Disk-based optical memory (such as CDs, DVDs, and Blu-ray disks) represents one of the major products in optical technology. However, other types of memory, such as hard-disk drives and semiconductor memory, have seen increases in storage capacity and access speed. In an advanced, ubiquitous information society, mobile use of data-storage media as well as the underlying communication technology is important because much information is transmitted and received by mobile devices. In this context, we are developing a tiny and secure data-storage medium that can be used as an identity tag.1–3
In our solution, data is stored as small absorbers in a 3D scattering medium. Strong scattering leads to a blurred intensity distribution, as if one were observing an image through broken glass. This effect can be avoided by measuring the intensity distribution with an interferometer. To reconstruct the absorption distribution we use diffuse optical-tomography techniques that must be solved numerically. When the distribution of the scattering coefficient is known and the absorption is weak, it is relatively easy to numerically estimate the absorption distribution using a model of the photonic medium. Consequently, we have devised a means of controlling the scattering coefficient using voids generated by femtosecond-laser-pulse irradiation. If the thickness of the photonic data-storage medium is less than 100μm (such as a glass cover for optical microscopy), it can be bent and attached to clothing or paper documents such as books and newspapers. But realizing a medium this thin requires a large scattering coefficient.
Figure 1 illustrates the concept of a photonic data-storage medium with correct and incorrect reconstructions of the input intensity. Information is stored by recording the 3D positions, sizes, structure, and spectral contents of the absorbers. Because a strong scattering coefficient can conceal the absorption distribution, input and output intensity distributions as well as a weight function must be calculated from the distribution of the scattering coefficient. In our reconstruction, we make a model of the medium where the distribution of the scattering coefficient is already known and the unknown parameter is the absorption distribution. The output intensity distribution can then be calculated by solving a numerical optical-diffusion equation, where the experimental intensity pattern is used as numerical input data. Initially, the numerical output intensity distribution differs from that obtained experimentally because our initial guess for the absorption distribution is incorrect. The latter is updated iteratively to minimize the difference between the numerical and experimental results.
Figure 1. Concept of our photonic data-storage medium.
We expect that our data-storage medium will eventually reach a volume of 20×20×1mm3, with an interval between absorbers of 20μm and supporting a spectral content of 20 colors, leading to a storage capacity of ~125MB. This is enough to store an Internet movie file. There are two ways to develop a secure photonic data-storage medium. One is less secure but offers more storage capacity, and cheaper optical equipment suffices for widely available use. The other is more secure but offers less storage capacity and requires more expensive optical elements for authentication. The desired solution can be selected based on the level of complexity of the distribution of the scattering coefficient.
We have proposed a method to control the scattering coefficient based on randomly embedded voids created by focused femtosecond-laser pulses in a transparent material.2 The void structure results in large refractive-index differences relative to the surrounding bulk material, which can be used as a scattering seed. The important feature of this technique is that the scattering coefficient can be controlled by varying the void density. We fabricated our scattering media using poly(methyl methacrylate) (PMMA): see Figure 2. We introduced a 3D layered structure combined with a periodic pattern of voids in each layer. We made the voids by focusing single femtosecond-laser pulses from a regeneratively amplified titanium:sapphire laser (with a central wavelength of 800nm, a pulse width of 100fs, and a repetition rate of 1kHz) using an objective lens with a numerical aperture of 0.8. Figure 3 shows an example of our scattering medium (with a size of 20×20×0.62mm3). The intervals between the voids were selected randomly from 3 to 7μm in any given layer, with a layer separation of 10μm and a total number of voids of approximately 5×108.
Figure 2. Schematic of void structure (black squares) for controlling the scattering coefficient.
Figure 3. Our newly developed scattering medium.
We measured the width of the output intensity distribution as a function of void density. Figure 4 shows our optical setup. A helium-neon laser beam with a wavelength of 594nm and a beam diameter of 0.76mm illuminates the medium's front surface. The output beam at the rear surface is observed by a CCD image sensor. Our fabricated region is 3×3×1mm3. We defined the output beam width as 1/e2 times the full width, obtained by fitting a Gaussian function to the measured beam intensity. To calculate the void density we assumed that a void is ~2×2×6.4μm3, based on optical-microscope images (although their volume changes with depth because of spherical aberration). Figure 5(a) shows that the output beam width increased monotonically with increasing void density and decreased after reaching a peak at a void density of 21%. Figure 5(b) shows the output beam width as a function of scattering coefficient based on Monte Carlo simulations. Both profiles are very similar. Therefore, the scattering coefficient can be controlled by changing the void density. The quantitative difference can be reduced by precise measurements of void size with depth.
Figure 4. Optical setup for measuring the width of the output beam. NDF: Neutral-density filter. He, Ne: Helium, neon.
Figure 5. Beam width (in arbitrary units) as a function of (a) void density and (b) scattering coefficient.
To create absorbers in a scattering medium, we can use photochromic or photobleaching effects. We have been trying to develop a method to simultaneously create the scattering medium and absorbers in a layered structure. In a highly scattering medium, ballistic and snake light is lost during multiple scattering events. Therefore, we cannot apply computer tomography techniques to numerically recover the absorption distribution from the output intensity field. It is also impossible to completely measure the 3D absorption distribution in a highly scattering medium using an interferometer, although we could rely on diffusion optical tomography. In this technique, we make a model that is based on the distributions of the scattering and absorption coefficients.3 We update the absorption distribution at each voxel (3D or volumetric pixel) to reduce the difference between the experimental output intensity distributions and the numerical calculation. We also use a weight function that yields the rate of change of the output intensity with slight absorption-coefficient variations.
For simplicity, it is much easier to reconstruct the data based on a priori information about the distribution of the scattering coefficient. Its complicated structure renders the system more secure. Figure 6 shows a three-layered material with different scattering coefficients. Figure 6(a) and (b) shows the distributions of the scattering and absorption coefficients, respectively. In Figure 6(a), the scattering coefficient in the top and the bottom layers is 30/mm, while it is 10/mm in the middle layer. (The medium's thickness is 1.0mm.) Three absorbers are distributed separately into three layers. Figure 7(a) and (b) shows our numerical reconstructions of the absorption distributions using correct and incorrect distributions of the scattering coefficient, respectively. The former can be used to reconstruct the three absorbers: see Figure 7(a). If we assume a scattering coefficient in the middle layer of 30.0/mm, the quality of the reconstructed absorption coefficient is very poor. This indicates that the distribution of the scattering coefficient is very important for accurate reconstruction of the absorption distribution.
Figure 6. Three-layered scattering medium. Distributions of (a) the scattering and (b) the absorption coefficient.
Figure 7. Numerical reconstruction using (a) the correct and (b) incorrect scattering-coefficient distributions.
In summary, we have presented a novel kind of optical memory that uses absorbers as data in a highly scattering medium. The scattering properties can protect the data from techniques to reconstruct its 3D distribution using computer or optical coherence tomography. Because the thickness of the medium can be less than 100μm, our newly developed memory can be attached to paper documents or clothing. To recover the absorption distribution, we employ a numerical reconstruction method using a priori information about the distribution of the scattering coefficient. We have also proposed a method to control the scattering coefficient using voids generated by a femtosecond-laser pulse. Based on preliminary experiments, the scattering coefficient can be controlled by the void density. We are currently refining our experimental data-reconstruction technique.
This work was supported by the Industrial Technology Research Grant Program of the New Energy and Industrial Development Organization of Japan in 2008 (grant 08A16006d).
Department of Computer Science and Systems Engineering
Osamu Matoba received his PhD in applied physics from Osaka University (Japan) in 1996. He was a research associate at the Institute of Industrial Science of the University of Tokyo (Japan) from 1996 to 2002. He is now a professor.