Abstract

We present a method for optical encryption of information, based on the time-dependent dynamics of writing and erasure of refractive index changes in a bulk lithium niobate medium. Information is written into the photorefractive crystal with a spatially amplitude-modulated laser beam which when overexposed significantly degrades the stored data making it unrecognizable. We show that the degradation can be reversed and that a one-to-one relationship exists between the degradation and recovery rates. It is shown that this simple relationship can be used to determine the erasure time required for decrypting the scrambled index patterns. In addition, this method could be used as a straightforward general technique for determining characteristic writing and erasure rates in photorefractive media.

© 2013 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]

2009

2006

2005

2000

1998

L. Arizmendi, E. de Miguel-Sanz, and M. Carrascosa, “Lifetimes of thermally fixed holograms in LiNbO3:Fe crystals,” Opt. Lett.23, 960–962 (1998).
[CrossRef]

K. Buse, A. Adibi, and D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature (London)393, 665–668 (1998).
[CrossRef]

1996

N. Fressengeas, J. Maufoy, and G. Kugel, “Temporal behavior of bidimensional photorefractive bright spatial solitons,” Phys. Rev. E.54, 6866–6875 (1996).
[CrossRef]

1995

1994

1993

M. Morin, G. Duree, G. Salamo, and M. Segev, “Waveguides formed by quasi-steady-state photorefractive spatial solitons,” Opt. Lett.20, 2066–2068 (1993).
[CrossRef]

B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B.10, 446–453 (1993).
[CrossRef]

G. J. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett.71, 533–536 (1993).
[CrossRef] [PubMed]

1992

M. Segev, B. Crosignani, and A. Yariv, “Spatial solitons in photorefractive media,” Phys. Rev. Lett.68, 923–927 (1992).
[CrossRef] [PubMed]

1991

E. Maniloff and K. Johnson, “Maximized photorefractive holographic storage,” J. Appl. Phys.70, 4702–4707 (1991).
[CrossRef]

1979

N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics22, 949–960 (1979).
[CrossRef]

1977

H. Kurz, “Photorefractive recording dynamics and multiple storage of volume holograms in photorefractive LiNbO3,” Opt. Act.24, 463–473 (1977).
[CrossRef]

1966

A. Ashkin, G. Boyd, J. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3and LiTaO3,” Appl. Phys. Lett.9, 72–74 (1966).
[CrossRef]

Adibi, A.

K. Buse, A. Adibi, and D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature (London)393, 665–668 (1998).
[CrossRef]

Arizmendi, L.

Ashkin, A.

A. Ashkin, G. Boyd, J. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3and LiTaO3,” Appl. Phys. Lett.9, 72–74 (1966).
[CrossRef]

Ballman, A.

A. Ashkin, G. Boyd, J. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3and LiTaO3,” Appl. Phys. Lett.9, 72–74 (1966).
[CrossRef]

Boyd, G.

A. Ashkin, G. Boyd, J. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3and LiTaO3,” Appl. Phys. Lett.9, 72–74 (1966).
[CrossRef]

Buse, K.

Carrascosa, M.

Chauvet, M.

Crosignani, B.

G. J. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett.71, 533–536 (1993).
[CrossRef] [PubMed]

B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B.10, 446–453 (1993).
[CrossRef]

M. Segev, B. Crosignani, and A. Yariv, “Spatial solitons in photorefractive media,” Phys. Rev. Lett.68, 923–927 (1992).
[CrossRef] [PubMed]

de Miguel-Sanz, E.

Devaux, F.

Di Porto, P.

B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B.10, 446–453 (1993).
[CrossRef]

G. J. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett.71, 533–536 (1993).
[CrossRef] [PubMed]

Duree, G.

Duree, G. J.

G. J. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett.71, 533–536 (1993).
[CrossRef] [PubMed]

Dziedzic, J.

A. Ashkin, G. Boyd, J. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3and LiTaO3,” Appl. Phys. Lett.9, 72–74 (1966).
[CrossRef]

Engin, D.

B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B.10, 446–453 (1993).
[CrossRef]

Fressengeas, N.

N. Fressengeas, J. Maufoy, and G. Kugel, “Temporal behavior of bidimensional photorefractive bright spatial solitons,” Phys. Rev. E.54, 6866–6875 (1996).
[CrossRef]

Fu, G.

Gao, Y.

Guo, R.

Hashimoto, Y.

Jaatinen, E.

Johnson, K.

E. Maniloff and K. Johnson, “Maximized photorefractive holographic storage,” J. Appl. Phys.70, 4702–4707 (1991).
[CrossRef]

Kawata, S.

Kawata, Y.

Krätzig, E.

Kugel, G.

N. Fressengeas, J. Maufoy, and G. Kugel, “Temporal behavior of bidimensional photorefractive bright spatial solitons,” Phys. Rev. E.54, 6866–6875 (1996).
[CrossRef]

Kukhtarev, N.

N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics22, 949–960 (1979).
[CrossRef]

Kurz, H.

H. Kurz, “Photorefractive recording dynamics and multiple storage of volume holograms in photorefractive LiNbO3,” Opt. Act.24, 463–473 (1977).
[CrossRef]

Levinstein, J.

A. Ashkin, G. Boyd, J. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3and LiTaO3,” Appl. Phys. Lett.9, 72–74 (1966).
[CrossRef]

Li, H.-Y.

Liu, S.

Liu, Z.

Maniloff, E.

E. Maniloff and K. Johnson, “Maximized photorefractive holographic storage,” J. Appl. Phys.70, 4702–4707 (1991).
[CrossRef]

Markov, V.

N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics22, 949–960 (1979).
[CrossRef]

Maufoy, J.

N. Fressengeas, J. Maufoy, and G. Kugel, “Temporal behavior of bidimensional photorefractive bright spatial solitons,” Phys. Rev. E.54, 6866–6875 (1996).
[CrossRef]

Mok, F.

Morin, M.

Nassau, K.

A. Ashkin, G. Boyd, J. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3and LiTaO3,” Appl. Phys. Lett.9, 72–74 (1966).
[CrossRef]

Neurgaonkar, R.

G. J. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett.71, 533–536 (1993).
[CrossRef] [PubMed]

Odulov, S.

N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics22, 949–960 (1979).
[CrossRef]

Peithmann, K.

Psaltis, D.

K. Buse, A. Adibi, and D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature (London)393, 665–668 (1998).
[CrossRef]

D. Psaltis, F. Mok, and H.-Y. Li, “Nonvolatile storage in photorefractive crystals,” Opt. Lett.19, 210–212 (1994).
[CrossRef] [PubMed]

Salamo, G.

M. Chauvet, G. Fu, and G. Salamo, “Assessment method for photo-induced waveguides,” Opt. Express14, 10726–10732 (2006).
[CrossRef] [PubMed]

G. J. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett.71, 533–536 (1993).
[CrossRef] [PubMed]

B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B.10, 446–453 (1993).
[CrossRef]

M. Morin, G. Duree, G. Salamo, and M. Segev, “Waveguides formed by quasi-steady-state photorefractive spatial solitons,” Opt. Lett.20, 2066–2068 (1993).
[CrossRef]

Sando, D.

Segev, M.

M. Morin, G. Duree, G. Salamo, and M. Segev, “Waveguides formed by quasi-steady-state photorefractive spatial solitons,” Opt. Lett.20, 2066–2068 (1993).
[CrossRef]

B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B.10, 446–453 (1993).
[CrossRef]

G. J. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett.71, 533–536 (1993).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, and A. Yariv, “Spatial solitons in photorefractive media,” Phys. Rev. Lett.68, 923–927 (1992).
[CrossRef] [PubMed]

Sharp, E.

G. J. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett.71, 533–536 (1993).
[CrossRef] [PubMed]

Shultz, J.

G. J. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett.71, 533–536 (1993).
[CrossRef] [PubMed]

Smith, R.

A. Ashkin, G. Boyd, J. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3and LiTaO3,” Appl. Phys. Lett.9, 72–74 (1966).
[CrossRef]

Song, T.

Soskin, M.

N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics22, 949–960 (1979).
[CrossRef]

Ueki, H.

Vinetskii, V.

N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics22, 949–960 (1979).
[CrossRef]

Wiebrock, A.

Yariv, A.

B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B.10, 446–453 (1993).
[CrossRef]

G. J. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett.71, 533–536 (1993).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, and A. Yariv, “Spatial solitons in photorefractive media,” Phys. Rev. Lett.68, 923–927 (1992).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. Lett.

A. Ashkin, G. Boyd, J. Dziedzic, R. Smith, A. Ballman, J. Levinstein, and K. Nassau, “Optically-induced refractive index inhomogeneities in LiNbO3and LiTaO3,” Appl. Phys. Lett.9, 72–74 (1966).
[CrossRef]

Ferroelectrics

N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics22, 949–960 (1979).
[CrossRef]

J. Appl. Phys.

E. Maniloff and K. Johnson, “Maximized photorefractive holographic storage,” J. Appl. Phys.70, 4702–4707 (1991).
[CrossRef]

J. Opt. Soc. Am. B

J. Opt. Soc. Am. B.

B. Crosignani, M. Segev, D. Engin, P. Di Porto, A. Yariv, and G. Salamo, “Self-trapping of optical beams in photorefractive media,” J. Opt. Soc. Am. B.10, 446–453 (1993).
[CrossRef]

Nature (London)

K. Buse, A. Adibi, and D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature (London)393, 665–668 (1998).
[CrossRef]

Opt. Act.

H. Kurz, “Photorefractive recording dynamics and multiple storage of volume holograms in photorefractive LiNbO3,” Opt. Act.24, 463–473 (1977).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Rev. E.

N. Fressengeas, J. Maufoy, and G. Kugel, “Temporal behavior of bidimensional photorefractive bright spatial solitons,” Phys. Rev. E.54, 6866–6875 (1996).
[CrossRef]

Phys. Rev. Lett.

G. J. Duree, J. Shultz, G. Salamo, M. Segev, A. Yariv, B. Crosignani, P. Di Porto, E. Sharp, and R. Neurgaonkar, “Observation of self-trapping of an optical beam due to the photorefractive effect,” Phys. Rev. Lett.71, 533–536 (1993).
[CrossRef] [PubMed]

M. Segev, B. Crosignani, and A. Yariv, “Spatial solitons in photorefractive media,” Phys. Rev. Lett.68, 923–927 (1992).
[CrossRef] [PubMed]

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Figures (7)

Fig. 1
Fig. 1

The experiment layout.

Fig. 2
Fig. 2

(a) The input amplitude mask: white regions are transparent, black regions are opaque. (b) A typical readout image. (c) The region of interest (ROI) used for data analysis.

Fig. 3
Fig. 3

The row average P(x) of the ROI for the write and erase process. The bright stripes bifurcate once, then twice, during the degradation process, and during erasure the reverse progression is observed. The two circles on the figure indicate a point in time where the write and erase dynamics are matched (in this case, where the stripe at x = 1.3 mm splits into two).

Fig. 4
Fig. 4

(a) A recorded pattern after 6 minutes exposure; after 15 minutes exposure the pattern is extensively degraded in (b). Upon optical erasure for 44 minutes (total time 69 minutes), the original pattern is recovered in (c).

Fig. 5
Fig. 5

Demonstration of the matching of features for a single stripe (at x = 1.3 mm) over the write/erase process. Labels 1–6 indicate times when the refractive index variations are approximately equal during write/erase.

Fig. 6
Fig. 6

The relationship between erase time te + t0 and write time tw for three different stripe widths. The linear trends indicate that the treatment presented here is valid for a range of pattern sizes and write beam intensities.

Fig. 7
Fig. 7

Comparison of P(x) over (a) write process, and (b) over the erase process with a rescaled (and reversed) time axis for stripe size of 73 μm. This comparison clearly shows that the correlation relationship is indeed accurate.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Δ n Δ n s = 1 exp ( t w / τ w )
Δ n Δ n s = { 1 exp ( t 0 / τ w ) } exp ( t e / τ e )
ln ( t e / t 0 ) = A ln ( t w ) + B
t e = exp ( B ) ( t w ) A + t 0

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