1. Introduction

Holographic memory is expected to form the next-generation high-capacity data storage technology, exceeding 1 TB/disk while affording fast data transfer rates [1–7]. To record data on holographic memory, two-dimensionally coded signal and reference light beams are made incident on a medium, and the resulting interference fringes are recorded in the recording material. To read out the data, only the reference light beam is made incident on the interference fringes to reconstruct the signal image. In holographic memory, multiple signals of two dimensional page data can be recorded and read selectively from a single position. These characteristics permit high recording densities and high data transfer rates. The holographic versatile disk has acquired the international standard for holographic memory, and it employs a collinear holographic system that can write and read data using a single optical axis with a spatial light modulator (SLM) as the key device [7–10]. Magnetic holograms are rewritable holograms and are recorded as magnetization directions through thermomagnetic recording with use of magnetic films as recording media instead of conventional polymer media, which affords long term stability [11–18]. Recently, we demonstrated that a hologram can be magnetically written using thermomagnetic writing　and reconstructed from transparent magnetic rare earth iron garnet films of Bi_1.3Dy_0.85Y_0.85Fe_3.8Al_1.2O₁₂ (Bi:RIG) using a collinear holographic system [18]. However, the reconstructed images were not sufficiently clear for practical recording applications.

In order to improve the diffraction efficiency, we found that the use of the optical artificial magnetic lattice of magneto photonic microcavities (MPMs) or magneto photonic crystals as recording media affords high diffraction efficiency because the Faraday rotation angle and the depth of the formed magnetic fringes increase [19–21]. The MPM structure is a stacked medium in which a transparent magnetic film is sandwiched between two Bragg mirrors, and this structure acts as an optical cavity for enhancing the Faraday rotation angle [22–25]. In addition, the localization of light in the magnetic layer results in deep holographic writing via modulation of the interference of light in the microcavity [19, 20]. However, thermomagnetic writing with high incident optical power for forming deep magnetic fringes generates excessively high temperatures near the medium surface. This excess heat in the high temperature region diffuses laterally, and the fringes grow wider and merge with adjacent fringes near the surface [26]. Owing to this undesirable merging, the information recorded in the fringes is lost. To suppress the heat diffusion effect and to control the fringes’ shapes, a stacking structure composed of magnetic garnet and transparent heat sink layers (HSLs) has been found to be effective for diffusing the excess heat from garnet layers into HSLs [27].

In addition to these approaches focusing on recording media with high Faraday rotation angle and the capability of forming deep magnetic fringes, the improvement of the collinear optical system and recording condition is also important to achieve clear reconstructed images. Originally, we used an optical diffuser to prevent excess concentration of the optical energy at the focal point. However, the use of the diffuser was found to distort the image, leading to increase in the number of errors in the reconstructed image. In this work, we focus on improving the optical system and recording conditions without the use of the diffuser for obtaining clear reconstructed images. First, we treat magnetic holograms as binary holograms with two states, and we investigate the effect of defocus on the recording pattern by numerical calculations. Second, we experimentally record and reconstruct magnetic holograms under defocused conditions without the diffuser and investigate the preferable signal pattern on an SLM. Using this preferable condition, we evaluate the error ratio in the reconstructed data using several modulation schemes.

2. Experimental

In the collinear interferometer, incident signal and reference patterns are focused and coaxially made to interfere through an objective lens. Figure 1(a) shows the schematic of our collinear holographic interference setup. A pulsed laser with a wavelength of 532 nm and a pulse width of 50 ps was used for recording, and this laser with a power of 10 mW and frequency of 10 kHz was used for reconstruction. A red laser (λ = 633 nm) was used as a focusing mechanism to adjust the position of the recording garnet film. In our collinear system, we used a digital micromirror device (DMD, Discovery 1100) as the SLM. In this setup, when a laser beam is incident on the DMD, many diffracted light signals emerge from it, as shown in Fig. 1(b). Among these signals, we used four spots of the seventh and eighth diffracted light beams; these four beams are individually focused on the recording medium, as schematically shown in Fig. 1(c), leading to the formation of one image on the imaging plane of the CCD camera. In this system, the incident beam should ideally be diffused through an optical diffuser to avoid strong concentration of light at a point, and/or the recording medium should be set in the defocused position at which the interference “behavior” is significantly dependent on the defocus length. Originally, we used an optical diffuser with diffusion angle of 0.5° to suppress excessive energy concentration at the focal point on the medium during the recording process. However, the image from the DMD when directly observed with the CCD through the diffuser was not clear due to the distorted shape of each pixel (Fig. 1(d)) while the image without the diffuser was clear (Fig. 1(e)). Therefore, we attempted to determine a suitable recording condition without the use of the diffuser.

 

Fig. 1 (a) Schematic of optical setup for collinear holography, (b) schematic of diffracted light signals from the digital mirror device for holographic recording, (c) tracing of light signals near the medium, and the spatial light modulator (SLM) images of signal pattern observed with the CCD (d) through diffuser and (e) without diffuser.

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To determine favorable recording conditions without the use of the diffuser, we performed a simple numerical simulation on the collinear interference. The interference patterns were calculated with the use of the Fresnel–Kirchhoff (FK) diffraction formula:

Here, E(X, Y, Z) and E(x, y, 0) represent the complex electric field amplitudes at the medium and input plane, respectively, r the vector from an input point (x, y) to a point (X, Y) on the medium, $\widehat{r}$the unit vector along the r vector, $\widehat{n}$the unit normal vector to the input plane, and $(\widehat{n},\widehat{r})$ the angle between the two vectors, $\widehat{n}$ and $\widehat{r}$, as shown in Fig. 2(a). The input patterns, corresponding to E(x, y, 0), used in the calculations are shown in Fig. 2(b). The pattern for the recording process is composed of a coaxial torus reference portion and circle signal portion with a white rate of 50%. In this analysis, the diameter of the signal beam, d_sig, was varied from 0.45 mm to 1.8 mm. For the reconstruction process, only the reference signal is irradiated onto the recorded holograms. The pupil function, U(x, y), representing the phase transformation of the lens (f = 4 mm) is expressed as follows:

 

Fig. 2 (a) Model geometry for Fresnel–Kirchhoff diffraction formula and (b) typical input pattern.

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Next, we carried out the recording and reconstruction of a magnetic collinear hologram with the use of the optical setup shown in Fig. 1 without the diffuser at various recording positions shifted from the focal point, and we investigated suitable recording conditions using a Bi:RIG film with a thickness of 2.6 µm as the recording medium, which was deposited on nonmagnetic substituted gadolinium gallium garnet (SGGG) substrate by radio frequency magnetron sputtering at 200 °C using the oxide target with the composition of Bi:Dy:Y:Fe:Al = 1.5:1.0:1.0:3.8:1.2 [18, 26]. The deposited garnet films were crystallized by rapid thermal annealing at 750 °C for 10 min in air because the as-deposited films were not crystallized. The Faraday rotation of the film was about 2.7 degree/µm after annealing at 532 nm. Under suitable recording conditions, various signal patterns with a size of 48 × 48 px were recorded with different encoding methods based on 2:4, 3:9, and 3:16 modulation schemes [7, 28] to evaluate the error ratio, which was defined as the ratio of the number of correctly reconstructed bits to the number of all bits (48 × 48) of each reconstructed image, obtained by comparing the original and the corresponding reconstructed patterns.

3. Results and discussion

Figure 3(a) shows the calculated intensity profile at the center of the interference pattern shown in the inset at df = 150 µm when normalized with the total optical intensity. The interference between the reference and signal beams yielded a pulsed, sharp intensity distribution. This interference pattern should be recorded as a hologram to store the interference state including the information of the input signal. The magnetic hologram is recorded by means of the thermomagnetic recording process, and thus, the possibility of recording of the magnetic hologram is determined by whether the temperature of medium exceeds a threshold temperature determined by conditions such as the Curie temperature. Since the increase in temperature is proportional to the absorbed light energy at each position, the temperature at the position is determined by the local intensity of light and the absorption coefficient of the medium. That is, the magnetic hologram can be recorded at a position where the light intensity exceeds a threshold, I_th, to heat the medium to a temperature higher than the threshold temperature. For instance, the binarized intensity distributions with I_th = 0.70 × 10⁻³ (threshold A) and I_th = 1.15 × 10⁻³ (threshold B) are shown in Figs. 3(b) and 3(c), respectively. In the case of threshold B with larger I_th, which means a relatively high threshold temperature or low recording energy, the intensity distribution in the torus region can be recorded. In contrast, for the case of threshold A, which corresponds to a relatively low threshold temperature or high recording energy, the interference pattern at the central region can also be recorded while the magnetizations of all torus regions thermally disappear, and the difference in intensity in the torus region cannot be recorded. As a result, the binarized pattern contains no interference information in the torus region. This result indicates that the determination of the threshold, i.e., the selection of a suitable recording energy level, is important to record domains containing the interference information including the signal pattern. That is, if the information of signal pattern contains mainly in the torus region, the selection of threshold B is suitable for recording, and vice versa. So the knowledge of the regions in which the information of signal pattern is recorded is important to determine the suitable recording conditions such as threshold.

 

Fig. 3 Normalized intensity distribution of calculated interference pattern. (a) Intensity profile along the horizontal centerline shown in inset, and binarized intensity distributions for threshold intensities of (b) I_th = 0.70 × 10⁻³ and (c) I_th = 1.15 × 10⁻³. (d) Statistical result of interference profile showing the light intensity band between I_MAX and I_MIN wherein the interference information is included.

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To determine the region wherein the shape of the interference pattern quantitatively changes depending on the signal pattern, we studied changes in the interference patterns for 100 different random signal patterns. The used recording patterns contain a random signal part with a fixed white rate of 50% and a reference part same as Fig. 2(b). The light intensity distributions in the interference pattern for every image were calculated according to Eq. (1), and the maximum and minimum values in the 100 calculated interference patterns, I_MAX(X, Y) and I_MIN(X, Y), respectively, at each position were extracted to determine the envelope of the “interfered” intensities. Figure 3(d) shows the change in the intensity of the interference pattern, where the red and blue lines denote the minimum and maximum intensities I_MIN and I_MAX, respectively, and the light blue region sandwiched between these is the region whose intensity changes according to the signal pattern. The intensity threshold, I_th, should lie in this light blue region (called the information region hereafter) in order to ensure that the interference pattern with the signal information is effectively recorded.

Next, we define the recording efficiency, η_ref, as follows:

Here, I_ref represents the total intensity of the reference beam and i_ref (X, Y) the intensity of the reference beam at a certain point $(X,Y,f-df)$. This integration is performed over the information region (S*) for a certain intensity threshold, I_th. This efficiency parameter indicates the total reference beam intensity passing through the information region, and it varies from 0 to 1. Figure 4 shows the calculation results of the recording efficiency for several signal sizes, d_sig, where the recording efficiency is at the maximal value for each defocus length via adjusting the intensity threshold, I_th. The efficiency exhibits a maximum at around df = 150 μm regardless of d_sig. The images in the left and right panels in Fig. 4 show the shapes of the information region (in white), with the orange color indicating the null-information regions where the intensity is always higher than I_th for all signal patterns. At df = 150 μm, the information region distributes in the central and torus regions. Hence, the reference and signal beams can sufficiently and suitably interfere, and the signal may be effectively stored as a magnetic binary hologram. When df > 150 μm, since the signal and reference beams are spatially separated, there is no effective interference between these two beams. The information region lies in the central portion, while the intensity corresponding to the torus region is too large (always exceeding the threshold, I_th). On the other hand, in the case of near focus (df < 150 μm), the intensities of the signal and reference beams are strongly concentrated at a very small point, and most of the central region contains no information. As a result, signal information may not be effectively recorded.

 

Fig. 4 Effect of defocus length on the recording efficiency for several signal sizes. The images in the left and right panels show the calculated shapes of the information region at several points, with the white color corresponding to the information region and the orange color corresponding to zero information (wherein the intensity always exceeds the threshold regardless of the signal pattern).

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Based on these simulation results, we next experimentally studied the effect of the defocus length on the reconstructed image. Figure 5(a) shows the effect of the recording energy and distance from the focal point on the reconstruction of a magnetic hologram. In this set of experiments, we used a proportionally reduced overall pattern composed of a square signal pattern of about 0.7 x 0.7 mm² and a torus reference pattern with an outer diameter of 2.5 mm and inner diameter of 1.7 mm. From the figure, we note that when the recording medium is set at a defocus length of less than 150 µm, either the medium is easily ablated due to the concentrated energy density or no magnetic fringe is observed. On the other hand, magnetic fringes are observed in the defocus-length range between 150 and 250 µm; however, no reconstructed image is obtained in contrast to the calculation results that indicate that effective magnetic fringes can be recorded in this range. In our study, reconstructed images could eventually be obtained only at distances >250 µm from the focal point.

 

Fig. 5 (a) Effect of defocus length and recording energy on the reconstruction of signal pattern in collinear hologram without optical diffuser. Upper panels (b, c) depict schematic images of interference at four diffraction spots wherein the reference part of each diffraction spot is shown as a different color, while the bottom photos show the corresponding shapes of the magnetic fringes for the original ring pattern reference beam with (b) df = 150 µm and (c) df = 400 µm. The upper panel in (d) depicts the schematic image for the modified square reference pattern with df = 400 µm, while the bottom panel shows the corresponding photograph of the signal region.

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To determine why a reconstructed image could be obtained at positions different from those calculated by numerical methods, we observed the magnetic fringes with a polarized optical microscope. Figures 5(b) and 5(c) show the images of magnetic fringes recorded without a diffuser at (b) df = 150 µm, 15 µJ/pulse and (c) df = 400 µm, 25 µJ/pulse, respectively. In the figure, we can observe four spots due to four diffracted light beams from the DMD. As shown in Fig. 5(b), these four spots are recorded separately (upper panel), as expected. However, probably due to inhomogeneous energy distribution and poor recording energy to record information in the hologram, no reconstructed image is observed for this case. On the other hand, in Fig. 5(c), we observe that these four spots overlap with each other in the case of df = 400 µm, corresponding to the obtainment of a reconstructed image. That is, as schematically shown in the upper panel of Fig. 5(c), the adjacent signal and reference portions exhibit an overlap under this condition. This overlap may lead to effective interference and result in the reconstruction of the magnetic hologram. To enhance the quality of interference and hence the reconstructed image based on this idea, we used a pattern in which the signal beam was sandwiched between four square reference parts; for this pattern, since the distance between the bright spots and their size on the recording position are determined by the optical system, it is possible to design the sizes and position of the signal light and the reference light to overlap completely on the recording position for yielding uniform interference fringes (upper panel of Fig. 5(d)). In addition, even in other cases, since the angle of the lights diffracted from DMD is known, we can design the optical system properly to overlap the adjacent signal and reference beams completely by using lens having an appropriate size and focal length. The bottom panel of Fig. 5(d) shows the polarized optical image of the magnetic fringe corresponding to our modified square reference pattern. When compared with Fig. 5(c), in Fig. 5(d), we observe clear interference patterns, and the reconstructed image also exhibits an improvement. Consequently, our following experiments were carried out with this new reference beam pattern.

Using this new square reference pattern, we recorded and reconstructed various signal patterns encoded with 2:4, 3:9, and 3:16 modulation schemes and evaluated the error ratio. Figure 6(a) shows reconstructed images corresponding to each modulation scheme recorded at 80 µJ/pulse; the signal patterns can be clearly observed for all modulation schemes. Figure 6(b) shows the average error ratio evaluated from at least 10 different reconstructed images for each recording condition. For comparison, the error ratios from a hologram recorded in our original system with a diffuser are also shown in inset of Fig. 6(b). In the original system, the error ratio is as high as about 10% for all recording conditions, while the error ratios from the holograms recorded with the new reference pattern without diffuser are less than 2%. This suggests that the distorted pixels in the original system with diffuser may be a reason for large number of errors in the reconstructed image, and the modified recording conditions without diffuser suitably facilitate the recording of clear magnetic holograms. On the other hand, the error ratio gradually decreases with increasing recording energy, and this reduction of error ratio at high recording energy may attribute to the formation of deep hologram in the medium, which increases the brightness of reconstructed image through improvement of diffraction efficiency [26]. Eventually, error-free reconstructed images were obtained for all modulation schemes at a recording energy of 80 µJ/pulse. In particular, with the application of the 3:16 modulation scheme, which has the lowest write ratio of 19%, we obtained non-error reconstruction at a low recording energy of 50 µJ/pulse. This result indicates that magnetic fringes can be recorded precisely under such recording energy conditions. In addition, since the encoded pattern prohibits the state where adjacent pixels are turned “on” in order to suppress the DC component of the Fourier transform, the error ratios corresponding to the small white ratio (3:16 modulation) were smaller than those of a higher ratio (2:4 modulation). This suggests that the signal pattern including the encoding method also forms an important parameter to achieve high-quality reconstructed images without error. The effect of this encoding method on the error ratio will need further investigation in future. In our study, we were eventually able to record magnetic holograms and reconstruct the data without error, thereby enabling us to realize a rewritable hologram memory.

 

Fig. 6 (a) Examples of reconstructed images recorded at 80 µJ encoded with 2:4, 3:9, and 3:16 modulation schemes. (b) The error ratio in reconstructed images without diffuser for various modulation schemes and with diffuser for 3:16 modulation scheme shown in inset.

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4. Conclusion

In our study, we determined the optimal recording conditions of a collinear holographic interferometer without an optical diffuser for achieving a clear image via both numerical simulations and experiments. We could obtain clear reconstructed images by recording holograms at a defocus point (thereby preventing excess concentration of recording energy without a diffuser) utilizing four diffracted light beams from a DMD. Utilizing this unique concept, we achieved error-free reconstructed images by using a 3:16 modulation scheme for signal encoding. Our results indicate that magnetic holograms can potentially be exploited as holographic memory technology. We believe that our approach is an important step toward the realization of rewritable holographic memory.