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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] or otherwise [2, 3]), photorefractive solitons [4–6], and optically-induced waveguides [7, 8]. 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], 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]. For light-induced waveguides and solitons, the temporal buildup of the refractive index change follows a similar exponential trend [8, 11]. 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], 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.
Here we propose a novel process that will allow data to be optically written into an optically thick PR medium, and then deliberately overexposed to encrypt the data. Since the technique is not holographic in nature, it does not rely on beam interference and therefore is insensitive to environmental perturbations such as vibrations. The approach is based on our previous work which showed that data stored in a lithium niobate crystal were degraded when overexposed [13]. The degradation of the data patterns was characterized by a splitting of the stored refractive index changes into finer filaments of higher spatial frequency. Even under low irradiances (∼mW/mm2) the degradation of these patterns was so extensive that the original pattern was completely obscured. Here we show that the photorefractive writing and erasure processes are related and that through incoherent erasure with a halogen lamp, the degradation process can be reversed, revealing the original encrypted information. We show that information recovery is only possible by linking the time at which specific features appear during writing, with the time at which the same feature appears during erasure. To calculate the required erasure time for recovery of a specific written pattern, we must determine a time-dependent function that depends on user-defined features, such as beam properties and data dimensions. This functionality can be utilized for data encryption.
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]. 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. 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, 11, 15], the magnitude of the change in refractive index of the pattern’s stripe regions (normalized to the saturation value), during writing is described by
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].If the time taken to write the data is t0, and erasure starts shortly after, the normalized index change is described by
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).
During writing or erasure, the intensity, P(x), at a particular location x, e.g. at x = 1.3 mm, is observed to oscillate as the bifurcation process evolves. For example, as shown in Fig. 3, the value of P(1.3) reaches a maximum when the bright stripe that represents the datum is well-formed (at t = 4 minutes) and then reaches a minimum after the first bifurcation (at t = 8 minutes). The same pattern appears in the reverse order during erasure, i.e. at t = 132 minutes (maximum) and 105 minutes (minimum). These extrema are displayed more clearly in Fig. 5, where the normalized intensity P(x) at x = 1.3 mm is plotted for the write and erase process as a function of time. It can be seen that there is striking agreement between the two intensity profiles, implying that a correlation exists between the three-dimensional refractive index distributions within the medium during writing and erasure. Figure 5 shows the various maxima and minima produced by bifurcation (labeled 1–6) that can be matched to deduce the write time tw and erase time te when the medium’s spatial refractive index distributions are equivalent. The data presented in Fig. 5 show the oscillatory behavior of P(x) for just one location x. By considering many other locations, e.g. the x corresponding to the regions between the bright stripes, or on the edges of the bright stripes, we can match write and erase times for various defined features to build up a relationship that links the write and erase dynamics.
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.
Plotting the erasure time (te + t0) against the writing time tw for specific spatial features to appear at several locations during both writing and erasure shows that the two time scales are related by a one-to-one functional relationship as shown in Fig. 6. This confirms that a direct correlation exists between the degradation and recovery processes, with the specific nature of the correlation under user control through choice of experimental parameters. This is demonstrated by Fig. 6 which shows the correlation plots between the erasure and writing time scales when the incident 532 nm beam was focused to three different sizes after transmission through the mask. Focusing alters the writing intensity and feature size, which modifies the time required for writing specific features and the time required to erase the overexposed pattern until the feature returns. For the plots shown in Fig. 6, the generic relationship between tw and (te + t0) is:
where A and B are constants found using regression. The values of A and B depend on the intensity of the write and erase beams, as well as material properties of the medium, and the feature size. The data in Fig. 6 show that over a range of write intensities (∼ 1 mW/cm2 up to 40 mW/cm2) and pattern feature sizes, the correlation relationship given by Eq. (3) holds. The constants A and B, therefore, uniquely define the experimental parameters used during the writing and erasure processes.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:
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] 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.
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