1. Introduction
With the rapid development of computer science in today’s digital era, data storage is crucial in diverse fields including artificial intelligence, astronomy, and biology
[1],
[2]. Currently, popular electronic or magnetic storage devices, such as semiconductor flash devices
[3] and hard disk drives
[4], have low durability and high energy consumption because of their use of large data centers. In contrast, optical data storage (ODS)
[5],
[6],
[7],
[8],
[9] is more durable and less expensive and can be a possible substitute for traditional storage devices. However, commercial ODS devices, such as compact discs (CDs), digital video discs (DVDs) and blue-ray discs, have limited data storage density
[5],
[10] and cannot meet the demands of data centers for high-capacity storage.
Most ODS systems encode the data into a spot array, where each pixel with or without a recording spot refers to the data of 1 or 0, respectively. To enhance ODS storage capacity, a straightforward strategy is to reduce the volume of the recording spots by using two-photon absorption
[11],
[12], super-resolution photoinduction-inhibition nanolithography (SPIN)
[13],
[14], or super-resolution focal-volume technology
[15]. For example, SPIN utilizes one Gaussian beam to excite molecules and another doughnut beam to inhibit the surrounding molecules
[14], yielding a subdiffraction-limit recording spot for high-capacity ODS. Another approach is to multiplex each recording pixel with multiple orthogonal degrees of freedom, such as the wavelength, polarization, and orbital angular momentum of light
[16],
[17],
[18], thereby offering more channels to increase the data capacity. Nevertheless, due to the limitations of materials and optical diffraction, the recording spots cannot be shrunk or multiplexed unboundedly in a single recording layer.
The use of multiple vertical recording layers has become an efficient approach to further increase the capacity of ODS. However, the binary-amplitude recording spots in each layer lead to severe crosstalk between two neighboring layers
[13],
[14]. Very recently, transparent fluorescent recording spots on a dye-doped photoresist film were proposed to avoid such interlayer crosstalk, enabling 100 recording layers with petabit-level capacity
[8]. This technology reveals the great potential of a multilayer architecture in enhancing the ODS capacity. In theory, more layers can be used to further enhance the capacity, but this approach is constrained by the finite working distances of writing and reading objectives with ultrahigh numerical apertures
[8]. Since these multiple recording layers (MRLs) are built with physical entities that have rigid spatial volumes, the optical performances (e.g., working distances and resolutions) of the writing and reading systems are inevitably challenged. A natural question arises: Can we construct virtual recording layers without occupying rigid space in order to increase the ODS capacity?
To address this problem, we propose the establishment of high-orthogonality random meta-channels, where each recording pixel in a single physical layer is encoded with a designed phase to create multiple virtual recording layers via holographic reconstruction, which we call “hybrid-layer data storage.” To demonstrate the proof of this concept, we experimentally designed and fabricated geometric metasurfaces as a physical layer with 32 orthogonal channels that multiplex 16 pairs of complementary printed images. The encoded phase in each channel reconstructs one holographic pattern in the virtual layer, resulting in 32 holographic images for storage. In this way, a total of 48 images are stored in both the physical and virtual layers, yielding an experimental storage density of 2.5 Tbit·cm−3. More virtual layers were also simulated to investigate the feasibility of higher-capacity storage with this hybrid-layer approach.
2. Concept of hybrid-layer ODS
The proposed concept of hybrid-layer storage based on metasurfaces
[19],
[20],
[21],
[22],
[23],
[24],
[25],
[26],
[27] is illustrated in
Fig. 1(a). Here, metasurfaces are used to increase the spatial resolution of the physical layer for subwavelength pixels and reconstruct the virtual layer for the powerful functionality of phase modulation. The physical layer (
z = 0, where
z is the propagation distance) can be divided into different orthogonal channels ranging from
to
, where
N is the total number of channels and
N = 32 is exemplified for the purpose of demonstration. Light passing through the channel
is diffracted into a spherical space (
Fig. 1(b)) with a radial position
r, a polar angle
, and an azimuthal angle
, so the channel
is labeled
for better discussion. Observing the physical layer (i.e., the surface of the metasurfaces) by addressing the designed directions, we can obtain
N printed patterns, half of which are complementary to each other (e.g
., channels
and
in
Fig. 1(c)). Thus, only
N/2 independent images are stored in the physical layer. Beyond these printed images at the surface, each channel in the physical layer also carries an extra holographic phase to reconstruct multiple virtual layers at different diffraction distances—that is,
z =
z1,
z2, …,
zM, where
M is the number of virtual layers. At each virtual layer, one independent image can be reconstructed for data storage, yielding
NM images. Thus, with this hybrid-layer approach, we can store a total of
N/2 +
NM images, including
N/2 printed images in the physical layer and
NM holographic images in the virtual layers.
To reduce crosstalk among these stored images, all the channels are structured with high spatial orthogonality and randomly distributed apertures, based on the following three considerations. First, in the physical layer, all the pixels in any channel have no spatial overlap with those in other channels; that is, , where the real numbers Ln and Lm denote the apertures of the nth and mth channels, respectively. The summation (i.e., ) over all the apertures yields a rectangular aperture, which is shared by all the apertures of the channels. Assuming that a plane wave (with a constant electric field of A0) passing through the nth channel has a complex amplitude of = A0·Ln, we can check its orthogonality with any other channel by using (m ≠ n). Thus, we can obtain high spatial orthogonality among these channels in the physical layer.
Second, the pixels in each channel are located randomly to avoid the high-order diffractions that usually appear for periodic pixels. The physical layer shown in
Fig. 1(a) contains sketches of these random pixels, which are sufficient to show the complementary images (
Fig. 1(c)). To multiplex multiple channels, each pixel of one channel is located randomly in one super-pixel, as illustrated in
Fig. 1(d). It should be noted that each super-pixel contains
N/2 pixels in a square. Because all the super-pixels are distributed periodically in the panel of the physical layer, the randomness of each channel can be realized by the random pixels in each super-pixel. The images printed in the physical layer have sparse pixels (
Fig. 1(c)) that are randomly distributed in each super-pixel.
Third, to realize the virtual layers, every pixel in all channels in the physical layer is made of an array of
Nm ×
Nm meta-atoms (
Fig. 1(e)), which encode the required phase for reconstructing the virtual layers. To reduce the crosstalk among channels, each array is imprinted with two kinds of phase profiles—namely,
ψholo and
ψangle, where the holographic phase
ψholo is used to create holographic images and the tilting phase
ψangle is responsible for guiding light from each channel to different solid angles (
Fig. 1(f)). Limited by the finite aperture of each channel, the diffracted holographic patterns have a fixed range of
for the polar angle and
for the azimuthal angle. To obtain high orthogonality at the output terminals, two adjacent channels
and
can be chosen to satisfy
and
. Thus, since the diffracting field
Vn of each channel has no spatial overlap, we obtain the equation
(
m ≠
n), which indicates that all the channels in the virtual layers are mutually orthogonal.
Benefiting from the high orthogonality of both the recording and output terminals, we can construct virtual layers by encoding the holographic phase in each pixel. Although each pixel is sparse in one channel, the encoded phase realized by the geometric metasurfaces
[28],
[29],
[30],
[31],
[32],
[33],
[34] (
Figs. 1(d) and
(e)) can guide light from its own channel in the same direction for interference, thereby forming the designed holographic images.
3. Design of meta-channels
To demonstrate the proof of concept, metasurfaces with subwavelength nanostructures were designed to construct holographic images in a single virtual layer (i.e.,
M = 1). The metasurfaces are located on the
X–Y plane, and the virtual layer is formed on a spherical surface, as shown in
Fig. 1(b). For a better experimental characterization, the deflecting direction
of each meta-channel is constrained in the red area, where the polar angle
θ satisfies
, and the azimuthal angle
φ satisfies
. According to the optical diffraction from the nanostructures, the maximum polar angle
is determined by the period (labeled as
Pmeta) of the pixel in the metasurfaces. At the designed wavelength of 633 nm, the pixel pitch
Pmeta ×
Pmeta is chosen to be 250 nm × 250 nm, which is nearly half the wavelength needed for higher conversion efficiency.
Fig. 2(a) shows a pixel made of a crystalline silicon (c-Si) nanobrick with an in-plane orientation angle of
on a sapphire substrate. When passing through nanobricks, incident circularly polarized (CP) light is transformed into crossed CP light with an additional geometric phase
[28],
[29],
[30],
[31],
[32],
[33],
[34],
[35],
[36],
[37]. The conversion efficiency is numerically simulated using a finite-domain time-difference (FDTD) method, in which we employ periodic boundary conditions along the
X and
Y directions and a perfectly matched layer (PML) along the
Z axis. The nanobricks have a height of 300 nm, which is determined by the thickness of our own c-Si film sitting on the sapphire substrate.
Fig. 2(b) shows the simulated conversion efficiency for c-Si nanobricks with different widths and lengths, suggesting that the highest conversion efficiency occurred at a length of 160 nm and a width of 90 nm (highlighted by a blue dot). At the chosen parameters, the nanobricks have a theoretical conversion efficiency of 99% with good tolerance to dimension variation, which facilitates the fabrication of metasurfaces.
Fig. 2(c) shows experimental efficiencies of 50%–80% at the different wavelengths from
λ = 600 nm to
λ = 650 nm. The deviation from the simulated efficiency may be caused by imperfect fabrication of the nanostructures and the inaccuracy of measured refractive indices.
With the designed metasurfaces, we can calculate the maximum polar angle
. According to the generalized Snell’s law of refraction
[19], the propagation direction of light can be manipulated by introducing an abrupt phase gradient at the subwavelength scale. To achieve a higher diffraction efficiency in holographic reconstruction, at least four meta-pixels are needed to cover the phase range from 0 to
. In this work, four meta-pixels have a length of
(= 250 nm × 4). At
, we can obtain the maximum polar angle
∼39.27°. Since the propagation distance is
z1 = 1500
and the reconstructed holographic images have a size of about
, the diffracted range
of one holographic image can be calculated from the formula
. To avoid crosstalk between adjacent holographic images, the polar angle should be greater than Δ
θ = 8.36°. Based on the above considerations, the 32 holographic images are categorized into four polar angles, where
θ1–4 = ∼8.6° for channels 1–4,
θ5–12 = ∼17.2° for channels 5–12,
θ13–24 = ∼25.8° for channels 13–24, and
θ25–32 = ∼34.4° for channels 25–32. For one selected polar angle
, the number of channels is different to avoid crosstalk between two neighboring channels in the azimuthal direction. These channels at one polar angle
θ are distributed uniformly in the azimuthal direction
φ. For example, at a polar angle
θ = ∼17.2°, we set up eight channels (from channel 5 to channel 12) with azimuthal coordinates ranging from
φ5 = 0 to
φ12 = 7π/4, with an interval of π/4. The manipulation of the designed
θ and
φ is realized by using the tilting phase
ψangle, which behaves like a blazed grating. Its phase gradient is used to control the polar angle
θ, and the orientation of the grating is responsible for the azimuthal angle
φ. The pixels of one meta-channel (i.e.,
Fig. 1(e)) are encoded with the same tilting phase
ψangle so that the light diffracted from all these sparse pixels in this meta-channel can be guided in the identical direction for holographic reconstruction via optical interference.
Fig. 1(c) shows the spatial distributions of channel
(red squares) and its complementary channel
(blue squares) in the physical layer. The deflection directions of these two complementary patterns have a centrosymmetric distribution—that is,
and
. The metasurfaces are composed of 50 × 50 super-pixels, each of which contains 4 × 4 pixels (
Fig. 1(d)). Each pixel is composed of 8 × 8 meta-pixels in this work. Because the pixels of the printed images are located in one super-pixel, the spatial resolution of the printed images is determined by the size of one super-pixel. Each pixel functions like a phase-encoded point source for the reconstruction of holographic images in the virtual layers. Considering that these two complementary patterns are responsible for holographic images in different deflecting directions, each pattern should contain nearly the same number of pixels. Therefore, all the other complementary patterns in the physical layer are adjusted relatively with a spatial occupancy ratio of 50:50 to balance the holographic performance. Due to the existence of two complementary patterns, we have 32 meta-channels for reconstructing the virtual layers.
Beyond the tilting phase
ψangle, each meta-channel must load an additional holographic phase for the creation of the required virtual layer at the designed position (e.g.,
z1 = 1500 μm). The holographic phase
ψholo of each meta-channel is independently designed using the Gerchberg−Saxton algorithm
[20],
[38], where the propagation of light is simulated using the Rayleigh–Sommerfeld diffraction integral with the help of fast Fourier transform
[39]. Notably, since each channel has a specially shaped aperture
Ln (e.g., the star pattern for meta-channel 1), it is necessary to consider the optical modulation of the aperture shape (i.e., the incident field of the hologram is described using
A0·
Ln) during the design of
ψholo. Once the holographic phase
ψholo is obtained, the total phase encoded in this meta-channel can be derived using
ψangle +
ψholo. Importantly, the phase in each pixel is realized by high-spatial-resolution metasurfaces that offer a sufficient degree of freedom to construct holographic images, which is not possible for traditional diffractive optical elements with pixel pitches larger than one wavelength
[40]. After finishing the phase design for all the meta-channels, we combine them into one, yielding the total phase in
Fig. 2(d). Because the apertures
Ln of all the meta-channels are spatially orthogonal, the combined phase in
Fig. 2(d) has no spatial overlap between two arbitrary meta-channels. Thus, the experimental realization of each combined phase is the same as that of previously reported meta-holograms
[41],
[42]; that is, the designed phase is correlated with the orientation angle
α in a pixel-by-pixel way.
4. Printed images in the physical layer
To verify this concept, we fabricated geometric metasurfaces by means of standard electron beam lithography with a dry-etching process (Fig. S1 in Appendix A). Fabrication details are provided in Appendix A Section S1.
Fig. 2(e) shows scanning electron microscopy (SEM) images of the fabricated sample, where the good profiles of both the shapes and sidewalls of the nanobricks indicate high-quality fabrication.
To characterize the performance, we first measured the printed images in the physical layer.
Fig. 3(a) illustrates the detailed channel distributions with the designed polar angle
θ and azimuthal angle
φ. To capture the printed images at different angles, the recording system in
Fig. 3(b) was rotated during the characterization using a homemade experimental setup. A laser beam with a wavelength of 633 nm was spatially filtered using a 10
pinhole and collimated by a lens to illuminate the sample after passing through a CP generator composed of a linear polarizer and quarter waveplate. The light transmitted through the metasurfaces was collected by an imaging system consisting of an objective lens, a pinhole, and a charge-coupled-device (CCD) camera, which were mounted on a rotatable stage to record the printed images at different spherical coordinates.
Fig. 3(c) exhibits the experimentally captured images printed directly in the physical layer by addressing the designed spherical coordinates
θ and
φ. The simulated pattern of each image is provided at the top-left corner of each panel. The patterns of the printed images are basically similar to those of the simulated images. Distortion appears in the images with a large polar angle
θ, which is caused by the inevitable obliquity between the experimental images and the CCD plane. At each polar coordinate, two complementary patterns can be experimentally found at centrosymmetric positions, where their azimuthal angles have a difference of π. Benefitting from this difference, the printed images have little crosstalk with the neighboring channels, indicating good orthogonality in the experiment.
5. Holographic images in the virtual layer
To observe the encoded images in the virtual layer (
Fig. 4(a)), we use the experimental setup shown in
Fig. 4(b), where the imaging system is used to capture the images in the virtual layer by moving 1.5 mm away from the sample. Because each holographic phase is encoded into its corresponding printed image, the holographic image is created at the same spherical coordinate as the printed image.
Fig. 4(c) shows the holographic images measured by addressing the polar angle
θ and the azimuthal angle
φ. Due to optical propagation over
z1 = 1.5 mm, the holographic images are relatively separated from the surrounding channels, so that the crosstalk among the holographic images is naturally suppressed in the virtual layer. Similarly, distortions at a large polar angle
θ of measurement still exist; this is experimentally inevitable for an off-axis measurement system in a laboratory environment and can be solved by using mature industrial equipment. Nevertheless, the reconstructed images are consistent with the simulated holographic images (Section S2 in Appendix A). Notably, speckles exist in both the simulated and experimental holographic images due to the randomly distributed pixels in each meta-channel and the high-coherence laser source used in our experiment
[43],
[44]. Fortunately, the speckles have a lower intensity than the holographic images, so the expected images in the experiment can still be seen. All the measured holographic images with recognized features confirm the feasibility of our proposed hybrid layers for data storage. To evaluate the image quality quantitatively, the root-mean-square errors (RMSEs) between the ideal and experimental images were used, as shown in
Fig. 4(c) (the digits at the upper-right corner of each image), yielding experimental RMSEs from 0.41 to 0.74.
Fig. 4(d) shows a detailed comparison of the simulated (data provided in Appendix A Fig. S2) and experimental RMSEs, which have average values of 0.454 and 0.571, respectively. Although these demonstrated holographic images are not as good as the ideal ones, they can still be distinguished for the purpose of data storage. The discrepancy between the experimental and simulated results may come from the inevitable crosstalk, as the orthogonality among channels is still not optimal under the current parameters chosen in this work (Fig. S3 in Appendix A). Suggested methods to enhance the orthogonality are provided in Appendix A Section S3.
6. Discussion
Our proposed hybrid-layer ODS can extend the recording medium of data into virtual layers for better reading because the virtual layers do not occupy rigid space. To evaluate its performance, we employ the standard method of calculating the capacity (Section S4 in Appendix A), which is expressed as ), where is the number of bits in a single holographic image (Nbit = 50 × 50), is the number of stored images, and d and are the lateral length and thickness of the device, respectively. For the results demonstrated in this work, Nbit = 50 × 50 = 2500, Nimage = N/2 + NM = 48, d = 400 μm, and t = 300 nm, which yields a raw capacity of 2.5 Tbit·cm−3.
Although the achieved capacity is not high compared with that of other methods
[11],
[12],
[13],
[14],
[15],
[16],
[17],
[18] (Fig. S4 and Table S1 in Appendix A), it can be further enhanced by using more virtual layers (i.e., increasing
M), which results in a larger
Nimage for enhanced information capacity. To demonstrate the feasibility of using more virtual layers, we simulated holographic images of two virtual layers (i.e.,
M = 2) (details provided in Appendix A Section S5). To facilitate the simulation, the 16 printed images and 32 holographic images (Fig. S5(a) in Appendix A) in the first virtual layers were the same as those in
Fig. 3,
Fig. 4. The second virtual layer was reconstructed at a propagation distance of
z2 = 2.5 mm, making it possible to obtain another 32 new holographic images (Fig. S5(b) in Appendix A) at the same spherical coordinates as those in the first virtual layer. From the simulated images in the second virtual layer, highly distinguishable patterns could be observed without remarkable noise or crosstalk between two neighboring virtual layers. The realization of more virtual layers (up to 1000 layers in theory
[45]) through holography techniques is also possible by using high-dimensional random vectors to suppress interlayer crosstalk. Furthermore, it is possible to introduce orthogonality into the holographic layers in each channel. For example, the odd layers could be reconstructed by using left-handed circular polarization of the incident light, while the even layers could function for the illumination of right-handed circular polarization. Due to the orthogonality of both circular polarizations, the odd and even layers have no crosstalk. Thus, the crosstalk between the odd (or even) layers dominates. Since the longitudinal distances between two neighboring odd (or even) layers are twice the distance of the interlayer interval in this work, high-fidelity holographic images can be reconstructed more easily due to the lower influence from the other layers, thereby decreasing the crosstalk of this technology.
In principle, the proposed hybrid-layer data storage via holography has larger capacity than traditional point-by-point data storage. For one pixel in point-by-point storage, the binary data of 0 and 1 has a bit depth of 1, which can be calculated using the Shannon information entropy
[46],
[47], where
is the probability. Thus, its information in one layer can be evaluated by using the total number of all the pixels—that is,
NV ×
NR, where
NV and
NR are the numbers of the pixels in the columns and rows, respectively. In contrast, the data at each pixel of phase-type metasurface holograms can take on multiple values, so it is much larger than the binary data in point-by-point storage. Our proposed approach with phase modulation has a bit depth greater than 1, thereby offering greater capacity for information storage. For example, a hologram with a binary phase of 0 and π can theoretically diffract only about 40% of its incident light into the expected image
[48], while more light (∼81%) is manipulated for a four-level (i.e., a bit depth of 2) phase modulation
[49], indicating higher capability in holographic reconstruction. However, when evaluated on the basis of energy efficiency, the information capacity increases nonlinearly with increasing bit depth because the increment of efficiency is very slow for a large bit depth. Thus far, we have not found a viable method to efficiently calculate the information capacity of multi-level-phase holograms, despite the consensus that phase holograms with a larger bit depth have higher information capacity
[50]. The correct evaluation method is important because it can help to find the theoretical limitation of our proposed storage capacity, which is directly determined by the information capacity of the phase hologram.
As a proof-of-concept demonstration, the current work still needs further improvement in increasing the total number of meta-channels and virtual layers, suppressing the speckles, enhancing the signal-to-noise ratio, and removing the distortion of the stored images. Beyond these issues, we must emphasize that our demonstrated data capacity (i.e., ∼2.5 Tbit·cm−3) is still much lower than the information capacity carried by the phase hologram in the physical layer. The underlying reason originates from the information redundancy of computer-generated holograms during the reconstruction of expected images; that is, the information capacity of a reconstructed image is always smaller than that on the initial holographic plane. Although such redundancy is necessary to reconstruct an arbitrarily shaped image, it still leaves much room to reduce the information redundancy and increase the information capacity of the reconstructed images. Currently, the issue of how the redundancy can be decreased remains an open question for the entire holography community.
A metasurface was used to realize the designed phase because of its high spatial accuracy, despite the difficulties in fabrication and reconfigurability. The subwavelength pixel pitches make it possible to multiplex the polar angle
θ in a large range so that the crosstalk between different channels can be significantly suppressed. If traditional diffractive optical elements (e.g., liquid-crystal-based spatial light modulators
[51]) are used, the maximum diffraction angle
θ is limited to several degrees, which is determined by large pixel pitches. Currently, for optical devices based on liquid crystals, it is challenging to suppress pixel pitch down to the subwavelength scale. The fundamental reasons are twofold
[52]: First, liquid crystal molecules require a spatial range of several hundred nanometers for the transition from one state at a pixel to another state at a neighboring pixel. The use of pixels with dimensions smaller than the transition distance will lead to severe crosstalk between two neighboring pixels, such that both pixels lose their modulation functionalities. Second, due to the limited birefringence of liquid crystal molecules, the liquid crystals must be several or tens of micrometers thick to realize sufficient phase or amplitude modulation. If each pixel pitch has a subwavelength dimension, the light incident on this pixel will diverge severely through the liquid crystals over such a large thickness, creating another key source of crosstalk. Considering the above issues, we chose to use metasurfaces instead of liquid crystal materials. Nevertheless, metasurfaces present intractable problems such as high-cost fabrication and poor reconfigurability, although satisfying solutions may be found in the near future. The high cost of fabrication can be solved by the development of mature semiconductor manufacturing tools. If dynamic metasurfaces become available, they will extend the current static read-only mode to a more important rewritable mode.
7. Conclusions
In summary, we have demonstrated hybrid-layer ODS based on high-orthogonality random meta-channels realized by the use of geometric metasurfaces made of c-Si nanobricks. A total of 48 images, including 16 printed images in the physical layer and 32 holographic images in the virtual layer, were stored with a capacity of 2.5 Tbit·cm−3 and successfully read in the experiment. Encoding the data into multiple virtual layers can enhance the optical storage capacity by increasing the number of virtual layers via holography, making this approach a promising candidate for next-generation high-capacity ODS.
Acknowledgments
Kun Huang thanks the National Key Research and Development Program of China (2022YFB3607300), the National Natural Science Foundation of China (62322512 and 12134013), the Chinese Academy of Sciences Project for Young Scientists in Basic Research (YSBR-049), and support from the University of Science and Technology of China’s Center for Micro and Nanoscale Research and Fabrication. This work was partially supported by the China Postdoctoral Science Foundation (2023M743364). The numerical calculations were performed on the supercomputing system in Hefei Advanced Computing Center and the Supercomputing Center of University of Science and Technology of China.
Compliance with ethics guidelines
Dong Zhao, Hongkun Lian, Xueliang Kang, and Kun Huang declare that they have no conflict of interest or financial conflicts to disclose.
Appendix A. Supplementary material
Supplementary data to this article can be found online at
https://doi.org/10.1016/j.eng.2024.10.014.
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(3138KB)
