Abstract

Interpixel cross talk decreases the quality of a reconstructed signal in holographic data storage and imposes a limitation on its storage capacity. To reduce the interpixel cross talk, an orthogonal polarization encoding method is proposed. In the proposed method, the polarization state of each pixel is set to be orthogonal with that of surrounding pixels. This prevents the interference between nearest-neighboring pixels and significantly reduces the gross of the interpixel cross talk. The quality of the data page obtained with the proposed method is numerically and experimentally evaluated. Those results suggest that the proposed method can improve the quality of a reconstructed signal.

© 2017 Optical Society of America

1. Introduction

Holographic data storage simultaneously provides large storage capacity and fast data transfer rate owing to multiplexing and page-wise recording processes [1, 2]. The storage capacity of holographic data storage is proportional to the areal information density D which is given by D = M · P · S−1, where M, P, and S are the number of multiplexed volume holograms, the amount of data in a single data page, and a recording area on a medium, respectively [2, 3]. So that, the characteristic factors of M and P should be large, and S should be small. The values of each parameter have been steadily improved by a lot of researchers over a long period, as outlined below.

In order to increase the number of multiplexed volume holograms M, various multiplexing techniques such as angle, phase-encoded, and shift multiplexing have been proposed [2–6]. These techniques allow multiple volume holograms to be stored in the same volume by changing the optical property of a reference beam or displacing a recording medium.

As an approach for increasing the amount of data P, multilevel recording methods have been proposed. In most of the holographic data storage systems, digital data are represented by just binary amplitude values of “0” and “1”. By utilizing the gray scale amplitude values between “0” and “1”, it is possible to increase the amount of data [7]. In addition to the amplitude values, phase values can be used as information [8–10]. These encoding methods increase the coding rate of a data page, and thus increase storage capacity and data transfer rate simultaneously.

For decreasing the recording area S, a square aperture is generally used in most of the holographic data storage systems. A square aperture restricts the exposure area, preventing the unnecessary consumption of a recording medium. The use of a small aperture allows high storage densities since a data page is stored in a small area of a recording medium [1–3]. However, the small square aperture acts as a spatial low-pass filter to the data page. High frequency components of a data page is not recorded in a recording medium. As a result, a beam propagated from each pixel of a data page is spread out and interferes with that from neighbor pixels. The interference between neighbor pixels decreases the quality of reconstructed data pages, which leads to data errors. This degradation tends to be large with a decrease in the aperture size. The source of this degradation is called interpixel cross talk [11–13]. The interpixel cross talk therefore imposes a limitation in decreasing the recording area S. In general, to reduce the interpixel cross talk, digital data are subject to a modulation code such as 3:16 and 1:4 coding methods [14, 15]. An introduction of a modulation code prevents specific arrangements of data pixels that cause the interpixel cross talk. In addition, the use of the modulation code makes the intensity of each data page constant regardless of digital data to be stored. Although the quality of a reconstructed signal can be improved by the introduction of a modulation code, the constraints in the effective code modulation often leads to a decrease in the coding rate, or the amount of data P.

In this paper, we aim to reduce the interpixel cross talk that can be brought about the increase of the storage capacity through reducing the size of the exposure area S or relaxing the constraints in modulation codes for the data page. For the purpose, we propose an orthogonal polarization encoding method. In the proposed method, the polarization state of each pixel is orthogonal with that of the four surrounding pixels. This arrangement allows the reduction of the interpixel cross talk because a beam propagated from each pixel is incoherent with that from the nearest-neighboring pixels. A similar approach was proposed and demonstrated to suppress the speckle in holographic imaging [16]. In this method, two holograms are sequentially recorded by angular multiplexing. During reconstruction, reference beams from two light sources, which are incoherent with each other, illuminate the double holograms. This results in the suppression of the speckle. Although this method might be applicable in holographic data storage, the use of two light sources is not preferable for realizing practical holographic storage systems. Unlike the above method, our proposed encoding method makes use of the polarization state of a beam and uses only a single light source. In general, it is impossible to record and retrieve the polarization state of a beam with traditional photopolymer materials in conventional holography [1, 2]. However, by introducing a technique of polarization holography, the polarization state can be recorded and retrieved with a polarization-sensitive medium [17, 18]. We therefore record and retrieve proposed data pages on the basis of polarization holography instead of conventional holography.

This paper is organized as follows. In Section 2, we briefly review interpixel cross talk. Moreover, the principle of the proposed encoding method is described. In Section 3, numerical simulations are carried out to validate the feasibility of the proposed encoding method. In Section 4, the proposed method is experimentally demonstrated with low-pass filtering. Subsequently, the feasibility of the proposed encoding method is validated through experimentally recording a volume polarization hologram on a polarization-sensitive medium. Finally, we provide our conclusion in Section 5.

2. Orthogonal polarization encoding for reduction of interpixel cross talk

Before describing the proposed encoding method, we briefly review interpixel cross talk. Figure 1 shows a schematic of a holographic storage system. A spatial light modulator (SLM) generates a signal beam according to a data page. The generated signal beam is optically Fourier transformed by a lens. The Fourier spectrum of a signal beam is incident on a recording medium. A reference beam is simultaneously superimposed onto the Fourier spectrum of a signal beam, which results in an interference pattern. The interference pattern is recorded as a volume hologram in a recoding medium. When the volume hologram is illuminated by the reference beam, the Fourier spectrum of a signal beam is reconstructed. The reconstructed beam is subsequently Fourier transformed by a lens. An image sensor detects the intensity distribution of the resulting beam, and thus the original data page can be retrieved. To restrict a recording area, a square aperture with a width of w is often placed in front of a recording medium. The minimum width of the square aperture that called Nyquist size is given by

w=fλd,
where f is the focal length of a lens, λ is a wavelength of a light source, and d is each size of ON and OFF regions. This square aperture is known as the Nyquist aperture [1, 2]. Although the use of a small aperture leads to the increase in the areal information density, the quality of a reconstructed data page deteriorates. This is because restricting the recording area with the aperture corresponds to low-pass filtering. A reconstructed data page on an image sensor is given by the convolution between an original data page and the Fourier transform of a square aperture. The Fourier spectrum of the square aperture is a 2D sinc function. A propagated beam from each pixel is therefore blurred according to the sinc function. A resulting beam causes interference between neighbor pixels, thus decreasing the quality of a reconstructed data page on an image sensor. The interpixel cross talk is therefore caused by the interference owing to the low-pass filtering.

 

Fig. 1 Schematic of a holographic data storage system.

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To reduce the interpixel cross talk, we propose an orthogonal polarization encoding method. Figure 2 shows the polarization distribution of conventional and proposed data pages. The squares indicate ON or OFF pixels of a data page, and each pixel size is d × d. The arrows in the pixels indicate the direction of linear polarization. When a signal beam is generated, the amplitude of linear polarization in each pixels is modulated according to a data page to be stored. In addition, the phase distribution is also modulated according to a random phase mask [19] to suppress a high-intensity dc component in the Fourier plane.

 

Fig. 2 Polarization distribution of (a) conventional and (b) proposed data pages.

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In the conventional data page indicated in Fig. 2(a), the polarization states of whole pixels are the same. This is why the quality of reconstructed data pages deteriorates due to the interpixel cross talk. Unlike the conventional data page, the proposed one consists of two orthogonal polarization states, as indicated in Fig. 2(b). Each pixel has an orthogonal polarization state to four surrounding pixels. Therefore, any interference between the nearest neighboring pixels does not occur on a detector plane. Interpixel cross talk can therefore be reduced by virtue of the orthogonal polarization. Note that this arrangement suppresses only the interference from the four surrounding pixels. This means the proposed method cannot suppress the interference from the diagonal and other surrounding pixels. However, the interpixel cross talk is mainly caused by the interference from four surrounding pixels, as pointed in previous articles [11, 12]. Thus, it can be anticipated that the efficient reduction of the interpixel cross talk from the four surrounding pixels results in the improvement in the quality of a reconstructed data page. In this paper, we therefore devise the above mentioned method.

The advantage of the proposed method can be explained from the aspect of a spatial frequency bandwidth. Figure 3 shows the spatial frequency bandwidth of data pages shown in Fig. 2. The broken line indicates the Nyquist aperture for the conventional data page. In contrast, the solid line in Fig. 3 indicates the Nyquist aperture for each polarization state of the proposed method. The proposed data page can be regarded as the incoherent summation of two data pages with orthogonal polarization states, as shown in Fig. 4. The sampling period of each data page shown in Fig. 4 is sparser than that of the conventional data page shown in Fig. 2(a). The pixels are sampled in a grid tilted by 45 degrees, and the sampling period is 2d. The Nyquist size for each data page in Fig. 4 is therefore 2w/2. This means that in the proposed data page significant spectrum information concentrates at low-frequency region as compared with the conventional data page. For instance, in the case of using a square aperture with a size of w to restrict a recording area, additional frequency information over the Nyquist size can be recorded as a volume hologram in the proposed method.

 

Fig. 3 Spatial frequency bandwidth of conventional and proposed data pages.

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Fig. 4 Sampling period of each polarization state in the proposed data page. (a) Horizontally and (b) vertically polarized beams.

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3. Numerical simulation

In this section, we carried out numerical simulations to validate the feasibility of the proposed method. Figure 5 shows a numerical simulation model. This numerical simulation calculates spatial low-pass filtering to a signal beam. Although here we ignore the effect of a recording medium and a reference beam, it is possible to evaluate the effect of only the interpixel cross talk on a reconstructed data page [11]. In practical holographic storage systems, a recording area is restricted with a square aperture whose size is larger than the Nyquist size w. Although there is the trade off between the areal information density and the quality of reconstructed data, the recording performance is maximized when the aperture is close to the Nyquist size w [1,13,20]. From this aspect, we numerically compare the conventional and the proposed methods in the case of using a square aperture with the Nyquist size w.

 

Fig. 5 Numerical simulation model for evaluating the effect of the interpixel cross talk.

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Figure 6 shows data pages to be used in this numerical simulation. Each data page consists of 8 × 8 pixels. The number of pixels of each data page shown in Fig. 6 is smaller than that of data pages as used in practical holographic storage systems. However, it is possible to evaluate the effect of the interpixel cross talk by using such data pages since the main contribution comes from the four surrounding pixels as noted above. The amount of interpixel cross talk on reconstructed data pages is different depending on the arrangement of the ON pixels [11–13]. There are two simple ways to decrease the interpixel cross talk. One is a reduction of the number of ON pixels, and the other is to make an arrangement of the ON pixels in the data page sparsely. Therefore, to reduce the interpixel cross talk, digital data are generally subject to a modulation code such as 3:16 and 1:4 coding methods [14, 15]. This prevents to use specific arrangements of data pixels that are relatively susceptible to the interpixel cross talk.

 

Fig. 6 Data pages designed with a 1:2 coding. Data page (a) #1, (b) #2, (c) #3, (d) #4, and (e) #5.

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In this paper, we aim to investigate the effect of our proposed method under the pixel arrangement condition in which the interpixel cross talk frequently occurs. For the purpose, we use a 1:2 coding [21] for generating data pages shown in Fig. 6. In a 1:2 coding, a single symbol consists of a single ON (bright) pixel and a single OFF (dark) pixel. This makes the intensity of each data page constant regardless of digital data to be stored. A 1:2 coding is known as that the modulation method is susceptible to the interpixel cross talk because of the dense ON pixels, as compared with 1:4 and 3:16 coding methods. Therefore, the use of the 1:2 coding method allows us to validate the feasibility of the proposed method under such disadvantageous situation that relatively susceptible to interpixel cross talk. Although the data pages shown in Fig. 6 are generated so that ON and OFF pixels are randomly distributed on each data page for preventing partially localized Fourier spectra, each data page contains all possible arrangements in the 1:2 coding that each of ON and OFF pixels is surrounded by one, two, or three ON pixels. By using such data pages, it is possible to evaluate the effect of the interpixel cross talk of the all arrangements in the 1:2 coding.

Numerical simulations are performed as follows. ON and OFF pixels are represented by 32 × 32 pixels in this simulation, respectively. A data page is thus represented by 256 × 256 pixels. The SLM and the detector were assumed to be full fill factor, and these are pixel-matched. According to a data page, the amplitude distribution is generated. In addition to the amplitude modulation, phase distribution is modulated with a random phase mask [19] as used in practical holographic storage systems. The random phase mask has binary phase values, 0 and π. The phase distribution of the random phase mask is indicated in the inset of Fig. 5. The black and white show the phase value 0 and π, respectively. For the numerical simulation of the conventional method, the polarization state of whole pixels are set to be the same. The generated beam is numerically Fourier transformed. In the Fourier plane, the spectrum is spatially filtered with the Nyquist aperture. The filtered beam is numerically Fourier transformed. In the detector plane, the intensity distribution of the resulting beam is obtained. The intensity distributions of conventional data pages are shown in Figs. 7(a)7(e). High frequency components are removed by low-pass filtering with the Nyquist aperture. In addition, there is destructive interference between the ON pixels which have the phase difference π.

 

Fig. 7 Numerically low-pass filtered data pages. Conventional data page (a) #1, (b) #2, (c) #3, (d) #4, and (e) #5. Proposed data page (f) #1, (g) #2, (h) #3, (i) #4, and (j) #5.

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For the numerical simulation of the proposed method, each data page with the random phase mask is generated in the same way as the simulation for the conventional method. The polarization distribution is modulated according to the inset of Fig. 5. The polarization state of each of ON pixels is orthogonal to that of four surrounding pixels. To calculate the Fourier transform of such a vector optical field of the proposed method, the beam is divided into the horizontally and vertically linear polarization components [22]. Each polarization component is numerically Fourier transformed and filtered with the Nyquist aperture. In the detector plane, the intensity distributions of each polarization state are summed, and a reconstructed image can be obtained. Figures 7(f)7(j) show the intensity distributions of the proposed data pages. In comparison with the conventional method shown in Figs. 7(a)7(e), there is less destructive interference between ON pixels in Figs. 7(f)7(j). This comes from the orthogonality of the polarization state in the proposed method.

To evaluate the data error rate of each intensity distribution shown in Fig. 7, we identified ON and OFF pixels by comparing the brightness between two pixels in each symbol of the 1:2 coding method. Brighter and darker pixels are assigned as ON and OFF pixels, respectively. As a result, the original data pages can be retrieved in the conventional and the proposed methods without any error from all obtained intensity distributions. Subsequently, we evaluated the quality of each intensity distribution shown in Fig. 7 by means of a signal-to-noise ratio (SNR). The SNR is defined as

SNR=μonμoff(σon2+σoff2)1/2,
where μon and μoff are the means, and σon2 and σoff2 are the variances, of the ON and the OFF pixels in a reconstructed image, respectively [1]. The SNRs of conventional and proposed methods are shown in the top of each image in Fig. 7. The SNRs of all data pages are improved by the proposed method although the improvement ratio is different depending on a data page. The average SNRs of conventional and proposed methods are 2.17 and 4.86. On average, the SNR of the proposed method is 2.24 times higher than that of the conventional method. Although original data pages can be retrieved from the conventional and the proposed data pages in Fig. 7 without any error, the higher SNR is preferable for practical systems. Since the high SNR can be expected by the proposed encoding method, the system employing our method is surely tolerant toward other noises caused by an SLM, a recording medium, and a detector.

Instead of improving the noise tolerance of a recording system, the proposed method can be applied for reducing the aperture size. It is possible to record volume holograms using a smaller aperture than the Nyquist size while maintaining the same SNR level as the conventional method. Therefore the areal information density D can be increased. Alternatively, the proposed method can relax constraints for the modulation codes. This means that a coding rate of a modulation code can be increased, and thereby the amount of data P can be increased.

4. Experiments

In this section, we experimentally verify the feasibility of the proposed method. Similar to the numerical simulation in Section 3, we first evaluate the quality of low-pass filtered data pages simply using a spatial aperture. In this evaluation, a recording medium is not inserted in an experimental setup. Conventional and proposed data pages are optically generated by the SLMs and low-pass filtered by the aperture. The SNRs of the resulting data pages are assessed and compared. Subsequently, we record volume holograms of conventional and proposed data pages on a recording medium. Unlike conventional data pages, the proposed data pages possess polarization distribution. To record such data pages, we make use of polarization holography [17, 18]. In addition to the amplitude and the phase, the polarization can be stored on a polarization-sensitive medium as a volume polarization hologram. Through the above experiments, we show that the proposed method can reduce the interpixel cross talk.

4.1. Evaluation without recording volume holograms

Figure 8 shows an experimental setup for evaluating the effect of the interpixel cross talk on conventional and proposed data pages. A mode-hop-free single-mode laser with a wavelength of 405 nm was used as a coherent light source. By using a half wave plate and a polarizer, the direction of the linear polarization was oriented at 45 degrees. A collimated beam was obtained through a spatial filter and a collimating lens. The collimated beam was divided into two beams using a non-polarizing beam splitter. The phase distributions of the divided beams were modulated with two phase-only SLMs which have 800 × 600 pixels with a pixel pitch of 20 μm (X10468-01, Hamamatsu Photonics K. K.) to generate a vector beam which has arbitrary amplitude, phase, and polarization distribution. Two SLMs were carefully set to as the difference in the optical path length between the two SLMs from the beam splitter is equal to or less than the coherence length of the light source. In general, to modulate amplitude, phase, and polarization distribution at the same time, four SLMs are required [23]. However, it is possible to generate an arbitrary vector beam using only two phase-only SLMs with the help of a phase hologram [24, 25]. In order to generate the required polarization distribution, it is possible to use only one spatial light modulator. However, it is not easy to obtain an actual array of the half-wave plate that is matched to the dimensions of the SLM pixels, and also costs a lot. Also, in the case of the introduction of gratings, light efficiency is limited at the very low value. Therefore, we have decided to employ the way to use two spatial light modulators in this experiment. There are other techniques for arbitrarily controlling the polarization state on each pixel. One example is a method using metasurface. [26, 27].

 

Fig. 8 Optical setup for evaluating the effect of the interpixel cross talk on conventional and proposed data pages. HWP, half wave plate; P, polarizer; SF, spatial filter; Li, Lens; SLMi, phase-only spatial light modulator; M, Mirror.

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The generation process of an arbitrary vector beam is briefly described below. An arbitrary vector beam is given by two orthogonal complex amplitude, E1 and E2, on the basis of Jones formalism:

(E1(x,y)E2(x,y))=(a1(x,y)exp{iϕ1(x,y)}a2(x,y)exp{iϕ2(x,y)}),
where a1 and a2 are the amplitudes, and ϕ1 and ϕ2 are the phases, of linearly polarized beams, respectively. Each complex amplitude En(x, y) (n=1,2) can be generated with a phase hologram [28–30]. The phase hologram ψn(x, y) for generating En(x, y) is given by
ψn(x,y)=an(x,y){ϕn(x,y)+ϕc(x,y)},
where ϕc is a linear phase distribution, which is required to separate a desired component from unnecessary diffracted beams in the Fourier plane. It should be noted that Eq. (4) is valid for binary amplitude distribution such as data pages in holographic data storage [31, 32]. When one generates multilevel amplitude values with a phase hologram, it is required to modify Eq. (4). According to the phase holograms ψ1 and ψ2, the phase distribution of the divided beams are modulated using two phase-only SLMs. The alignment direction of the liquid crystal molecules of two phase-only SLMs were orthogonal with each other. These phase-only SLMs therefore separately modulate the horizontal and vertical components of the linearly polarized beam oriented at 45 degrees. The phase-modulated beams were recombined though a non-polarizing beam splitter and Fourier transformed by a lens. In the Fourier plane, an aperture removes undesired spectra due to the phase holograms and the pixelated structure of the SLMs. Concerning the energy efficiency of the proposed method is not quite high, since the half of the incident beam is eliminated at each element by the beam splitter and the aperture at the Fourier plane, respectively. However, it could be improve if we could employ a transmissive SLM or a Mach-Zehnder interferometric arrangement. The filtered beam is subsequently Fourier transformed. As a result, any desired vector beams described by Eq. (3) can be generated. The more details for generating an arbitrary vector beam are described in [24, 25].

In this experiment, conventional and proposed data pages were generated using the above mentioned technique. For example, in the case of generating the data page #1 shown in Fig. 6(a) with the conventional method, the phase hologram shown in Fig. 9(a) is displayed on the SLM 1, and the SLM 2 is inactive. When the data page #1 is generated with the proposed method, the phase holograms shown in Figs. 9(b) and 7(c) are displayed on the SLM 1 and SLM 2, respectively. For the generation of a data page based on the conventional method, the phase hologram of Fig. 9(a) is inputted into the SLM 1 and the intensity distribution shown in Fig. 9(d) is obtained via Nyquist aperture. In contrast, for the generation of a data page based on the proposed method, the phase hologram of Figs. 9(b) and 9(c) are inputted into the SLM 1 and SLM 2, respectively. These SLMs are arranged orthogonal to each other, namely the alignment directions of the liquid crystals of each SLM make an orthogonal relationship. Therefore, the orthogonality of the polarization of the two patterns generated from each phase hologram is maintained. The intensity distributions generated from each phase hologram are shown in Figs. 9(e) and 9(f), respectively. The Nyquist aperture removes not only the undesired spectra due to the phase holograms and the SLMs but also the high frequency components of data pages. The filtered beams were captured with a CMOS camera which has 2592 × 1944 pixels and a pixel pitch of 2.2 μm. Note that a recording medium was not used for this experiment. The data pages were just low-pass filtered with the Nyquist aperture.

 

Fig. 9 Phase holograms for generating the data page #1. (a) Phase hologram displayed on the SLM 1 for demonstrating the conventional method. (b), (c) Phase holograms displayed on the SLM 1 and 2 for demonstrating the proposed method. (d)–(f) Intensity distributions of a generated beam from each phase hologram of (a), (b), and (c), respectively.

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Figure 10 shows captured intensity distributions with the CMOS camera. The top and bottom rows indicate the low-pass filtered data pages with the conventional and the proposed methods, respectively. Similar to the numerical results shown in Fig. 7, blurred intensity distributions are obtained. By thresholding on the basis of the 1:2 coding method, original data pages can be retrieved from all experimental results without any error. The quality of each low-pass filtered data page is assessed with the SNR. The SNRs are shown in the top of images in Fig. 10. As confirmed in the numerical simulations, the SNRs of all data pages are improved by the proposed method. The average SNRs of conventional and proposed methods are 2.44 and 4.49. The SNR of the proposed method is, on average, 1.84 times higher than that of conventional method. The SNRs of the experiment are different from that of the numerical simulation. These differences are mainly caused by the misalignment of two phase-only SLMs and the Nyquist aperture. Although the improvement ratio is smaller than the numerical results, the experimental results show that the proposed method can eliminate the interpixel cross talk as expected in the numerical results. In this experiment, a recording medium is not used. In the next subsection, we evaluate the effect of the interpixel cross talk by recording the volume holograms of data pages on a recording medium.

 

Fig. 10 Experimentally low-pass filtered data pages. Conventional data page (a) #1, (b) #2, (c) #3, (d) #4, and (e) #5. Proposed data page (f) #1, (g) #2, (h) #3, (i) #4, and (j) #5.

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4.2. Evaluation with recording volume holograms

For recording volume holograms of data pages, we set a polarization-sensitive medium in the back focal plane of the lens L4, as indicated by the broken line in Fig. 8. The polarization-sensitive medium contains a photodegradative aromatic ketone derivative (AK1) [33, 34]. The thickness of the polarization-sensitive medium is 500 μm. Although the polarization-sensitive medium with the AK1 is initially isotropic, illumination with a polarized beam induces linear anisotropy via axis-selective photoreaction [33, 35]. The polarization-sensitive medium with the AK1 is applicable for recording not only volume intensity holograms but also volume polarization holograms as demonstrated in [25, 33, 34]. Therefore it is possible to demonstrate the conventional and the proposed methods using the same experimental setup. For recording volume holograms on the medium with the AK1, we applied coaxial holographic recording [25, 36–38]. In coaxial holographic data recording, a data page is generally centered at a ring-shaped reference pattern. In our experiment, a data page is generated with a phase hologram, as indicated in the previous subsection. Similar to the data page, we also generate a ring-shaped reference beam with a phase hologram, computer-generated reference pattern (CGRP) [39]. A phase hologram for generating a data page is centered at the CGRP, as shown in Fig. 11(a). Although we do not describe the design process of the CGRP in detail, the CGRP can be obtained with optimized calculation such as simulated annealing. By using the CGRP, the light efficiency and the SNR of reconstructed data pages can be improved as compared with conventional reference beams [39]. Volume holograms of data pages are recorded and reconstructed as follows. When recording volume hologram of the data page #1 with the conventional method, the phase hologram shown in Fig. 11(a) is displayed on the SLM 1. In contrast, the SLM 2 is inactive. As a result, the polarization state of signal and reference beams are the horizontally linear polarization. These beams interfere in the medium, and thus a volume intensity hologram is recorded. During reconstruction process, the volume hologram is illuminated with the reference beam, and a reconstructed image can be obtained. When recording the volume hologram of the data page #1 with the proposed method, the phase holograms shown in Figs. 11(b) and 11(c) are displayed on the SLM 1 and SLM 2, respectively. A signal beam consists of horizontal and vertical linearly polarized beams. In contrast, a reference beam consists of only the horizontal linearly polarized beam. These beams interfere in the medium, which results in a volume polarization hologram. By illuminating the volume polarization hologram with the reference beam, the reconstructed image can be obtained in the same way as the volume intensity hologram.

 

Fig. 11 Phase holograms for generating the data page #1 and a reference beam. (a) Phase hologram displayed on the SLM 1 for demonstrating the conventional method. (b), (c) Phase holograms displayed on the SLM 1 and 2 for demonstrating the proposed method.

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Figure 12 shows the reconstructed data pages of conventional and proposed methods. The SNRs are shown in the top of each image. The average SNRs of conventional and proposed methods are 1.40 and 2.01. On average, the SNR of the proposed method is 1.44 times higher than that of the conventional method. The SNR improvement is smaller than the results of the numerical simulation and the experiment without recording volume holograms. Unlike the numerical and experimental evaluations, the results contain the noise such as scattering from a medium, the nonlinearity of a medium, and the blur according to the autocorrelation of the ring-shaped reference beam [37–39]. Moreover, in the volume polarization hologram, the intensity ratio of horizontal and vertical components is changed according to a medium and recording conditions [18, 40, 41]. These noises lead to the low SNRs compared with the experimental results shown in Fig. 10. Each reconstructed data page is decoded by the thresholding process. The amount of data error is evaluated with a symbol error rate (SER). The SER is given by

SER=EsymbolNsymbol×100[%],
where Esymbol and Nsymbol denote the number of error and the total symbols in a reconstructed data page. Conventional data pages shown in Figs. 12(b) and 12(e) contain data error. Both SERs are 0.03%. These error might be caused by the above mentioned noises. In contrast, the SER is totally reduced by the proposed method, as shown in Figs. 12(f)12(j). Similar to the numerical and experimental results in previous sections, the experimental results with the medium show that the proposed method can improve the SNR of reconstructed data pages by reducing the interpixel cross talk. Since the proposed method is robust to the noises, the aperture size in the Fourier plane can be reduced as compared with the conventional method. Alternatively, the proposed method can relax the constraints in the modulation coding because it is possible to reduce the interpixel cross talk caused by four surrounding pixels. These contribute to decreasing the recording area S or increasing the amount of data P, which increases the storage capacity.

 

Fig. 12 Reconstructed data pages. Conventional data page (a) #1, (b) #2, (c) #3, (d) #4, and (e) #5. Proposed data page (f) #1, (g) #2, (h) #3, (i) #4, and (j) #5.

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5. Conclusion

We have proposed an orthogonal polarization encoding to reduce the interpixel cross talk in holographic data storage. In the proposed method, the polarization state of each pixel is orthogonal with that of four surrounding pixels. Numerical and experimental evaluations using the Nyquist aperture show the proposed method can improve the SNR of reconstructed data pages by the reduction in the interpixel cross talk from four surrounding pixels. In the numerical and experimental evaluations, we employed rather disadvantageous situation where the interpixel cross talk is large as compared with practical holographic storage systems by using the 1:2 coding and the Nyquist aperture. Under this situation, we have shown the feasibility of the proposed method. This means that the proposed method would be also effective in practical holographic storage systems regardless of the coding method and the aperture size.

Although the quantitative evaluation on the improvement in the storage capacity by employing the proposed method is the further research subject, it should be pointed out that the proposed method has two benefits for holographic data storage in principle. One is increasing the areal information density D, and the other is increasing the amount of data P, as mentioned at the end of Section 3.

The possible disadvantage of the proposed method is the requirement of recording the polarization distribution of a beam. In our experiment, we used a polarization-sensitive medium to record the polarization distribution on the basis of polarization holography. As mentioned in subsection 4.2, the intensity ratio of horizontally and vertically linear polarization is generally changed depending on a medium and recording parameters in polarization holography [18, 41]. This causes the low SNR in the proposed method. To solve the problem, we need to optimize the recording conditions. Alternatively, it is possible to record the polarization distribution on the conventional recording media (photopolymer), which is insensitive to the polarization, by using two orthogonal reference beams [42]. For example, it could be easily execute if we could employ two lasers. Therefore, our method is also applicable for the conventional recording medium and promising for current and future technologies of holographic data storage

In holographic data storage, the polarization has been used for the information carrier [43], multiplexing [40, 44–46], or reducing the intensity variation in reconstructed data pages [47]. In this paper, we show that the interpixel cross talk can be reduced by making use of the polarization. We consider that the use of the polarization stimulates the development of novel recording techniques in holographic data storage. In addition, a lot of researchers have made proposals on various crosstalk noise reduction methods based on designing a phase mask [12], the shape of an aperture [32, 48], and a data coding method [14]. By combining these techniques with the proposed method, further improvement in the SNR can be expected.

Funding Information

Japan Science and Technology Agency (JST) under the Strategic Promotion of Innovation Research and Development Program.

References and links

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2. L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92(8), 1231–1280 (2004). [CrossRef]  

3. N. Kinoshita, T. Muroi, N. Ishii, K. Kamijo, H. Kikuchi, N. Shimidzu, and O. Matoba, “Half-data-page insertion method for increasing recording density in angular multiplexing holographic memory,” Appl. Opt. 50(16), 2361–2369 (2011). [CrossRef]   [PubMed]  

4. K. Anderson and K. Curtis, “Polytopic multiplexing,” Opt. Lett. 29(12), 1402–1404 (2004). [CrossRef]   [PubMed]  

5. C. Denz, G. Pauliat, and G. Roosen, “Volume hologram multiplexing using a deterministic phase,” Opt. Commun. 85, 171–176 (1991). [CrossRef]  

6. G. Barbastathis, M. Levene, and D. Psaltis, “Shift multiplexing with spherical reference waves,” Appl. Opt. 35(14), 2403–2417 (1996). [CrossRef]   [PubMed]  

7. G. W. Burr, G. Barking, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, and M. A. Neifeld, “Gray-scale data pages for digital holographic data storage,” Opt. Lett. 23(15), 1218–1220 (1998). [CrossRef]  

8. G. Berger, M. Dietz, and C. Denz, “Hybrid multinary modulation codes for page-oriented holographic data storage,” J. Opt. A: Pure Appl. Opt. 10(11), 115305 (2008). [CrossRef]  

9. T. Nobukawa and T. Nomura, “Multilevel recording of complex amplitude data pages in a holographic data storage system using digital holography,” Optics Express , 24(18), 21001–21011 (2016). [CrossRef]   [PubMed]  

10. T. Sato, K. Kanno, and M. Bunsen, “Complex linear minimum mean-squared-error equalization of spatially quadrature-amplitude-modulated signals in holographic data storage,” Jpn. J. Appl. Phys. 55(9S), 09SA08 (2016). [CrossRef]  

11. J. Hong, I. McMichael, and J. Ma, “Influence of phase masks on cross talk in holographic memory,” Opt. Lett. 21(20), 1694–1696 (1996). [CrossRef]   [PubMed]  

12. M.-P. Bernal, G. W. Burr, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, E. Oesterschulze, R. M. Shelby, G. T. Sincerbox, and M. Quintanilla, “Effects of multilevel phase masks on interpixel cross talk in digital holographic storage,” Appl. Opt. 36(14), 3107–3115 (1997). [CrossRef]   [PubMed]  

13. M.-P. Bernal, G. W. Burr, H. Coufal, and M. Quintanilla, “Balancing interpixel cross talk and detector noise to optimize areal density in holographic storage systems,” Appl. Opt. 37(23) 5377–5385 (1998). [CrossRef]  

14. B. M. King and M. A. Neifeld, “Sparse modulation coding for increased capacity in volume holographic storage,” Appl. Opt. 39(35), 6681–6688 (2000). [CrossRef]  

15. K. Nishimoto, F. Naito, and M. Yamamoto, “Soft-decision Viterbi decoding for 2/4 modulation code in holographic memory,” Jpn. J. Appl. Phys. 45(5A), 4102–4106 (2006). [CrossRef]  

16. M. Kato and Y. Okino, “Speckle reduction by double recorded holograms,” Appl. Opt. 12(6), 1199–1201 (1973). [CrossRef]   [PubMed]  

17. L. Nikolova and P. S. Ramanujam, Polarization holography (Cambridge University, 2009). [CrossRef]  

18. K. Kuroda, Y. Matsuhashi, R. Fujimura, and T. Shimura, “Theory of polarization holography,” Opt. Rev. 18(5), 374–382 (2011). [CrossRef]  

19. C. B. Burckhardt, “Use of a random phase mask for the recording of Fourier transform holograms of data masks,” Appl. Opt. 9(3), 695–700 (1970). [CrossRef]   [PubMed]  

20. V. Vadde, B. V. K. Vijaya Kumer, G. W. Burr, H. Coufal, J. A. Hoffnagle, and C. M. Jefferson, “A figure of merit for the optical aperture used in digital volume holographic data storage,” Proc. SPIE 3401, 194–200 (1998). [CrossRef]  

21. J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994). [CrossRef]   [PubMed]  

22. I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Jones matrix treatment for optical Fourier processors with structured polarization,” Opt. Express 19(5), 4583–4594 (2011). [CrossRef]   [PubMed]  

23. W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21(18), 20692–20706 (2013). [CrossRef]   [PubMed]  

24. I. Moreno, J. A. Davis, T. M. Hernandez, D. M. Cottrell, and D. Sand, “Complete polarization control of light from a liquid crystal spatial light modulator,” Opt. Express 20(1), 364–376 (2012). [CrossRef]   [PubMed]  

25. T. Nobukawa, T. Fukuda, D. Barada, and T. Nomura, “Coaxial polarization holographic data recording on a polarization-sensitive medium,” Opt. Lett. 41(21), 4919–4922 (2016). [CrossRef]   [PubMed]  

26. X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgral, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012). [CrossRef]   [PubMed]  

27. X. Ding, F. Monticone, K. Zhang, L. Zhang, D. Gao, S. N. Burokur, A. D. Lustrac, Q. Wu, C. W. Qiu, and A. Alù, “Ultrathin Pancharatnam-Berry metasurface with maximal cross-polarization efficiency,” Adv. Mater. 27, 1195–1200 (2015). [CrossRef]  

28. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38(23), 5004–5013 (1999). [CrossRef]  

29. V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A. 24(11), 3500 (2007). [CrossRef]  

30. E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett. 38(18), 3546–3549 (2013). [CrossRef]   [PubMed]  

31. T. Nobukawa and T. Nomura, “Linear phase encoding for holographic data storage with a single phase-only spatial light modulator,” Appl. Opt. 55(10), 2565–2573 (2016). [CrossRef]   [PubMed]  

32. T. Nobukawa and T. Nomura, “Digital super-resolution holographic data storage based on Hermitian symmetry for achieving high areal density,” Opt. Express 25(2), 1326–1338 (2017). [CrossRef]   [PubMed]  

33. T. Fukuda, E. Uchida, K. Masaki, T. Ando, T. Shimizu, D. Barada, and T. Yatagai, “An investigation on polarization-sensitive materials,” in Proceedings of IEEE 2011 ICO Conference on Information Photonics (IEEE, 2011), 21–22.

34. T. Ando, K. Masaki, and T. Shimizu, “Page data multiplexing for vector wave memories having polarization recording material doped with aromatic ketone derivative,” Jpn. J. Appl. Phys. 52(9S2), 09LD15 (2013). [CrossRef]  

35. T. Fukuda, E. Uchida, K. Masaki, T. Ando, T. Shimizu, D. Barada, and T. Yatagai, “Polarization-sensitive recording medium based on axis-selective photoreaction mechanism,” in Proceedings of International Workshop on Holographic Memories & Display, Digests (2010) paper 15C-1.

36. H. Horimai, X. Tan, and J. Li, “Collinear holography,” Appl. Opt. 44(13), 2575–2579 (2005). [CrossRef]   [PubMed]  

37. T. Shimura, S. Ichimura, R. Fujimura, K. Kuroda, X. Tan, and H. Horimai, “Analysis of a collinear holographic storage system: introduction of pixel spread function,” Opt. Lett. 31(9), 1208–1210 (2006). [CrossRef]   [PubMed]  

38. C. C. Sun, Y. W. Yu, S. C. Hsieh, T. C. Teng, and M. F. Tsai, “Point spread function of a collinear holographic storage system,” Opt. Express 15(26), 18111–18118 (2007). [CrossRef]   [PubMed]  

39. T. Nobukawa and T. Nomura, “Design of high-resolution and multilevel reference pattern for improvement of both light utilization efficiency and signal-to-noise ratio in coaxial holographic data storage,” Appl. Opt. 53(17), 3773–3781 (2014). [CrossRef]   [PubMed]  

40. T. Ochiai, D. Barada, T. Fukuda, Y. Hayasaki, K. Kuroda, and T. Yatagai, “Angular multiplex recording of data pages by dual-channel polarization holography,” Opt. Lett. 38(5), 748–750 (2013). [CrossRef]   [PubMed]  

41. J. Zang, A. Wu, Y. Liu, J. Wang, X. Lin, X. Tan, T. Shimura, and K. Kuroda, “Characteristics of volume polarization holography with linear polarization light,” Opt. Rev , 22(5), 829–831 (2015). [CrossRef]  

42. H. Wei, L. Cao, Z. Xu, Q. He, G. Jin, and C. Gu, “Orthogonal polarization dual-channel holographic memory in cationic ring-opening photopolymer,” Opt. Express 14(12), 5135–5142 (2006). [CrossRef]   [PubMed]  

43. K. Kawano, T. Ishii, J. Minabe, T. Niitsu, Y. Nishikata, and K. Baba, “Holographic recording and retrieval of polarized light by use of polyester containing cyanoazobenzene units in the side chain,” Opt. Lett. 24(18), 1269–1271 (1999). [CrossRef]  

44. S. H. Lin, S. L. Cho, S. F. Chou, J. H. Lin, C. M. Lin, S. Chi, and K. Y. Hsu, “Volume polarization holographic recording in thick photopolymer for optical memory,” Opt. Express 22(12), 14944–14957 (2014). [CrossRef]   [PubMed]  

45. C. Li, L. Cao, Z. Wang, and G. Jin, “Hybrid polarization-angle multiplexing for volume holography in gold nanoparticle-doped photopolymer,” Opt. Lett. 39(24), 6891–6894 (2014). [CrossRef]   [PubMed]  

46. J. Zang, G. Kang, P. Li, Y. Liu, F. Fan, Y. Hong, Y. Huang, X. Tan, A. Wu, T. Shimura, and K. Kuroda, “Dual-channel recording based on the null reconstruction effect of orthogonal linear polarization holography,” Opt. Lett. 42(7), 1377–1380 (2017). [CrossRef]   [PubMed]  

47. K. Kawano, J. Minabe, T. Ishii, T. Maruyama, and S. Yasuda, “Polarization encoding for digital holographic storage,” Jpn. J. Appl. Phys. 41(3B), 1855–1859 (2002). [CrossRef]  

48. H. Gu, S. Yin, Q. Tan, L. Cao, Q. He, and G. Jin, “Improving signal-to-noise ratio by use of a cross-shaped aperture in the holographic data storage system,” Appl. Opt. 48(32), 6234–6240 (2009). [CrossRef]   [PubMed]  

References

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  1. K. Curtis, L. Dhar, A. Hill, W. Wilson, and M. Ayres, Holographic Data Storage: From Theory to Practical Systems (Wiley, 2010).
    [Crossref]
  2. L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92(8), 1231–1280 (2004).
    [Crossref]
  3. N. Kinoshita, T. Muroi, N. Ishii, K. Kamijo, H. Kikuchi, N. Shimidzu, and O. Matoba, “Half-data-page insertion method for increasing recording density in angular multiplexing holographic memory,” Appl. Opt. 50(16), 2361–2369 (2011).
    [Crossref] [PubMed]
  4. K. Anderson and K. Curtis, “Polytopic multiplexing,” Opt. Lett. 29(12), 1402–1404 (2004).
    [Crossref] [PubMed]
  5. C. Denz, G. Pauliat, and G. Roosen, “Volume hologram multiplexing using a deterministic phase,” Opt. Commun. 85, 171–176 (1991).
    [Crossref]
  6. G. Barbastathis, M. Levene, and D. Psaltis, “Shift multiplexing with spherical reference waves,” Appl. Opt. 35(14), 2403–2417 (1996).
    [Crossref] [PubMed]
  7. G. W. Burr, G. Barking, H. Coufal, J. A. Hoffnagle, C. M. Jefferson, and M. A. Neifeld, “Gray-scale data pages for digital holographic data storage,” Opt. Lett. 23(15), 1218–1220 (1998).
    [Crossref]
  8. G. Berger, M. Dietz, and C. Denz, “Hybrid multinary modulation codes for page-oriented holographic data storage,” J. Opt. A: Pure Appl. Opt. 10(11), 115305 (2008).
    [Crossref]
  9. T. Nobukawa and T. Nomura, “Multilevel recording of complex amplitude data pages in a holographic data storage system using digital holography,” Optics Express,  24(18), 21001–21011 (2016).
    [Crossref] [PubMed]
  10. T. Sato, K. Kanno, and M. Bunsen, “Complex linear minimum mean-squared-error equalization of spatially quadrature-amplitude-modulated signals in holographic data storage,” Jpn. J. Appl. Phys. 55(9S), 09SA08 (2016).
    [Crossref]
  11. J. Hong, I. McMichael, and J. Ma, “Influence of phase masks on cross talk in holographic memory,” Opt. Lett. 21(20), 1694–1696 (1996).
    [Crossref] [PubMed]
  12. M.-P. Bernal, G. W. Burr, H. Coufal, R. K. Grygier, J. A. Hoffnagle, C. M. Jefferson, E. Oesterschulze, R. M. Shelby, G. T. Sincerbox, and M. Quintanilla, “Effects of multilevel phase masks on interpixel cross talk in digital holographic storage,” Appl. Opt. 36(14), 3107–3115 (1997).
    [Crossref] [PubMed]
  13. M.-P. Bernal, G. W. Burr, H. Coufal, and M. Quintanilla, “Balancing interpixel cross talk and detector noise to optimize areal density in holographic storage systems,” Appl. Opt. 37(23) 5377–5385 (1998).
    [Crossref]
  14. B. M. King and M. A. Neifeld, “Sparse modulation coding for increased capacity in volume holographic storage,” Appl. Opt. 39(35), 6681–6688 (2000).
    [Crossref]
  15. K. Nishimoto, F. Naito, and M. Yamamoto, “Soft-decision Viterbi decoding for 2/4 modulation code in holographic memory,” Jpn. J. Appl. Phys. 45(5A), 4102–4106 (2006).
    [Crossref]
  16. M. Kato and Y. Okino, “Speckle reduction by double recorded holograms,” Appl. Opt. 12(6), 1199–1201 (1973).
    [Crossref] [PubMed]
  17. L. Nikolova and P. S. Ramanujam, Polarization holography (Cambridge University, 2009).
    [Crossref]
  18. K. Kuroda, Y. Matsuhashi, R. Fujimura, and T. Shimura, “Theory of polarization holography,” Opt. Rev. 18(5), 374–382 (2011).
    [Crossref]
  19. C. B. Burckhardt, “Use of a random phase mask for the recording of Fourier transform holograms of data masks,” Appl. Opt. 9(3), 695–700 (1970).
    [Crossref] [PubMed]
  20. V. Vadde, B. V. K. Vijaya Kumer, G. W. Burr, H. Coufal, J. A. Hoffnagle, and C. M. Jefferson, “A figure of merit for the optical aperture used in digital volume holographic data storage,” Proc. SPIE 3401, 194–200 (1998).
    [Crossref]
  21. J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
    [Crossref] [PubMed]
  22. I. Moreno, C. Iemmi, J. Campos, and M. J. Yzuel, “Jones matrix treatment for optical Fourier processors with structured polarization,” Opt. Express 19(5), 4583–4594 (2011).
    [Crossref] [PubMed]
  23. W. Han, Y. Yang, W. Cheng, and Q. Zhan, “Vectorial optical field generator for the creation of arbitrarily complex fields,” Opt. Express 21(18), 20692–20706 (2013).
    [Crossref] [PubMed]
  24. I. Moreno, J. A. Davis, T. M. Hernandez, D. M. Cottrell, and D. Sand, “Complete polarization control of light from a liquid crystal spatial light modulator,” Opt. Express 20(1), 364–376 (2012).
    [Crossref] [PubMed]
  25. T. Nobukawa, T. Fukuda, D. Barada, and T. Nomura, “Coaxial polarization holographic data recording on a polarization-sensitive medium,” Opt. Lett. 41(21), 4919–4922 (2016).
    [Crossref] [PubMed]
  26. X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgral, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
    [Crossref] [PubMed]
  27. X. Ding, F. Monticone, K. Zhang, L. Zhang, D. Gao, S. N. Burokur, A. D. Lustrac, Q. Wu, C. W. Qiu, and A. Alù, “Ultrathin Pancharatnam-Berry metasurface with maximal cross-polarization efficiency,” Adv. Mater. 27, 1195–1200 (2015).
    [Crossref]
  28. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, and I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38(23), 5004–5013 (1999).
    [Crossref]
  29. V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A. 24(11), 3500 (2007).
    [Crossref]
  30. E. Bolduc, N. Bent, E. Santamato, E. Karimi, and R. W. Boyd, “Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram,” Opt. Lett. 38(18), 3546–3549 (2013).
    [Crossref] [PubMed]
  31. T. Nobukawa and T. Nomura, “Linear phase encoding for holographic data storage with a single phase-only spatial light modulator,” Appl. Opt. 55(10), 2565–2573 (2016).
    [Crossref] [PubMed]
  32. T. Nobukawa and T. Nomura, “Digital super-resolution holographic data storage based on Hermitian symmetry for achieving high areal density,” Opt. Express 25(2), 1326–1338 (2017).
    [Crossref] [PubMed]
  33. T. Fukuda, E. Uchida, K. Masaki, T. Ando, T. Shimizu, D. Barada, and T. Yatagai, “An investigation on polarization-sensitive materials,” in Proceedings of IEEE 2011 ICO Conference on Information Photonics (IEEE, 2011), 21–22.
  34. T. Ando, K. Masaki, and T. Shimizu, “Page data multiplexing for vector wave memories having polarization recording material doped with aromatic ketone derivative,” Jpn. J. Appl. Phys. 52(9S2), 09LD15 (2013).
    [Crossref]
  35. T. Fukuda, E. Uchida, K. Masaki, T. Ando, T. Shimizu, D. Barada, and T. Yatagai, “Polarization-sensitive recording medium based on axis-selective photoreaction mechanism,” in Proceedings of International Workshop on Holographic Memories & Display, Digests (2010) paper 15C-1.
  36. H. Horimai, X. Tan, and J. Li, “Collinear holography,” Appl. Opt. 44(13), 2575–2579 (2005).
    [Crossref] [PubMed]
  37. T. Shimura, S. Ichimura, R. Fujimura, K. Kuroda, X. Tan, and H. Horimai, “Analysis of a collinear holographic storage system: introduction of pixel spread function,” Opt. Lett. 31(9), 1208–1210 (2006).
    [Crossref] [PubMed]
  38. C. C. Sun, Y. W. Yu, S. C. Hsieh, T. C. Teng, and M. F. Tsai, “Point spread function of a collinear holographic storage system,” Opt. Express 15(26), 18111–18118 (2007).
    [Crossref] [PubMed]
  39. T. Nobukawa and T. Nomura, “Design of high-resolution and multilevel reference pattern for improvement of both light utilization efficiency and signal-to-noise ratio in coaxial holographic data storage,” Appl. Opt. 53(17), 3773–3781 (2014).
    [Crossref] [PubMed]
  40. T. Ochiai, D. Barada, T. Fukuda, Y. Hayasaki, K. Kuroda, and T. Yatagai, “Angular multiplex recording of data pages by dual-channel polarization holography,” Opt. Lett. 38(5), 748–750 (2013).
    [Crossref] [PubMed]
  41. J. Zang, A. Wu, Y. Liu, J. Wang, X. Lin, X. Tan, T. Shimura, and K. Kuroda, “Characteristics of volume polarization holography with linear polarization light,” Opt. Rev,  22(5), 829–831 (2015).
    [Crossref]
  42. H. Wei, L. Cao, Z. Xu, Q. He, G. Jin, and C. Gu, “Orthogonal polarization dual-channel holographic memory in cationic ring-opening photopolymer,” Opt. Express 14(12), 5135–5142 (2006).
    [Crossref] [PubMed]
  43. K. Kawano, T. Ishii, J. Minabe, T. Niitsu, Y. Nishikata, and K. Baba, “Holographic recording and retrieval of polarized light by use of polyester containing cyanoazobenzene units in the side chain,” Opt. Lett. 24(18), 1269–1271 (1999).
    [Crossref]
  44. S. H. Lin, S. L. Cho, S. F. Chou, J. H. Lin, C. M. Lin, S. Chi, and K. Y. Hsu, “Volume polarization holographic recording in thick photopolymer for optical memory,” Opt. Express 22(12), 14944–14957 (2014).
    [Crossref] [PubMed]
  45. C. Li, L. Cao, Z. Wang, and G. Jin, “Hybrid polarization-angle multiplexing for volume holography in gold nanoparticle-doped photopolymer,” Opt. Lett. 39(24), 6891–6894 (2014).
    [Crossref] [PubMed]
  46. J. Zang, G. Kang, P. Li, Y. Liu, F. Fan, Y. Hong, Y. Huang, X. Tan, A. Wu, T. Shimura, and K. Kuroda, “Dual-channel recording based on the null reconstruction effect of orthogonal linear polarization holography,” Opt. Lett. 42(7), 1377–1380 (2017).
    [Crossref] [PubMed]
  47. K. Kawano, J. Minabe, T. Ishii, T. Maruyama, and S. Yasuda, “Polarization encoding for digital holographic storage,” Jpn. J. Appl. Phys. 41(3B), 1855–1859 (2002).
    [Crossref]
  48. H. Gu, S. Yin, Q. Tan, L. Cao, Q. He, and G. Jin, “Improving signal-to-noise ratio by use of a cross-shaped aperture in the holographic data storage system,” Appl. Opt. 48(32), 6234–6240 (2009).
    [Crossref] [PubMed]

2017 (2)

2016 (4)

T. Nobukawa and T. Nomura, “Linear phase encoding for holographic data storage with a single phase-only spatial light modulator,” Appl. Opt. 55(10), 2565–2573 (2016).
[Crossref] [PubMed]

T. Nobukawa, T. Fukuda, D. Barada, and T. Nomura, “Coaxial polarization holographic data recording on a polarization-sensitive medium,” Opt. Lett. 41(21), 4919–4922 (2016).
[Crossref] [PubMed]

T. Nobukawa and T. Nomura, “Multilevel recording of complex amplitude data pages in a holographic data storage system using digital holography,” Optics Express,  24(18), 21001–21011 (2016).
[Crossref] [PubMed]

T. Sato, K. Kanno, and M. Bunsen, “Complex linear minimum mean-squared-error equalization of spatially quadrature-amplitude-modulated signals in holographic data storage,” Jpn. J. Appl. Phys. 55(9S), 09SA08 (2016).
[Crossref]

2015 (2)

X. Ding, F. Monticone, K. Zhang, L. Zhang, D. Gao, S. N. Burokur, A. D. Lustrac, Q. Wu, C. W. Qiu, and A. Alù, “Ultrathin Pancharatnam-Berry metasurface with maximal cross-polarization efficiency,” Adv. Mater. 27, 1195–1200 (2015).
[Crossref]

J. Zang, A. Wu, Y. Liu, J. Wang, X. Lin, X. Tan, T. Shimura, and K. Kuroda, “Characteristics of volume polarization holography with linear polarization light,” Opt. Rev,  22(5), 829–831 (2015).
[Crossref]

2014 (3)

2013 (4)

2012 (2)

I. Moreno, J. A. Davis, T. M. Hernandez, D. M. Cottrell, and D. Sand, “Complete polarization control of light from a liquid crystal spatial light modulator,” Opt. Express 20(1), 364–376 (2012).
[Crossref] [PubMed]

X. Chen, L. Huang, H. Mühlenbernd, G. Li, B. Bai, Q. Tan, G. Jin, C. Qiu, S. Zhang, and T. Zentgral, “Dual-polarity plasmonic metalens for visible light,” Nat. Commun. 3, 1198 (2012).
[Crossref] [PubMed]

2011 (3)

2009 (1)

2008 (1)

G. Berger, M. Dietz, and C. Denz, “Hybrid multinary modulation codes for page-oriented holographic data storage,” J. Opt. A: Pure Appl. Opt. 10(11), 115305 (2008).
[Crossref]

2007 (2)

V. Arrizón, U. Ruiz, R. Carrada, and L. A. González, “Pixelated phase computer holograms for the accurate encoding of scalar complex fields,” J. Opt. Soc. Am. A. 24(11), 3500 (2007).
[Crossref]

C. C. Sun, Y. W. Yu, S. C. Hsieh, T. C. Teng, and M. F. Tsai, “Point spread function of a collinear holographic storage system,” Opt. Express 15(26), 18111–18118 (2007).
[Crossref] [PubMed]

2006 (3)

2005 (1)

2004 (2)

K. Anderson and K. Curtis, “Polytopic multiplexing,” Opt. Lett. 29(12), 1402–1404 (2004).
[Crossref] [PubMed]

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92(8), 1231–1280 (2004).
[Crossref]

2002 (1)

K. Kawano, J. Minabe, T. Ishii, T. Maruyama, and S. Yasuda, “Polarization encoding for digital holographic storage,” Jpn. J. Appl. Phys. 41(3B), 1855–1859 (2002).
[Crossref]

2000 (1)

1999 (2)

1998 (3)

1997 (1)

1996 (2)

1994 (1)

J. F. Heanue, M. C. Bashaw, and L. Hesselink, “Volume holographic storage and retrieval of digital data,” Science 265, 749–752 (1994).
[Crossref] [PubMed]

1991 (1)

C. Denz, G. Pauliat, and G. Roosen, “Volume hologram multiplexing using a deterministic phase,” Opt. Commun. 85, 171–176 (1991).
[Crossref]

1973 (1)

1970 (1)

Alù, A.

X. Ding, F. Monticone, K. Zhang, L. Zhang, D. Gao, S. N. Burokur, A. D. Lustrac, Q. Wu, C. W. Qiu, and A. Alù, “Ultrathin Pancharatnam-Berry metasurface with maximal cross-polarization efficiency,” Adv. Mater. 27, 1195–1200 (2015).
[Crossref]

Anderson, K.

Ando, T.

T. Ando, K. Masaki, and T. Shimizu, “Page data multiplexing for vector wave memories having polarization recording material doped with aromatic ketone derivative,” Jpn. J. Appl. Phys. 52(9S2), 09LD15 (2013).
[Crossref]

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Figures (12)

Fig. 1
Fig. 1 Schematic of a holographic data storage system.
Fig. 2
Fig. 2 Polarization distribution of (a) conventional and (b) proposed data pages.
Fig. 3
Fig. 3 Spatial frequency bandwidth of conventional and proposed data pages.
Fig. 4
Fig. 4 Sampling period of each polarization state in the proposed data page. (a) Horizontally and (b) vertically polarized beams.
Fig. 5
Fig. 5 Numerical simulation model for evaluating the effect of the interpixel cross talk.
Fig. 6
Fig. 6 Data pages designed with a 1:2 coding. Data page (a) #1, (b) #2, (c) #3, (d) #4, and (e) #5.
Fig. 7
Fig. 7 Numerically low-pass filtered data pages. Conventional data page (a) #1, (b) #2, (c) #3, (d) #4, and (e) #5. Proposed data page (f) #1, (g) #2, (h) #3, (i) #4, and (j) #5.
Fig. 8
Fig. 8 Optical setup for evaluating the effect of the interpixel cross talk on conventional and proposed data pages. HWP, half wave plate; P, polarizer; SF, spatial filter; Li, Lens; SLMi, phase-only spatial light modulator; M, Mirror.
Fig. 9
Fig. 9 Phase holograms for generating the data page #1. (a) Phase hologram displayed on the SLM 1 for demonstrating the conventional method. (b), (c) Phase holograms displayed on the SLM 1 and 2 for demonstrating the proposed method. (d)–(f) Intensity distributions of a generated beam from each phase hologram of (a), (b), and (c), respectively.
Fig. 10
Fig. 10 Experimentally low-pass filtered data pages. Conventional data page (a) #1, (b) #2, (c) #3, (d) #4, and (e) #5. Proposed data page (f) #1, (g) #2, (h) #3, (i) #4, and (j) #5.
Fig. 11
Fig. 11 Phase holograms for generating the data page #1 and a reference beam. (a) Phase hologram displayed on the SLM 1 for demonstrating the conventional method. (b), (c) Phase holograms displayed on the SLM 1 and 2 for demonstrating the proposed method.
Fig. 12
Fig. 12 Reconstructed data pages. Conventional data page (a) #1, (b) #2, (c) #3, (d) #4, and (e) #5. Proposed data page (f) #1, (g) #2, (h) #3, (i) #4, and (j) #5.

Equations (5)

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w = f λ d ,
SNR = μ on μ off ( σ on 2 + σ off 2 ) 1 / 2 ,
( E 1 ( x , y ) E 2 ( x , y ) ) = ( a 1 ( x , y ) exp { i ϕ 1 ( x , y ) } a 2 ( x , y ) exp { i ϕ 2 ( x , y ) } ) ,
ψ n ( x , y ) = a n ( x , y ) { ϕ n ( x , y ) + ϕ c ( x , y ) } ,
SER = E symbol N symbol × 100 [ % ] ,

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