Shift-multiplexed self-referential holographic data storage

Shift-multiplexed self-referential holographic data storage Masanori Takabayashi, 1, * Atsushi Okamoto, 2 Taisuke Eto, 1 and Takashi Okamoto 1 1 Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka, Fukuoka 820-8502, Japan 2 Graduate School of Information Science and Technology, Hokkaido University, N14 W9 Kita-ku, Sapporo, Hokkaido 060-0814, Japan *Corresponding author: takabayashi@ces.kyutech.ac.jp Received 26 March 2014; revised 2 June 2014; accepted 2 June 2014; posted 3 June 2014 (Doc. ID 208958); published 2 July 2014 The feasibility and the properties of shift-multiplexed self-referential holographic data storage (SR-HDS) were investigated. Although SR-HDS has attractive features as typified by referenceless holographic recording, its multiplexing properties, which are consummately important for holographic data storage, have not been clarified until now. The results of numerical and experimental evaluations of medium shift dependence in SR-HDS clarified that the shift selectivity is almost the same as in collinear holography. Furthermore, 25 datapages were successfully shift-multiplexed with the shift pitch of 8.3 μm by the numerical simulation. 2014 Optical Society of America OCIS codes: (210.2860) Holographic and volume memories; (090.1970) Diffractive optics; (090.7330) Volume gratings. http://dx.doi.org/10.1364/ao.53.004375 1. Introduction As the demands for advanced information technology in many research and industrial fields are growing, the requirements for related technologies such as communication and processing become higher. In particular, storing and archiving huge amounts of information is one of the most important applications for future society. Nowadays, information can be stored in various ways, such as magnetically, optically, and electrically. Among them, optical data storage such as CDs, DVDs, and Blu-ray discs, has great advantages for data archiving because of its long archival life, environment resistance, thrifty power consumption, and so forth. Meanwhile, as is known, they are inferior to other storage systems such as magnetic memory in data density and data access rate. Holographic data storage (HDS), which can simultaneously achieve high data density and fast data 1559-128X/14/204375-07$15.00/0 2014 Optical Society of America access rate, has attracted much attention as a next-generation optical data storage technology [1]. Concretely, data density over 1 TB disc and data transfer rate over 1 Gbps can be realized by hologram multiplexing and by page-based parallel accessing, respectively [2,3]. In the long history of HDS, these technologies have been progressed by many researchers and engineers; however, the fundamental optical geometry has pretty much remained unchanged since its invention in 1963 [4] whereas the optical components such as spatial light modulator (SLM), imager, and recording medium have been drastically improved. Since it usually consists of two mutually coherent beams, named the signal and reference beams, the optical system will become enlarged and/or complex compared with the conventional optical data storage systems. Self-referential HDS (SR-HDS), invented in 2011, can holographically record and read information by a purely one-beam geometry [5 7]. In other words, SR-HDS does not need any additional optical path for a reference beam in the recording process. As a 10 July 2014 / Vol. 53, No. 20 / APPLIED OPTICS 4375

similar geometry, the collinear HDS system, in which one beam having signal and reference regions is focused to interfere these regions, has attracted attention and been developed [8 11]. However, the number of recordable data bits per illumination for recording in collinear HDS is lower than that in two-beam HDS, in which two arms are used for signal and reference beams. In contrast, since SR-HDS can use the full area of the writing beam for only a signal data page, it can be realized with few optical components and without sacrificing the data transfer rate; that is, it is a fast, compact, low-cost, and highly stable system. The reason why such attractive advantages can be realized is derived from its novel recording and reading procedures using phase modulation of the beam, and they are explained in Section 2. In our previous works [5 7], we have clarified the properties of SR-HDS with a focus on single page recording; that is, no hologram multiplexing has been assumed. However, in order to consider the performance of SR-HDS, clarifying the hologram multiplexing properties is one of the most important tasks. In this paper, we focus on the hologram multiplexing properties of SR-HDS, and shift multiplexing is assumed as its technique. First, we qualitatively explain the principle of SR-HDS and the behavior of the observed intensity at the imager when a recording medium is spatially shifted. Next, the shift selectivity, which indicates how large a shift distance is required for shift multiplexing, is evaluated both by numerical simulation and experiment. Finally, the multiplexing of 25 datapages is demonstrated by numerical simulation. 2. SR-HDS A. Procedures In the recording process, as shown in Fig. 1(a), we prepare datapage-like patterns named signal and additional patterns. Here, the signal pattern needs to be binary and is made from data to be recorded, whereas an arbitrary distribution is acceptable for the additional pattern. When a laser beam having uniform phase illuminates the phase-only SLM displaying the writing pattern which is the sum of the signal and the additional patterns, the beam is spatially phase modulated and the writing beam is generated. If the focal point is inside or near a recording medium, holograms are induced by interpixel interferences in the writing beam. In the reading process, as shown in Fig. 1(b), the pattern named the reading pattern is displayed onto the phase-only SLM. As is the case with the recording process, the reading beam is generated by illuminating the phase-only SLM displaying the reading pattern by the laser beam having uniform phase. The reading of the recorded datapage can be realized by illuminating the hologram with the reading beam. Then, the reading beam is divided into 0th diffracted (transmitted) and 1st diffracted beams. Since they propagate along the same path, they are coupled to each other. Then, it has been found that the observed intensity distribution by the coupling is similar to the signal pattern when the additional pattern used in the recording process is given as the reading pattern [5]. In other words, the signal pattern, which is phase-modulated to the beam in the recording process, is read as the intensity distribution as shown in Fig. 2. The detailed principles are explained in the next subsection and in [5]. B. Principles As mentioned in Section 2.A, the phase-modulated signal pattern is read as the intensity-modulated pattern in the reading process. To qualitatively explain how such recording and reading processes can be realized, the simplest case is assumed: only two pixels are on the SLM plane, and they are normally illuminated by a plane wave. In the recording process in the two-pixel model, as shown in Fig. 3, a plane wave illuminates a phaseonly SLM with only two active pixels, P 1 and P 2. Then we assume the phase difference between P 1 and P 2 is ϕ w. When it is assumed that the sizes of these pixels are extremely small, the beam after passing through these pixels can be regarded as a spherical beam. Furthermore, if the optical components configure a 4f optical system, these spherical beams are transformed to plane waves by the front Fig. 1. Optical configurations of SR-HDS. (a) Recording process. (b) Reading process. Fig. 2. Patterns used and observed in SR-HDS. 4376 APPLIED OPTICS / Vol. 53, No. 20 / 10 July 2014

1.0 Contrast [arb. units] 0.5 0.0-0.5 0 0.5 1 1.5 2 Fig. 3. Two-pixel model. lens as shown in Fig. 3. As a result of interference between these two beams (pixels), a hologram which is called the elemental hologram in this paper is induced. In the reading process, it is assumed that the phase difference between P 1 and P 2 is ϕ r. Then, as is the case with the recording process, two plane waves are generated. When these two beams illuminate the elemental hologram, they are divided into four components, namely the zeroth-order diffraction component of beam 1, b t 1 ; the first-order diffraction component of beam 1, b d 1 ; the zeroth-order diffraction component of beam 2, b t 2 ; and the firstorder diffraction component of beam 2, b d 2. Then bt 1 is coupled with b d 2, whereas bt 2 is coupled with bd 1 as shown in Fig. 3. In addition, the coupled beam of b t 1 and bd 2 and that of bt 2 and bd 1 reach the imager s pixels Q 1 and Q 2, respectively. Then, according to the coupled wave theory [12], the coupling characteristics of the beam to Q 1 and of the beam to Q 2 are different from each other when the amount of spatial phase shift of the elemental hologram that the reading beams feel, Δϕ ϕ w ϕ r, is not nπ (n:integer). Typically, when Δϕ nπ, the phase difference between b t 1 and bd 2 and that between bt 2 and bd 1 become π 2 Δϕ and π 2 Δϕ, respectively. Concretely, in the case of Δϕ 0, the coupling is symmetrical; that is, the same intensities are obtained at Q 1 and Q 2. Meanwhile, in the case of Δϕ 0, these beams are coupled asymmetrically; that is, different intensities, I 1 and I 2, are obtained at Q 1 and Q 2. Furthermore, the relationship between I 1 and I 2 can be controlled by Δϕ and is characterized by the value Contrast which is defined as Contrast I 1 I 2 I 1 I 2 : (1) -1.0 φ / π Fig. 4. Numerical simulation result of the relationship between Contrast and Δϕ. When the SLM has N pixels (N >2), the principle of SR-HDS can be qualitatively understood by regarding the behaviors of these N pixels as the multiplications of those of the two pixels. In other words, when pixels P 1 ;P 2 ; and P N are on the SLM, the output intensity of the kth pixel, P k, is decided by the superposition of the coupling between two pixels, P k and P i (i 1; 2; ;k 1;k 1; ;N). For example, in the case of N 4 as shown in Fig. 5, 4 C 2 6 types of couplings are superposed, namely coupling between P 1 and P 2, between P 1 and P 3, between P 1 and P 4, between P 2 and P 3, between P 2 and P 4, and between P 3 and P 4. When we focus on the coupling between P 2 and P 4 as an example, the sign of Contrast becomes negative because the phase difference satisfies Δϕ 0 3π 2 0 π π 2. Then the intensity of P 4 becomes stronger than that of P 2. As a result of the superposition of all couplings, it is found that the intensities of P 1 and P 4 tend to be stronger whereas those of P 2 and P 3 tend to be weaker. In other words, when the phase difference between the writing and the reading beams of each pixel is 0 (π 2), the intensity of the pixel tends to be stronger (weaker). Therefore, by designing the patterns appropriately as shown in Fig. 2, information can be recorded and read without using a reference beam. 3. Shift Multiplexing Properties in SR-HDS A. Principles of Shift Multiplexing in SR-HDS As shown in Fig. 4, SR-HDS is based on the energy coupling between two beams, and its coupling Figure 4 shows the relationship between Contrast and Δϕ and provides an important result: Contrast is related only to the phase difference between the recording pixels ϕ w, because the phase difference between the reading pixels ϕ r can be decided in the reading process. Therefore, information can be stored as the form of the phase difference of ϕ w and reconstructed as an intensity difference. Furthermore, Contrast is maximized when Δϕ is near π 2. This can be realized, for example, when ϕ w π 2 and ϕ r 0 are simultaneously satisfied. Fig. 5. Conceptual diagram of multipixel operation. 10 July 2014 / Vol. 53, No. 20 / APPLIED OPTICS 4377

interactions. The operation where the output intensity distribution keeps its uniformity before and after passing through holograms is similar to that when no hologram is recorded. It means that the operation of the SR-HDS in which an inhomogeneous intensity distribution is observed on an imager is lost by shifting the recording medium. As a result, when the recording medium is shifted until the output intensity distribution becomes uniform, a new datapage can be multiplexed. Fig. 6. Spatial phase shift that the reading beams feel when the recording medium is shifted. strength strictly depends on Δϕ. This means that the coupling property between two beams can be changed by shifting the recording medium along the grating wave vector of the hologram. Figure 6 shows the conceptual diagram of two-pixel interaction under a medium shift. The model depicts the case when the elemental hologram with the grating vector of K is shifted to the direction of d. Here, the magnitude of K and d is jkj 2π Λ and jdj, respectively, where Λ is the grating period of the elemental hologram. Because of the shift, the spatial phase shift that the reading beams feel is changed from Δϕ to Δϕ d K. As a result, the contrast is changed even if Δϕ equals π 2 as shown in Fig. 7. By using this feature, the shift multiplexing of the datapages can be realized. When there are N pixels (N >2) on the SLM plane, N C 2 elemental holograms are angularly multiplexed. Since the grating wave vectors of these elemental holograms are different from each other, the influences of the medium shift are also different. Therefore, the observed intensity distribution is the result of the superposition of these degraded energy interactions. When the number of pixels N is large and the recording medium is shifted, the observed intensity distribution tends to be uniform. In other words, the macroscopic energy interchanges between reading pixels are stopped by a number of superpositions of the degraded energy Contrast [arb. units] 1.0 0.5 0.0 0.0 2.0 4.0 6.0 8.0 10.0-0.5-1.0 Shift distance along the x-axis [µm] Fig. 7. Relationship between Contrast and shift distance obtained by numerical simulation. It is assumed that the x axis is parallel to the grating vector of the recorded hologram. B. Numerical Simulations and Experiments In order to prove that the datapages can be multiplerecorded by shifting the recording medium, we performed numerical simulations and experiments. Figure 8 and Table 1 show the simulation models and the parameters, respectively. The photopolymer medium with the resolution of (d x, d y, d z ) and without scattering noise was assumed as the recording medium. Here the M# [13] of the recording medium was about 23.6 mm 1 thickness. The simulations are based on the fast Fourier transform beam propagation method which can calculate three-dimensional light propagation inside a medium with an inhomogeneous refractive index [14]. First, we evaluated how much shift distance is required for the shift multiplexing. We used binary signal patterns with the phase difference of π 2, whereas binary additional patterns have a phase difference of π and 16 times as many pixels as signal patterns [7]. Furthermore, to compare with collinear holography, we performed the simulation with the same conditions as SR-HDS. Then, the shift selectivity of SR-HDS should be evaluated from the viewpoint of the uniformity of the output intensity distribution, whereas that of collinear HDS is usually evaluated by the diffraction efficiency. For the evaluation of the shift selectivity of SR-HDS, the following value is used as the index of the uniformity: D ave I ON I OFF : (2) I ON and I OFF are the average intensity of ON (pixels with phase status of 0 in recording) and OFF (pixels with phase status of π 2 in recording), respectively. In this paper, D ave of 0.0 means that the macroscopic energy interchanges between reading pixels are stopped. Figure 9 plots the simulation results of the shift selectivity. We should note that the vertical axis is normalized diffraction efficiency for collinear HDS and normalized D ave for SR-HDS. The result shows that the energy transfers from pixel to pixel in SR- HDS are apparently stopped when the recording medium is shifted about 2.0 μm. In addition, it can be found that the required shift distance in SR- HDS is not much different from that in collinear HDS. If the shift pitch and the maximum number of multiplexings are the same, it means that the data density of SR-HDS will be about 2 times higher than 4378 APPLIED OPTICS / Vol. 53, No. 20 / 10 July 2014

Table 1. Parameters in the Numerical Simulations Wavelength λ (nm) 532.0 Focal length f (mm) 9.0 Number of sig. pixels (N sx, N sy ) (64, 64) Number of add. pixels (N ax, N ay ) (256, 256) Width of sig. pixels (l sx, l sy )(μm) (90.0, 90.0) Width of add. pixel (l ax, l ay )(μm) (22.5, 22.5) Oversampling rate N 1 8 Zero padding ratio N 2 2 Phase status of signal pattern 0 or π 2 Phase status of additional pattern 0 or π Calc. area (M x, M y, L) (μm) (424.9, 424.9, 400.0) Calc. step (d x, d y, d z ) (nm) (415.0, 415.0, 202.2) Max.modulation depth Δn 4.0 10 3 Sensitivity (cm 2 J) 40.0 Recording time (s) 0.4 Recording power (mw) 1.0 we used a binary signal pattern with the phase difference of π 2 and a binary additional pattern with the phase difference of π and with 16 times as many pixels as the signal pattern. Figure 11(a) shows the observed intensity distribution with the recording medium shift. The reason why the shift distance is set to 10 μm is because the readable resolution of the micrometer head used in the experiment is 10 μm. It is found that the output intensity distribution is degraded by shifting the recording medium. Furthermore, it indicates almost the same trend as the simulation shown in Fig. 11(b) in which the focal point is shifted along the z axis to avoid degradations of the quality. Both in the simulation and the experimental results, obviously, the observed intensity distribution becomes more uniform as the shift distance increases. Fig. 8. Simulation models. (a) Optical configuration. (b) Calculation meshes on SLM plane. (c) Calculation meshes in recording medium. Intensity distribution (d) on focal plane (x y) and (e) on cross-sectional plane (x z). that of collinear HDS because the reference region, which occupies about 50 percent of the SLM region, is not required in SR-HDS. We also performed the experiment to confirm that the output intensity distribution is changed under the medium shift. Figure 10 shows the experimental setup, and the laser source is a diode-pumped solid state laser with the wavelength of 532.0 nm. The focal length of both the objective lenses, OBL1 and OBL2, is 9.0 mm, and high-resoluble photopolymer with a thickness of 400 μm is used as the recording medium [15]. The photopolymer medium is sandwiched by glass plates with thicknesses of 500 and 800 μm. As in the previous numerical simulation, Normalized value [arb. unit] 1.0 D ave for SR-HDS 0.8 Diffraction efficiency for collinear-hds 0.6 0.4 0.2 0.0-10.0-5.0 0.0 5.0 10.0-0.2 Shift distance along the x-axis [µm] Fig. 9. Numerically evaluated shift selectivities of SR-HDS and collinear HDS. Fig. 10. Experimental setup. 10 July 2014 / Vol. 53, No. 20 / APPLIED OPTICS 4379

where V ON and V OFF are the intensity variance of ON and OFF pixels, respectively. The graph shows that the SNR of datapage 1 is reduced as the number of multiplexings, m, increases, as in other types of HDS such as collinear HDS. By using an exponential approximation, this curve can be approximated by the following equation: Fig. 11. Observed intensity distributions on imager plane by (a) numerical simulation and (b) experiment. Finally, we demonstrated the shift multiplexing of 25 datapages by the numerical simulation. In the simulation, the conditions are the same as those in the previous evaluations: an additional pattern with 256 256 pixels is added to a signal patterns with 64 64 pixels. The datapages are multiplexed by spirally shifting the recording medium as shown in Fig. 12. Here, the scheduling theory of the recording time is not applied in the recording process [16]. In addition, the shift distances along both the x and y axes, Δx and Δy, were set to 8.3 μm. Figure 13(a) shows the relationship between the signal-to-noise ratio (SNR) of the first-recorded datapage and the number of multiplexings, m. Here, SNR is defined as SNR I ON I OFF V ON V OFF ; (3) Fig. 12. Recording layout. Fig. 13. Numerical simulation results of 25-multiplexed SR- HDS. (a) SNR of first datapage and the number of multiplexings. The dashed line is an exponentially approximated curve defined by Eq. (4). (b) Output intensity distribution when 1, 10, 20, and 25 hologram(s) are multiplexed. (c) SNR values of each multiplexed datapage. 4380 APPLIED OPTICS / Vol. 53, No. 20 / 10 July 2014

SNR 1 11.71e 0.056 m ; (4) as plotted in Fig. 13(a) (dashed line). Two reasons are cited as the possible causes for the SNR reduction. One is the interpage cross talk from the neighboring datapages. For example, at the appropriate position for reading datapage 1, if the intensity distribution of datapage 2 is not completely uniform, the nonuniform intensity distribution derived from datapage 2 is multiplied to the desired datapage 1 as noise. Another is the reduction of the diffraction efficiency at each elemental hologram. In general [13], the diffraction efficiency of a hologram is reduced by a factor of m 2. Therefore, the intensity difference between ON and OFF pixels, D ave, is reduced, and this results in the reduction of SNR. In the case of this simulation, it can be seen that the SNR values keep over 2.0, even when the number of multiplexings reaches 25. This shows the datapage can be successfully read from the multiple-recorded holograms, as shown in Figs. 13(b) and 13(c). This is the first verification that the datapages can be shift multiplexed in a local spot by SR-HDS, and it achieves the purpose of this paper: proving the feasibility of shift-multiplexed SR-HDS. For the practical use of SR-HDS, more datapages should be multiplexed with high SNR, that is, low error rate. The number of shift-multiplexed datapages will be able to increase by several approaches and by optimizing recording conditions such as numerical aperture of the lens, design of additional patterns, and recording scheduling techniques. In addition to the optical systems, clarifying and optimizing the relationship between the properties of the recording medium, such as scattering noise and resolution, and the SNR is one of the most important tasks in the future. 4. Conclusions The shift-multiplexing properties of SR-HDS have been evaluated. 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