In the information era, the importance of data storage technology has become primary^[1]. With the rapid development of big data and cloud computing, the demand for storage capacity continues to escalate. Traditional storage solutions, such as hard disk drives and magnetic tape drives, are encountering physical barriers in terms of capacity and performance, and they are unable to meet the escalating demands of data storage. Holographic data storage technology^[2–5], due to its high storage capacity, high storage density, and high information redundancy, has emerged as a promising candidate for next-generation data storage technology. Traditional holographic technology still falls short of fully exploiting the rich and multidimensional modulation parameters of light, limiting its capabilities to merely modulating two-dimensional information (amplitude and phase) while neglecting polarization information. Polarization holography has attracted attention due to its unique capability to encode amplitude, phase, and polarization information^[6–9]. Polarization holography technology utilizes polarization-sensitive materials to record and reconstruct the polarization information contained in the light field through the interference between the recording signal wave and the reference wave, where the two waves exist in distinct polarization states. This technology not only retains the amplitude and phase information inherent in traditional holography but also incorporates polarization information, thereby substantially increasing the dimensions of information storage and offering a novel solution to address the ever-growing demand for storage capacity.

Previous studies have explored the modulation of polarization alone^[10,11], modulation of amplitude-phase, modulation of amplitude-polarization^[12,13], and modulation of phase-polarization^[14,15] using polarization holography. Unlike previous studies, this study harnesses the polarization orthogonality in holography to generate unique reconstruction characteristics, enabling the storage of holographic data containing multidimensional modulation information that simultaneously carries amplitude, phase, and polarization. Based on calculations derived from tensor and vector wave theories, two holograms carrying multidimensional modulation information are sequentially recorded using orthogonally polarized light waves captured at a single point, effectively mitigating the imbalance in polarization and intensity response through precise control of exposure time^[16–18]. By manipulating orthogonally polarized light, we facilitate dynamic, crosstalk-free switching between two holograms under a special interference angle of 90°, where each encodes intricate three-dimensional information. Notably, the amplitude and phase information of a single polarization hologram is reconstructed with high accuracy, yielding amplitude and phase bit error rates (BERamp and BERpha) below 0.5%, and full orthogonal extinction in the polarization state is ensured. Holographic data storage technology that employs orthogonally polarized light for comprehensive modulation, including amplitude, phase, and polarization is an effective strategy to address the data storage challenges posed by big data. By integrating multidimensional modulation with polarization holography technology, the recording density and storage capacity of holographic data storage can be significantly enhanced, which effectively addresses the need for the long-term preservation and rapid access to vast quantities of data.

Polarization holography involves two distinct stages: recording and reconstructing. The schematic diagram for polarization holography with an interference angle of 90° is depicted in Fig. 1. Figure 1(a) illustrates the recording process, while Fig. 1(b) depicts the reconstruction process in a cube medium. We define θ=90° as the interference angle, which represents the angle between the signal and reference waves. Sig., Ref., Rd., and Rec. represent the signal wave, reference wave, reading wave, and reconstructed wave, respectively. k+ and k− denote the propagation vectors of the signal wave and the reference wave, respectively. The p polarization is defined as the electrical field oscillating along the intersection of the x–z plane and the cross-sectional plane of light wave, and the s polarization is parallel to the y-axis of the coordinate system. Consequently, the respective unit vectors are denoted as s=[010],pj=[cosθj0sinθj],(1)where s and pj represent the unit vectors of the s and p polarizations, the subscript j, which contains “+” or “−”, denotes the signal wave and reference wave, respectively, and the absolute difference between the angles θ+ and θ− is 90 deg.

Table 1 presents the theoretical derivations for recording and reconstructing, through polarization conversion, the dual channels that carry amplitude, phase, and polarization. These derivations are grounded in the principles of polarization holography^[7]. The rationale behind implementing this method lies in its ability to accurately reconstruct the three-dimensional information encoded in the signal wave in a single hologram, under the illumination of orthogonal polarization channels, while preventing any information crosstalk from other holograms. To achieve the crosstalk-free reconstruction of information in the two orthogonal polarization channels, the reconstruction results of a single hologram under these two channels must be analyzed independently. Essentially, achieving crosstalk-free results necessitates that the undesired hologram produces null reconstruction.

In Table 1, L₁ and L₂ represent the amplitude distribution functions, δ and ϕ represent the phase distribution functions, and B represents the coefficient for the tensor components of the recording medium. In addition, A represents the coefficient of the intensity components of the recording medium. The values of A and B are determined by the inherent properties of the material and vary with the exposure energy. According to tensor theory^[7], a dielectric tensor is introduced, with A and B used to characterize the grating and to facilitate the calculation of orthogonal conditions. In this study, a recording interference angle of 90° and orthogonally linearly polarized light are utilized, which effectively mitigates the need to address concerns regarding the balance of exposure energy, such as the condition A+B=0^[17].

The storage and retrieval of polarized holographic data encompass four key processes: encoding, recording, reconstructing, and decoding. During the encoding process, the original information is encoded into amplitude and phase data pages, utilizing a specific polarization to modulate the signal wave. We use the first hologram listed in Table 1 as an illustrative example. The signal wave, which carries the original information, exhibits p polarization, characterized by an amplitude and phase distribution denoted as L1eiδp+, whereas the reference wave exhibits s polarization.

During the recording process, the resultant electric field from the combined signal and reference waves within a polarization-sensitive medium, based on the theory of polarization holography^[7], is represented by G(r)=L1eiδp+eik+r+seik−r,(2)where r represents the position vector.

During the reconstruction process, we illuminate the first hologram in the medium with a reading wave that has two distinct orthogonal polarizations: s and p polarizations. According to the established vector wave theory^[7], the respective reconstructed waves are calculated as BL1eiδp+ and 0, as presented in the two rows corresponding to the second hologram in Table 1. It can be observed that when the medium is illuminated with an s-polarized wave, the reconstructed wave exhibits the same three-dimensional information as the original signal wave, including polarization, amplitude, and phase. Conversely, no diffracted wave is generated when a p-polarized wave is used to illuminate the medium. Similarly, the results presented in the last two rows of Table 1 reveal a contrary phenomenon for the second hologram compared to the first hologram: the recorded hologram information appears only when illuminated with p-polarized light, with no diffraction occurring under s-polarized light illumination. Hence, by switching the polarization state of the incident wave, orthogonal polarization holograms with distinct amplitude and phase distributions can be interchangeably activated without crosstalk.

Figure 2(a) illustrates the schematic of the optical setup for the experiment. A laser beam with a wavelength of 532 nm (MSL-FN-532) was collimated and expanded before irradiating spatial light modulator SLM1 (model HDSLM80RA, with an 8 µm pixel pitch). The half-wave plate HWP1 was employed to adjust the intensity ratios of two waves after passing through a polarizing beam splitter (PBS). Polarizers P1 and P2 are linear, with P1 horizontally polarized and P2 vertically polarized, enabling amplitude-only modulation for SLM1. The amplitude data page was loaded onto SLM1 to modulate the amplitude of the incident light. Subsequently, the amplitude-modulated light passed through two 4f systems, composed of lenses L1, L2, L3, and L4, ultimately irradiating SLM2 (model HDSLM80R-PLUS, also with an 8 µm pixel pitch). The phase data page was loaded onto SLM2 for phase modulation. An aperture filtered out the unmodulated wave. HWP2 and P3 were employed to adjust the polarization of the light wave to meet the requirements of SLM2. Two additional 4f systems, composed of L5, L6, L7, and L8, were employed in the recording and reconstruction optical paths. The calibration curves for the amplitude- and phase-modulated SLMs are presented in Figs. 2(b) and 2(c), respectively. Random third-order complex amplitude data encoding was executed based on the three-grayscale amplitude and phase values marked in Figs. 2(b) and 2(c), using a 30×30 encoding data matrix and an oversampling factor of 10. Therefore, the size of the final data page in real space was 2.4mm×2.4mm. After modulation, the light wave obtained at the back focal plane of Lens 8 propagated further for a distance of d=2mm in Fig. 2(a). The resulting diffraction pattern, with its complex amplitude intensity, was captured by a complementary metal–oxide semiconductor (CMOS) sensor (model CHUM-1228C, featuring a 4 µm pixel pitch), as shown in Fig. 2(d). The purpose of the additional propagation distance d=2mm was to enhance the clarity of the phase information, enabling deep learning to better grasp its phase characteristics^[19]. The polarization state in the signal optical path was adjusted by half-wave plate 3 (HWP3). Meanwhile, in the reference optical path, polarizer 4 (P4) and HWP4 collaborated to switch the output wave between distinct polarization channels: the s-channel (illuminated by an s-polarized reference wave) and the p-channel (illuminated by a p-polarized reference wave). The original amplitude and phase diagrams presented in Figs. 2(e) and 2(f) depict the distribution of complex amplitude information recorded in the s- and p-channels, respectively. For the s-channel, the amplitude and phase distribution diagram shown in Fig. 2(e) was uploaded to the respective SLMs, and then the polarization state of the signal wave was adjusted to p-polarized light via HWP3. The modified signal wave, with its three-dimensional characteristics, then intersected with the reference wave in a polarization-sensitive medium^[20–24]. The cubic-shaped recording material had a size of 10mm×10mm×30mm ensuring a 90° angle between the signal and reference waves. The recording duration was 1 min, with a signal wave with 10 µW power and a reference wave with 38 mW power. Despite a significant reduction in light intensity as the signal wave traversed through the two SLMs and numerous optical devices, the disparity in the power ratio between the signal wave and the reference wave did not impede the hologram recording process.

After successfully recording the three-dimensional data in the s-channel, the shutter (SH1) positioned on the signal wave path was closed, and the polarization channel shifted to the p-channel during the reconstruction process. The normalized diffraction efficiency of the reconstructed wave, during the transition of the polarization channel, was experimentally measured and depicted in Fig. 3. Upon rotating HWP4 in the reference optical path, the polarization of the reading wave transitioned from s polarization to p polarization. Under s polarization conditions, as detailed in Table 1, the information encoded in the first hologram was fully reconstructed, yielding a peak normalized diffraction efficiency of 1. As the s-component of the reading wave’s polarization diminished, the normalized diffraction efficiency correspondingly decreased. After rotating HWP4 by 45°, the polarization state of the reference wave underwent a complete transition to p-polarization, resulting in a minimum normalized diffraction efficiency of 0.0141 at that juncture. Throughout the entire process, the maximum contrast ratio observed for the normalized diffraction efficiency was 71:1. This crosstalk effect can be considered negligible. Following this, the amplitude and phase distribution diagram depicted in Fig. 2(f) was uploaded to the corresponding SLMs, and the polarization state was adjusted to s-polarized light utilizing HWP3. The modified signal wave, having undergone three-dimensional modulation, intersected with the reference wave of the p-channel at the identical spatial location on the medium, thereby enabling a second holographic recording with a recording duration of 1 min.

After successfully recording all the holograms, the signal optical path was blocked (by closing SH1), allowing only the reading wave to propagate and illuminate the medium. The diffraction intensity patterns of the reconstructed wave, captured by the CMOS sensor in the distinct polarization channels along the reconstruction optical path, are presented in Fig. 4. Upon changing the orthogonal polarization of the reading wave, the transformation of the reconstructed patterns was captured by the CMOS sensor and is shown in Figs. 4(a) and 4(f). Due to the faithful reconstruction effect of polarization holographic, the size of the reconstructed data page remained 2.4mm×2.4mm. Visualization 1 demonstrates the real-time evolution of the reconstructed patterns in response to toggling the orthogonal polarization state (for easy visual recognition, the letters “A” and “B” represent amplitude information, and the numbers “1” and “2” signify phase information).

To ensure the stability of the results reconstructed from the recorded information, we employed a two-step process for decoding the three-dimensional data. First, a polarizer was utilized for orthogonally polarized extinction detection in the reconstructed patterns under both the s-channel and p-channel, achieving complete extinction. Second, the amplitude and phase data for the reconstructed pattern were decoded using a deep learning method that demodulated the complex amplitude information from a single diffraction intensity pattern^[19]. Hao. et al. indicated that the complex amplitude diffraction intensity patterns can be demodulated effectively by extracting edge phase characteristics and center amplitude characteristics using convolutional neural networks (CNNs). In the experimental section, the CNN models were trained and validated on a large dataset of patterns showing the intensity of diffraction (consisting of unrecorded patterns), yielding highly precise demodulation results. Utilizing this method, we decoded the reconstructed patterns, innovatively employing the patterns of diffraction intensity obtained from signal wave patterns as the training set. For the s-channel reconstructed pattern [Fig. 4(a)], the decoded amplitude and phase data pages were presented in Figs. 4(b) and 4(d), respectively. We compared the decoded results with the original data page pattern that was uploaded to the signal optical path and found the BERamp (BER = number of error data/total number of data × 100%) and BERpha to be 0.22% and 0%, respectively. Similarly, the decoded amplitude and phase data pages for the p-channel reconstructed pattern [Fig. 4(f)] are shown in Figs. 4(g) and 4(i), respectively. When compared with the original data page pattern, the corresponding BERamp and BERpha were 0% and 0.22%, respectively. These high decoding accuracy rates validate the strong consistency of information between the amplitude and phase of the reconstructed wave and that of the signal wave.

It is evident that the utilization of orthogonally polarized light serves as an advantageous means to mitigate crosstalk among holograms. Additionally, the orthogonally polarized array^[25], formed through the combination of polarized light, can overcome the limitation traditionally posed using only two orthogonal polarizations. According to the principle of polarization holography, expanding the use of orthogonal polarizations is expected to enable the modulation of multidimensional information across more than two channels. This advancement enhances the storage capacity of holographic data storage through the application of holography technology and solidly establishes its multidimensional capabilities via multi-channel polarization modulation.

In this study, we utilized the reconstruction characteristics of holograms recorded with orthogonal polarization light to store holographic data that involved multi-dimensional modulation of amplitude, phase, and polarization. Our experimental result demonstrates a remarkable contrast extinction ratio of 71:1 for the two holograms operating on orthogonal polarization channels. Upon decoding the recorded multidimensional holograms, both exhibited amplitude and phase BERs of less than 0.5%, with the polarization state undergoing the corresponding orthogonal extinction. Remarkably, our study is the first to efficiently perform multiplexing and crosstalk-free switching of three-dimensional information in a coded data page format during experimentation, leveraging holographic techniques to manipulate orthogonally polarized light. This groundbreaking advancement facilitates novel avenues for the applications of orthotropic polarization holography in multi-dimensional data storage and retrieval systems.