. A. Rubin, H. J. Rosen, W. W. Tang, W. Imaino, and T. C. Strand, “Multilevel volumetric optical disk storage,” in Optical Data Storage, Proc. SPIE 2338, 247-250 (1994).

Teich, M. C.

B. E. A. Saleh and M. C. Teich, “Fundamentals of Photonics,” in Wiley Series in Pure and Applied Optics (2009), Ch. 3.

Terris, B. D.

B. D. Terris, H. J. Mamin, D. Rugar, W. R. Studenmund, and G. S. Kino, “Near-field optical data storage using a solid immersion lens,” Appl. Phys. Lett. 65, 388-390 (1994).
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Toriumi, A.

Trout, T. J.

W. J. Gambogi, A. M. Weber, and T. J. Trout, “Advances and applications of DuPont holographic photopolymers,” Proc. SPIE 2043, 2-13 (1993).

Uchiyama, H.

K. Saito, T. Horigome, H. Miyamoto, H. Yamatsu, N. Tanabe, K. Hayashi, G. Fujita, S. Kobayashi, T. Kudo, and H. Uchiyama, “Drive system and readout characteristics of micro-reflector optical disc,” in Int. Soc. Opt. Eng., Proc. SPIE 6620, 66200B (2007).
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Ueki, H.

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).
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Upatnieks, J.

van Heerden, P. J.

Waldman, D. A.

D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerimization methods for volume hologram recording,” Proc. SPIE 2689, 127-141 (1996).
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Walker, E.

E. Walker and P. Rentzepis, “Two-photon technology: A new dimension,” Nat. Photonics 2, 406-408 (2008).
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E. Walker, A. Dvornikov, K. Coblentz, and P. Rentzepis, “Terabyte recorded in two-photon 3D disk,” Appl. Opt. 47, 4133-4139 (2008).
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Y. Zhang, T. D. Milster, J. Butz, W. Bletcher, K. J. Erwin, and E. Walker, “Signal, cross talk and signal to noise ratio in bit-wise volumetric optical data storage,” in 2002 International Symposium on Optical Memory and Optical Data Storage Topical Meeting (IEEE, 2002), pp. 246-248.
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Walker, E. P.

H. Zhang, A. S. Dvornikov, E. P. Walker, N. H. Kim, and F. B. McCormick, “Single-beam two-photon-recorded monolithic multi-layer optical disks,” Proc. SPIE 4090, 174-178 (2000).
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Wang, M. M.

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).
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Webb, W. W.

Weber, A. M.

W. J. Gambogi, A. M. Weber, and T. J. Trout, “Advances and applications of DuPont holographic photopolymers,” Proc. SPIE 2043, 2-13 (1993).

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S. Homan and A. E. Wilner, “High-capacity optical storage using multiple wavelengths, multiple layers and volume holograms,” Electron. Lett. 31, 621-623 (1995).
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Wuttig, M.

A. Partovi, D. Peale, M. Wuttig, C. A. Murray, G. Zydzik, L. Hopkins, K. Baldwin, W. S. Hobson, J. Wynn, J. Lopata, L. Dhar, R. Chichester, and J. H.-J. Yeh, “High-power laser light source for near-field optics and its application to high-density optical data storage,” Appl. Phys. Lett. 75, 1515-1520 (1999).
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Wynn, J.

A. Partovi, D. Peale, M. Wuttig, C. A. Murray, G. Zydzik, L. Hopkins, K. Baldwin, W. S. Hobson, J. Wynn, J. Lopata, L. Dhar, R. Chichester, and J. H.-J. Yeh, “High-power laser light source for near-field optics and its application to high-density optical data storage,” Appl. Phys. Lett. 75, 1515-1520 (1999).
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Yamatsu, H.

K. Saito, T. Horigome, H. Miyamoto, H. Yamatsu, N. Tanabe, K. Hayashi, G. Fujita, S. Kobayashi, T. Kudo, and H. Uchiyama, “Drive system and readout characteristics of micro-reflector optical disc,” in Int. Soc. Opt. Eng., Proc. SPIE 6620, 66200B (2007).
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Yeh, J. H.-J.

A. Partovi, D. Peale, M. Wuttig, C. A. Murray, G. Zydzik, L. Hopkins, K. Baldwin, W. S. Hobson, J. Wynn, J. Lopata, L. Dhar, R. Chichester, and J. H.-J. Yeh, “High-power laser light source for near-field optics and its application to high-density optical data storage,” Appl. Phys. Lett. 75, 1515-1520 (1999).
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Zhang, H.

H. Zhang, A. S. Dvornikov, E. P. Walker, N. H. Kim, and F. B. McCormick, “Single-beam two-photon-recorded monolithic multi-layer optical disks,” Proc. SPIE 4090, 174-178 (2000).
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Zhang, Y.

Y. Zhang, T. D. Milster, J. Butz, W. Bletcher, K. J. Erwin, and E. Walker, “Signal, cross talk and signal to noise ratio in bit-wise volumetric optical data storage,” in 2002 International Symposium on Optical Memory and Optical Data Storage Topical Meeting (IEEE, 2002), pp. 246-248.
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A. Partovi, D. Peale, M. Wuttig, C. A. Murray, G. Zydzik, L. Hopkins, K. Baldwin, W. S. Hobson, J. Wynn, J. Lopata, L. Dhar, R. Chichester, and J. H.-J. Yeh, “High-power laser light source for near-field optics and its application to high-density optical data storage,” Appl. Phys. Lett. 75, 1515-1520 (1999).
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A. Partovi, D. Peale, M. Wuttig, C. A. Murray, G. Zydzik, L. Hopkins, K. Baldwin, W. S. Hobson, J. Wynn, J. Lopata, L. Dhar, R. Chichester, and J. H.-J. Yeh, “High-power laser light source for near-field optics and its application to high-density optical data storage,” Appl. Phys. Lett. 75, 1515-1520 (1999).
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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).
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Opt. Express (1)

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H. Zhang, A. S. Dvornikov, E. P. Walker, N. H. Kim, and F. B. McCormick, “Single-beam two-photon-recorded monolithic multi-layer optical disks,” Proc. SPIE 4090, 174-178 (2000).
[CrossRef]

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D. A. Waldman, R. T. Ingwall, P. K. Dhal, M. G. Horner, E. S. Kolb, H.-Y. S. Li, R. A. Minns, and H. G. Schild, “Cationic ring-opening photopolymerimization methods for volume hologram recording,” Proc. SPIE 2689, 127-141 (1996).
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Other (15)

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M. Mansuripur, The Physical Principles of Magneto-optical Recording (Cambridge U. Press, 1995), pp. 675-676.

The e−2 diameter of a two-photon feature at twice the wavelength is larger by a factor of 2, while the full-width half-max depth extent increases by a factor of 221/2−1.

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

K. A. Rubin, H. J. Rosen, W. W. Tang, W. Imaino, and T. C. Strand, “Multilevel volumetric optical disk storage,” in Optical Data Storage, Proc. SPIE 2338, 247-250 (1994).

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Figures (8)

Fig. 1
Fig. 1

Layout of 3D data storage in a homogenous volume. Bits are written by modifying material properties with the focused write beam positioned at any “virutal” layer within the material. The purpose of this paper is to calculate the Strehl ratio (SR) of the focused spot caused by the aberrations of the intervening layers. The plots on the right show the calculated index distribution recorded by a Gaussian beam for sublinear (left), linear (center), and superlinear (right) recording responses using a pulsed (top) and continuous (bottom) exposure.

Fig. 2
Fig. 2

Depth (left) and in-plane (right) cross-sections of a representative numerical space for calculating wavefront aberration of a focused beam, shown by the ray paths.

Fig. 3
Fig. 3

OPD calculation for OOK bits in a linear ( α = 1 ) medium. The depth slice through the index distribution (upper left) is overlayed with the ray paths of the Gaussian beam. The index space is transformed (upper right) to straighten the ray paths, which spreads the bits near the focus and warps them away from the beam axis. This transformed space is projected in z to calculate the OPD as shown for the third layer from the top (lower right) and all six layers (lower left). In this example, bits are placed on a regular Cartesian grid, causing a large OPD along the line y = 0 .

Fig. 4
Fig. 4

Peak (on axis) OPD in units of the Δ n z 0 versus the response of the material for an infinitely thick material. Closed-form values are indicated at α ¯ = 1 2 , 1 , 3 2 , 2 .

Fig. 5
Fig. 5

Comparisons of theoretical and numerical predictions of standard deviation of OPD for a single bit layer. The left figure plots Eq. (6) versus the average (circles) and standard deviation (bars) of 20 simulations for a square ( B = T ) grid of 0.2 NA bits placed halfway between the surface and the focus, which is at a depth z = 500 z 0 in a linear ( α = 1 ) material. The right figure plots Eq. (6) versus the average (circles) and standard deviation (bars) of 20 simulations for B = T = 2.5 (top) and B = T = 5 (bottom) versus the fraction of binary “ones” written. In this case, the bit layer is at 50 z 0 , which is again halfway between the surface and the focus at 100 z 0 .

Fig. 6
Fig. 6

Validation of statistical independence of optical path length of individual layers in multiple layer disks. The circles are numerically calculated for B = T = 2.5 , β = 0.5 , focal depth = 100 z 0 and bit planes spaced at 10 z 0 placed symmetrically around 50 z 0 . The solid curve is the square root of the number of layers, normalized to the single-layer result.

Fig. 7
Fig. 7

Projected optical path length function found for a six-layer disk with the same parameters as Fig. 3. The 980 × 980 × 100 cell simulation required 130   minutes on a dual core 2.66 GHz processor, illustrating the difficulty of scaling to large disk thickness. The SR found from the peak intensity of the BPM simulation was 0.69, while the value predicted by Eq. (9) is 0.67.

Fig. 8
Fig. 8

Relative disk capacity or, equivalently, storage density in bits/area as a function of the code balance, β, calculated via Eq. (12). The figure indicates infinite capacity as β approaches zero; however, this will be limited in reality by the allowable disk thickness, which increases rapidly at small β.

Equations (12)

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I 0 ( x , y , z ) = 1 1 + ( z z 0 ) 2 e 2 [ ( x w 0 ) 2 + ( y w 0 ) 2 ] [ 1 + ( z z 0 ) 2 ] ,
δ n ( x , y , z ) { I 0 α ( x + v t , y , z ) δ ( t ) d t = Δ n [ 1 + ( z z 0 ) 2 ] α e 2 α [ ( x w 0 ) 2 + ( y w 0 ) 2 ] [ 1 + ( z z 0 ) 2 ] OOK I 0 α ( x + v t , y , z ) d t = Δ n [ 1 + ( z z 0 ) 2 ] 1 2 α e 2 α ( y w 0 ) 2 [ 1 + ( z z 0 ) 2 ] PCM } .
S ( z ̃ 1 , z ̃ 2 ) = z 1 z 2 δ n ( 0 , 0 , z ) d z = Δ n z 0 [ z ̃ 2 F 1 2 ( 1 2 , α ¯ , 3 2 , z ̃ 2 2 ) z ̃ 1 F 1 2 ( 1 2 , α ¯ , 3 2 , z ̃ 1 2 ) ] = Δ n z 0 { π Γ ( α ¯ 1 2 ) Γ ( α ¯ ) if z ̃ 1 = z ̃ 2 arctan ( z ̃ 2 ) arctan ( z ̃ 1 ) if α ¯ = 1 π if α ¯ = 1 , z ̃ 1 = z ̃ 2 , }
α ¯ = { α OOK α 1 2 PCM , }
f ( x , y ) = exp { 2 α [ ( x w 0 ) 2 + ( y w 0 ) 2 ] } .
σ m = S ( z ̃ m 1 , z ̃ m 2 ) β f 2 β 2 f 2 = S ( z ̃ m 1 , z ̃ m 2 ) 1 2 π β B T α erf ( B α ) erf ( T α ) ( π β B T α erf ( B α 2 ) erf ( T α 2 ) ) 2 ,
σ Total = m = 1 M σ m 2 .
SR exp [ ( 2 π λ 0 ) 2 σ Total 2 ] 1 ( 2 π λ 0 ) 2 σ Total 2 = 1 M ( 2 π λ 0 ) 2 σ Layer 2 .
SR = 1 M B T π 2 [ π β erf ( B ) erf ( T ) 1 B T ( π β erf ( B 2 ) erf ( T 2 ) ) 2 ] ( Δ n z 0 π λ 0 ) 2 .
η = [ ( π λ 0 ) Δ n ( π z 0 2 ) ] 2 .
SR 1 4 M B T η 1 M η .
( locations area ) ( bits location ) β log 2 ( β ) ( 1 β ) log 2 ( 1 β ) π β erf ( B ) erf ( T ) 1 B T ( π β erf ( B 2 ) erf ( T 2 ) ) 2 .

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