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Optics Express

Optics Express

  • Editor: Andrew M. Weiner
  • Vol. 21, Iss. 17 — Aug. 26, 2013
  • pp: 19510–19517
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Optical data encryption using time-dependent dynamics of refractive index changes in LiNbO3

Daniel Sando and Esa Jaatinen  »View Author Affiliations


Optics Express, Vol. 21, Issue 17, pp. 19510-19517 (2013)
http://dx.doi.org/10.1364/OE.21.019510


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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

1. Introduction

The photorefractive (PR) effect is a nonlinear optical phenomenon whereby the refractive index of a medium is modified by exposure to light of the appropriate wavelength and intensity. The PR effect in inorganic crystals has been employed for applications in data storage (holographic [1

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

] or otherwise [2

2. 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]

, 3

3. Y. Gao, S. Liu, R. Guo, Z. Liu, and T. Song, “Transmission of digital images consisting of white-light dark solitons,” Appl. Opt. 44, 6948–6951 (2005). [CrossRef] [PubMed]

]), photorefractive solitons [4

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

6

6. 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]

], and optically-induced waveguides [7

7. 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]

, 8

8. M. Chauvet, G. Fu, and G. Salamo, “Assessment method for photo-induced waveguides,” Opt. Express 14, 10726–10732 (2006). [CrossRef] [PubMed]

]. In such applications, a laser beam with a specific intensity distribution is used to induce the desired refractive index changes in the medium.

For PR inorganic crystals (e.g. lithium niobate – LiNbO3, barium titanate – BaTiO3), the refractive index changes induced in these media can be erased and rewritten. This property enables a level of functionality that is important for random access memories and light-controlling-light devices. Erasure of the index changes is possible in such media because irradiation with a uniform light field (e.g. a halogen lamp) redistributes the charges, returning the refractive index to a uniform state.

Since first reported in 1966 [9

9. 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]

], the dynamics of writing and erasure of refractive index changes in PR media have been extensively investigated in situations where there is a high degree of symmetry or periodicity of the illuminating field. A well-known example of this is the two-wave mixing process for recording phase holograms in PR media. Studies have shown that in this application the diffraction efficiency of the hologram grows in a mono-exponential fashion with exposure time [10

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

]. For light-induced waveguides and solitons, the temporal buildup of the refractive index change follows a similar exponential trend [8

8. M. Chauvet, G. Fu, and G. Salamo, “Assessment method for photo-induced waveguides,” Opt. Express 14, 10726–10732 (2006). [CrossRef] [PubMed]

, 11

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

]. The dynamics of the optical erasure process are also important. For multiplexed holograms, it is important to take into account the partial erasure caused by the writing of successive holograms in the same location [12

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

], to be able to obtain holograms with the desired uniform diffraction efficiency. Intuitively, the optical erasure of phase holograms is expected to follow a similar exponential trend, with a time constant dependent on such parameters as light field intensity, pattern characteristics, and material properties such as electron mobility. For data storage applications, where performance is measured by speed and/or bit error-rates, it is essential to know the rates of writing/erasure and to determine the material and optical properties that dictate them. Control of these rates will also allow the merits of different PR media to be compared and allow suitable medium choice for a given application.

2. Experiment and analysis methods

The layout of the optical experiment is shown in Fig. 1. The amplitude mask used for impressing the data to be stored in the medium, shown in Fig. 2(a), is illuminated by an expanded and collimated Nd:YAG beam at λ = 532 nm. An image of the amplitude mask is focused onto the front face of the LiNbO3:Fe crystal (8 × 10 × 3 mm3) with the data stored in the medium as variations in the refractive index. To read out the information we use a 5 mW 633 nm He-Ne beam collimated by a 15× beam expander so that the intensity incident on the medium is effectively uniform. This readout wavelength was chosen so that the beam did not appreciably erase the recorded information [14

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

]. The readout beam counter-propagates to the writing beam through the medium. As the readout beam travels through the crystal, its intensity profile is modified by the index changes in the medium, and after emerging from the crystal it is focused on a CCD camera. The intensity profile observed at the camera is a reconstruction of the pattern stored in the medium. For erasure of the data, the 532 nm writing beam is turned off and the medium is illuminated with two 50 W halogen lamps.

Fig. 1 The experiment layout.
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.

The readout image is monitored constantly during the writing and erasure processes. A typical readout image is shown in Fig. 2(b), showing that the data are well-defined with good contrast between the stripes and background. Assuming mono-exponential growth and decay [8

8. M. Chauvet, G. Fu, and G. Salamo, “Assessment method for photo-induced waveguides,” Opt. Express 14, 10726–10732 (2006). [CrossRef] [PubMed]

, 11

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

, 15

15. N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979). [CrossRef]

], the magnitude of the change in refractive index of the pattern’s stripe regions (normalized to the saturation value), during writing is described by
ΔnΔns=1exp(tw/τw)
(1)
where tw is the time since writing commenced, and τw is the characteristic time constant for writing. This equation assumes that the writing beam intensity is uniform across the medium which is reasonable in this case, since the data are binary, with the light transmitted through the apertures having essentially the same intensity, while in the dark regions, 100% of the light is blocked by the metal mask. A non-uniform writing beam intensity would require a range of time constants [16

16. K. Peithmann, A. Wiebrock, K. Buse, and E. Krätzig, “Low-spatial-frequency refractive-index changes in iron-doped lithium niobate crystals upon illumination with a focused continuous-wave laser beam,” J. Opt. Soc. Am. B 17, 586–592 (2000). [CrossRef]

].

If the time taken to write the data is t0, and erasure starts shortly after, the normalized index change is described by
ΔnΔns={1exp(t0/τw)}exp(te/τe)
(2)
where te is the time since start of erasure and τe is the erasure time constant. Both the writing and erasure time constants can be controlled by the user as they depend on the following: beam properties such as intensity, wavelength and polarization; nonlinear material properties; and geometrical considerations like the size of the features to be recorded.

The stored data were continually monitored during the writing and erasure phases with a CCD camera that captured images with a resolution of 1024 (horizontal) pixels by 768 (vertical) pixels of the readout beam after propagation through the PR medium, as shown in Fig. 2(b). To characterize writing and erasure rates, a 300 px by 220 px Region of Interest (ROI), shown in Figs. 2(b)–(c), was analyzed. This region consists of a series of irregularly spaced bright and dark vertical stripes of uniform intensity in the vertical direction. By averaging the intensity of the ROI vertically, a horizontal intensity profile P(x) is obtained where x indicates the location across the mask as shown in Fig. 2. This ROI profile was measured during the write and erase process, allowing the evolution of the degradation and recovery processes to be directly observed as shown in Fig. 3. Starting from the left of Fig. 3, the four bright stripes soon bifurcate into eight and then 16 and so on, until the original data are no longer discernable. Typical readout images observed during this bifurcation process are shown in Fig. 4. Eventually, the data are no longer recognizable as shown in Fig. 4(b) when the medium was illuminated with the writing beam for 15 minutes. However, as shown in Fig. 3, during erasure this bifurcation process reverses in time sequence, allowing the data to be retrieved after a suitable erasure period as shown in Fig. 4(c). As the same bifurcations occur during writing and erasure we can use them as specific points in time where the image content and refractive index profiles are the same. This provides an excellent platform for temporal analysis of the photorefractive writing and erasure processes. An example of specific times where the image content during writing and erasure phases are equivalent is indicated by dashed circles in 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 (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 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 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.

3. Results and discussion

The potential of using the correlation between writing and erasure processes in an optically thick photorefractive lithium niobate crystal is demonstrated by using regression analysis to determine the constants, A and B defined in Eq. (3), for the writing and erasure conditions used to generate Fig. 3. Rearranging Eq. (3) allows the erasure time te to be expressed in terms of the writing time tw:
te=exp(B)(tw)A+t0
(4)
With A and B determined, Eq. (4) was then used to evaluate the time during erasure when the image has the same spatial features as the image observed at tw during writing. As shown in Fig. 7 very good agreement is observed between the evolution of the original written data and the refractive index distribution observed during erasure as predicted by Eq. (4). Figure 7 shows that the bifurcation process during erasure is indeed reversed with even the appearance of low-contrast image features satisfying Eq. (4). This indicates that the correlation between writing and erasure as described by Eq. (3), applies even to small magnitude variations in the spatial refractive index distribution, suggesting that high sensitivity and a good signal-to-noise ratio are possible.

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.

An example of the comparative quality of the written and recovered images is shown in Figs. 4(a) and (c) respectively. Prior to image recovery, the data were deliberately overwritten for 15 minutes, completely scrambling the data, rendering them unrecognizable as shown in Fig. 4(b). Using the evaluated values for A and B, the appropriate erasure time was calculated and the image observed at that time recorded and shown in Fig. 4(c). A comparison of Figs. 4(c) and (b) shows that the encryption has been completely removed, allowing the data to be revealed. Since photorefractive index changes can persist in media like lithium niobate for periods up to years [17

17. 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]

] it is possible to use this approach to store, encrypt and read out data over realistic, practical time-scales.

Now a final note regarding the integrity of the encryption process. This method could be potentially fairly facile to attack and recover the scrambled data: e.g. by simply setting up a readout system and erasing the refractive index changes. However, the strength in this encryption method, lies in the fact that the attacker does not know the exact format of the data, e.g. are the data encoded in the lengths of the stripes, the width of the stripes, the brightness etc., and thus the attacker would not know at which time the data are properly recovered.

4. Conclusion

We have presented a simple method to determine the characteristic time scales for writing and erasing of photo-induced refractive index changes in a lithium niobate crystal. The analysis method is based on correlating the appearance of matching features during the write and erase processes. By plotting the appearance time of specific features during erasure against the appearance time of the same feature during the writing process, an one-to-one relationship was shown to exist, and relevant constants that uniquely determine the experimental conditions were obtained. This relationship shows that the erasure process induces a reversal of the evolution of refractive index changes observed during writing. An application of this approach is the storage and encryption of data or images in optically thick photorefractive media. Here the information is deliberately scrambled through successive bifurcations that occur when the medium is overexposed. Successful recovery of the information through incandescent erasure of the refractive index distribution is only possible if the constants that correlate the writing and erasure processes are known. These constants uniquely define the specific experimental parameters and therefore they define the erasure exposure time required to retrieve the data.

This correlation could also be exploited to evaluate writing and erasure time constants for PR processes, and could be used as a diagnostic tool for general PR media. Here simple spatially-modulated light patterns – such as alternating regions of light and bright stripes with specific intensities and feature sizes – could be written into the PR media, and the time required for feature splitting measured. This could then be used to compare the photorefractive response of different PR media and thus provide some insight into their write and erase dynamics. In particular, it would allow analysis of charge transport and mobility rates and pave the way for measurement of charge drift and diffusion in photorefractive media.

References and links

1.

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

2.

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]

3.

Y. Gao, S. Liu, R. Guo, Z. Liu, and T. Song, “Transmission of digital images consisting of white-light dark solitons,” Appl. Opt. 44, 6948–6951 (2005). [CrossRef] [PubMed]

4.

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

5.

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]

6.

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]

7.

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]

8.

M. Chauvet, G. Fu, and G. Salamo, “Assessment method for photo-induced waveguides,” Opt. Express 14, 10726–10732 (2006). [CrossRef] [PubMed]

9.

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]

10.

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

11.

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

12.

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

13.

D. Sando, E. Jaatinen, and F. Devaux, “Reversal of degradation of information masks in lithium niobate,” Appl. Opt. 48, 4676–4682 (2009). [CrossRef] [PubMed]

14.

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

15.

N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics 22, 949–960 (1979). [CrossRef]

16.

K. Peithmann, A. Wiebrock, K. Buse, and E. Krätzig, “Low-spatial-frequency refractive-index changes in iron-doped lithium niobate crystals upon illumination with a focused continuous-wave laser beam,” J. Opt. Soc. Am. B 17, 586–592 (2000). [CrossRef]

17.

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]

OCIS Codes
(160.5320) Materials : Photorefractive materials
(190.5330) Nonlinear optics : Photorefractive optics
(210.4770) Optical data storage : Optical recording

ToC Category:
Optical Data Storage

History
Original Manuscript: June 10, 2013
Revised Manuscript: August 1, 2013
Manuscript Accepted: August 1, 2013
Published: August 12, 2013

Citation
Daniel Sando and Esa Jaatinen, "Optical data encryption using time-dependent dynamics of refractive index changes in LiNbO3," Opt. Express 21, 19510-19517 (2013)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-17-19510


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References

  1. K. Buse, A. Adibi, and D. Psaltis, “Non-volatile holographic storage in doubly doped lithium niobate crystals,” Nature (London)393, 665–668 (1998). [CrossRef]
  2. 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]
  3. Y. Gao, S. Liu, R. Guo, Z. Liu, and T. Song, “Transmission of digital images consisting of white-light dark solitons,” Appl. Opt.44, 6948–6951 (2005). [CrossRef] [PubMed]
  4. M. Segev, B. Crosignani, and A. Yariv, “Spatial solitons in photorefractive media,” Phys. Rev. Lett.68, 923–927 (1992). [CrossRef] [PubMed]
  5. 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]
  6. 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]
  7. 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]
  8. M. Chauvet, G. Fu, and G. Salamo, “Assessment method for photo-induced waveguides,” Opt. Express14, 10726–10732 (2006). [CrossRef] [PubMed]
  9. 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]
  10. H. Kurz, “Photorefractive recording dynamics and multiple storage of volume holograms in photorefractive LiNbO3,” Opt. Act.24, 463–473 (1977). [CrossRef]
  11. N. Fressengeas, J. Maufoy, and G. Kugel, “Temporal behavior of bidimensional photorefractive bright spatial solitons,” Phys. Rev. E.54, 6866–6875 (1996). [CrossRef]
  12. E. Maniloff and K. Johnson, “Maximized photorefractive holographic storage,” J. Appl. Phys.70, 4702–4707 (1991). [CrossRef]
  13. D. Sando, E. Jaatinen, and F. Devaux, “Reversal of degradation of information masks in lithium niobate,” Appl. Opt.48, 4676–4682 (2009). [CrossRef] [PubMed]
  14. D. Psaltis, F. Mok, and H.-Y. Li, “Nonvolatile storage in photorefractive crystals,” Opt. Lett.19, 210–212 (1994). [CrossRef] [PubMed]
  15. N. Kukhtarev, V. Markov, S. Odulov, M. Soskin, and V. Vinetskii, “Holographic storage in electrooptic crystals. I. Steady state,” Ferroelectrics22, 949–960 (1979). [CrossRef]
  16. K. Peithmann, A. Wiebrock, K. Buse, and E. Krätzig, “Low-spatial-frequency refractive-index changes in iron-doped lithium niobate crystals upon illumination with a focused continuous-wave laser beam,” J. Opt. Soc. Am. B17, 586–592 (2000). [CrossRef]
  17. 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]

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