Multiplexing Perfect Optical Vortex for Holographic Data Storage

Abstract

Holographic data storage (HDS) has emerged as a promising technology for high-capacity data storage. In this study, we propose a novel approach to enhance the storage density in HDS through a multiplexing perfect optical vortex (POV) hologram. By utilizing the orthogonality property of POV, different POV-recording holograms can be multiplexed to store multiple data pages within the single hologram. Compared with the conventional optical vortex, the better storage density of POV through proof-of-principle experiments is demonstrated. For the POV-multiplexing hologram of six data pages, each one can be reconstructed successfully. In addition, we investigate the impact of axicon periods and multiplexing numbers on the storage performance. Our results reveal that an appropriate selection of axicon periods and multiplexing numbers is crucial to balance storage density and bit error rate (BER). The proposed multiplexing approach offers a valuable solution for achieving high-density and secure holographic data storage systems.

1. Introduction

Holographic data storage (HDS) is a highly promising optical storage technology that represents the next generation of data storage solutions. It offers significant advantages such as large storage capacity, high-speed data transfer rates, and extended data lifetime compared to traditional storage technologies [1,2]. Holography harnesses the distinct characteristics of light, including its capacity to encode and carry information through various orthogonal physical dimensions such as amplitude, phase, and polarization. This unique property enables holography to store immense volumes of data within a single hologram. By leveraging these multiple dimensions, holographic data storage achieves high data density and the efficient utilization of storage resources [3,4,5]. In 2019, Bunsen et al. [3] focused on the transport of intensity equation method to detect the phase distribution of light waves quantitatively without using interferometry, contributing to the miniaturization of the optical system and the improvement in the vibration tolerance of HDS. In 2022, Hao et al. [4] proposed a phase retrieval combined with the deep learning denoising method in holographic data storage. By training a deep learning convolutional neural network, we can establish a strong understanding of the intricate noise patterns present in the captured intensity images. This is achieved by analyzing the relationship between these images and the corresponding simulation truth images. Hong et al. [5] introduced a compact system that utilizes a single phase-only liquid crystal on a silicon spatial light modulator for efficient phase and polarization modulation. This system enables simultaneous control over the holographic image and its polarization state, offering a streamlined approach to manipulating light properties in holography.

Optical vortices (OV) beams are captivating phenomena in the realm of optics, showcasing remarkable and distinct characteristics that have garnered significant attention in recent years. These beams possess an azimuthal phase dependence described by the mathematical expression $e^{i\ell \theta }$, where ℓ represents the topological charge (TC) and $\theta$ denotes the azimuthal angle [6]. The defining feature of optical vortices is the presence of a phase singularity, often referred to as a “twist”, within the spatial distribution of the optical wavefront. This twist engenders a helical phase structure, leading to the formation of a fascinating spiral-shaped intensity pattern. What makes optical vortices particularly intriguing is their capacity to exhibit an infinite number of orthogonal states, known as orbital angular momentum (OAM) modes. Each mode corresponds to a specific topological charge, which determines the number of complete twists along the beam’s propagation axis. The OAM modes carried by optical vortices possess angular momentum and can be envisioned as “corkscrew” beams with a well-defined helical wavefront. These beams possess a unique and intricate spatial phase profile that distinguishes them from conventional light waves. The topological charge ℓ serves as a parameter that characterizes the OAM mode, enabling the generation of different types of optical vortices with varying twist configurations.

In recent years, the utilization of optical vortices (OV) has gained significant attention as a new degree of freedom with infinite orthogonal states, propelling advancements in optical communication [7,8], optical sensors [9,10,11], and holographic data storage [12,13,14,15,16], etc. OV holography has demonstrated its capability to achieve remarkably high multiplexing density, presenting a promising approach to directly stpre data. The topological charge of an optical vortex, which determines the number of twists in its phase distribution, can be used as a label for data pages [12]. By assigning different topological charges to individual data pages, multiple pages can be stored within a single hologram, effectively increasing the storage density [13,14]. Furthermore, the orthogonality of OAM modes allows for selectively addressing and retrieving specific data pages [15,16]. By using reading beams with matching OAM modes, the desired data page can be reconstructed, while other pages remain undisturbed. This selective nature of optical vortices enhances the security and confidentiality of holographic data storage. In addition to increased storage capacity and improved security, optical vortices also offer advantages in terms of data transfer rates and system simplicity. The use of optical vortices enables parallel readout and parallel processing, allowing for faster data access compared to traditional serial readout methods. Moreover, the compact nature of optical-vortex-based holographic systems simplifies the optical setup and reduces the complexity of the storage architecture.

When the waist of the fundamental mode beam is fixed, the beam size (cross-sectional spot diameter) of the OV is dependent on the topological charge (ℓ) [17], which, naturally, affects the capacity of the holographic data storage. A larger absolute value of the topological charge corresponds to a larger spot diameter and a larger hollow region [18]. Hence, the utilization of OV holography for high multiplexing density encounters a fundamental sampling criterion that poses a challenge [19,20]. In order to mitigate strong multiplexing crosstalk, it is essential to adhere to the requirement that the sampling distance should not be less than the diameter of the largest addressable OV mode. Unfortunately, this criterion presents a significant hurdle in enhancing the resolution and capacity of OV holography. The potential of perfect optical vortex (POV) to address this challenge has received comparatively less attention. Unlike conventional optical vortices, the cross-sectional spot diameter of a perfect optical vortex (POV) remains constant regardless of its topological charge [21,22]. In traditional optical vortices, the spot diameter increases as the topological charge increases, leading to larger beam sizes and reduced spatial resolution. However, in the case of POV beams, the spot diameter remains unchanged regardless of the value of the topological charge. This unique property of POV beams is advantageous for applications where a consistent beam size is required in holographic data storage.

In this paper, we propose a multiplexing perfect optical vortex (POV) for holographic data storage. In this method, the robust selectivity of POV holography, characterized by the topological charge (ℓ), is considered as a distinctive label for each data page. In this approach, not only the spatial positions of the points within the data page but also their corresponding intensity levels serve as information carriers for data storage. Subsequently, the data page is reconstructed by illuminating the POV-recording hologram with a specialized POV beam possessing the opposite topological charge ( −ℓ), commonly referred to as the reading beam. By employing this reading beam, the data encoded within the hologram can be retrieved. The information can be read out by implementing distinct different intensity thresholds. To further enhance the storage capacity, a multiplexing technique is employed, whereby various POV-recording holograms are combined. This process involves coding different data pages into a POV-multiplexing hologram utilizing different topological charges. Moreover, the shorter sampling distance in the single data page is used to improve the storage density. The higher density and the multiplexing data pages are demonstrated in a proof-of-principle experiment to show the feasibility of the proposed method.

Compared to our previous approach [12], the proposed new method offers two main advantages. Firstly, the storage density is improved. The use of POV beams in data storage enables a higher storage density by designing more storage cells within the same storage area. This advancement contributes to the improvement in data capacity and efficiency, making it a valuable solution for modern data storage requirements. Secondly, the storage error is decreased. The utilization of POV beams in data storage results in a decrease in storage errors and crosstalk among POVs within a data page. This contributes to improved data integrity, accuracy, and reliability in holographic data storage systems.

2. Materials and Methods

The scheme of the proposed method is illustrated in Figure 1, where Figure 1a–c show the recording process, the multiplexing process, and the reconstructed process, respectively.

In the recording process (Figure 1a), the original data are a binary sequence, which can be mapped into four gray levels. In the Figure 1a, the original data are converted into adata page, which means that the single cell in the data page represents 2-bit binary data. To achieve the kth point-data page, the kth data page is multiplied by the sampling array, resulting in a representation known as

$$f_k(x,y)=D_k(x,y)\times \delta (x,y),$$

(1)

where $(x,y)$ represents the Cartesian coordinates, and $f_k(x,y)$, $D_k(x,y)$, and $\delta (x,y)$ represent the kth point-data page, the kth data page, and the sampling array, respectively. The sampling array can be described as

$$\delta (x,y)=\left\{\begin{array}{c}1x=x_p;y=y_q\hfill \\ 0x\ne x_p;y\ne y_q\hfill \end{array}\right.,$$

(2)

where $(x_p,y_q)$ represents the sampling point position with the sampling distance d ($x_p-x_{p-1}=d;y_q-y_{q-1}=d$). $(p,q)$ represents the rows and columns of the cell in data page. Hence, the kth point-data page ($f_k(x,y)$) can be expressed as

$$\begin{array}{cc}\hfill & f_k(x,y)=\sum _{\begin{array}{c}1\le p\le P\\ 1\le q\le Q\end{array}}{I}_{p,q}\delta (x-x_p,y-y_q)\hfill \\ \hfill & I_{p,q}=\left[I_1{I}_2{I}_3{I}_4\right],\hfill \end{array}$$

(3)

where $I_{p,q}$ represents the different intensity levels and $(P,Q)$ represents the total rows and columns of the point in the point-data page. The kth point-data page ($f_k(x,y)$) is discretely Fourier transformed into the computer-generated hologram (CGH, $F_k(u,v)$), which can be described as

$$\begin{array}{ccc}\hfill F_k(u,v)& =\hfill & \hfill \sum _{x=1}^M\sum _{y=1}^N{f}_k(x,y)exp\left[i(xu+yv)\right],\end{array}$$

(4)

where $(u,v)$ represents the orthogonal coordinates in the hologram. M and N are the boundary of the point-data page. In our experiment, for higher accuracy, the GSW algorithm [23] is used to implement the discrete Fourier transform. Then, to achieve the kth POV-recording hologram ($H_k(u,v)$), the kth CGH is multiplied by the optical vortex phase and axicon phase, which can be described as

$$H_k(u,v)=F_k(u,v)exp\left(i{\ell }_k\phi \right)exp\left(i\beta \left(d_{POV}\right)\right),$$

(5)

where ℓ_k is the topological charge of kth data page, which can achieve the OV selectivity. $\beta \left(k_r\right)$ represents the axicon phase, which can realize the perfect optical vortex [24]. The axicon phase can be described as

$$\beta \left(d_{POV}\right)=\frac{2\pi r}{d_{POV}},$$

(6)

where $d_{POV}$ and r are the axicon period and the radial coordinate, respectively. By inverse Fourier transform (IFT), the the kth POV-recording hologram ($H_k(u,v)$) can be transformed into the POV array ($h_k(x,y)$), and each POV carries a different intensity level, which can be described in Appendix A. The diameter of the single POV ($r_{POV}$) in the POV array is independent of its topological charge, and the minimum sampling distance of POV can be described as

$$d_{min}=MIN\left(r_{POV}\right)=\frac{\lambda f}{MAX\left(d_{POV}\right)},$$

(7)

where $MAX(·)$ and $MIN(·)$ represent the maximum and minimum values. $\lambda$ and f are the wavelength and the focal length of a spherical lens, respectively. On the other hand, the diameter of an OV ($r_{OV}$) is related to ℓ, and the minimum sampling distance of OV can be described as

$$d_{min}=MIN\left(r_{OV}\right)=2\sqrt{|{\ell }_{MAX}|+1}{\omega }_0,$$

(8)

where ${\omega }_0$ corresponds to the waist of the fundamental Gaussian beam. Hence, in the same storage space, the storage density of POV is better than that of OV. For instance, when considering the case of $\ell =10$ and $(p=1,q=2)$, the comparison between perfect optical vortex (POV) and optical vortex (OV) is illustrated in Figure 2. The results are obtained under the same conditions ($d=170$ pixels, $\lambda =632.8$ nm, ${\omega }_0=5$$\mathsf{\mu }$m, and $d_{POV}=0.36$).

In the multiplexing process (Figure 1b), the orthogonality of POV provides valuable selectivity to enhance the storage capacity through the multiplexing of the POV-recording holograms. The topological charge (ℓ) is considered a distinctive label for the POV-recording hologram. The multiple POV-recording holograms are superimposed to create a POV-multiplexing hologram, which can be described as

$$\begin{array}{c}\hfill H_{MUX}(u,v)=\sum _{k=1}^K{F}_k(u,v)exp\left(i{\ell }_k\phi \right)exp\left(i\beta \left(d_{POV}\right)\right),\end{array}$$

(9)

where K is the total multiplexing number. The POV-multiplexing hologram can be imprinted and recorded by a spatial light modulator (SLM) in our experiment. Some other storage media (such as Metasurface [25,26], Diffractive optical element (DOE) [27,28], etc.) can be used to record the POV-multiplexing hologram.

In the reconstruction process (Figure 1c), upon illuminating the POV-multiplexing hologram with the POV reading beam, characterized by an inverse topological charge ($-{\ell }_k$) and the axicon phase ($-\beta \left(d_{POV}\right)$), the POV undergoes a conversion to Gaussian mode. As a result of this conversion, the kth point-data page can be successfully retrieved, yielding an output represented as

$$\begin{array}{ccc}\hfill H_{MUX}(u,v)·\left[exp(-i{l}_k\phi )exp(-i\beta \left(d_{POV}\right))\right]& =& F_1(u,v)exp\left[i(l_1-l_k)\phi \right]\hfill \\ & & ⋮\hfill \\ & +& F_k(u,v)exp\left(i0\phi \right)\hfill \\ & & ⋮\hfill \\ & +& F_K(u,v)exp\left[i(l_K-l_k)\phi \right].\hfill \end{array}$$

(10)

From Equation (10), the kth point-data page is retrieved in Gaussian mode, and the remaining point-data pages maintain their original OV mode. This observation validates the preservation of the OV mode in the majority of the retrieved data. The acquired results reveal a distinct pattern in the reconstructed data: the kth point-data page exhibits a solid-spot structure with varying intensity levels, while the other point-data pages retain their characteristic “doughnut” shape. This distinction enables the implementation of a mode-selective aperture array, denoted ${\delta }^{{}^{\prime }}(x,y)$, to effectively obtain the Gaussian modes. After passing through the Fourier lens and the mode-selective aperture array, the kth reconstructed point-data page ($f_k^{{}^{\prime }}(x,y)$) can be obtained, that is,

$$f_k^{{}^{\prime }}(x,y)=IFT\left\{H_{MUX}(u,v)·\left[exp(-i{l}_k\phi )exp(-i\beta \left(d_{POV}\right))\right]\right\}·{\delta }^{{}^{\prime }}(x,y),$$

(11)

where $IFT\left\{·\right\}$ represents the inverse Fourier transform. In the decoding process, different intensity thresholds ($T_1$,$T_2$, and $T_3$) are set to recover 2-bit binary data. If the POV reading beam with $\ell =0$ or an unmatched topological charge is used, no data can be obtained. This observation also highlights the inherent confidentiality of the proposed method. Hence, the matched POV reading beam can retrieve corresponding data and the unmatched POV reading beam can obtain null.

3. Results

3.1. Optical Setup

In order to validate the efficacy of the proposed holographic data storage method, a proof-of-principle experiment was conducted. The optical setup for the reconstructed process is illustrated in Figure 3.

In our experimental setup, the wavelength of the laser was 632.8nm and its intensity could be changed with a variable neutral density filter (NDF). A halfwave plate (HWP) was used to adjust the polarized direction of the beam to match the spatial light modulator (SLM, Holoeye PLUTO-2). The process is as follows. As the laser beam traverses through the beam splitter (BS1), it is directed towards SLM1. At SLM1, a single perfect optical vortex (POV) hologram is imprinted with an inverse topological charge of ${\ell }_{\mathrm{reading}}=-5$ and the axicon period of $d_{\mathrm{POV}}=-0.8$ mm. The beam reflected from SLM1 serves as the POV reading beam and is further reflected towards SLM2 by the beam splitter (BS2). The SLM2, which is responsible for imprinting the POV-multiplexing hologram, consists of a grid of $9\times 9$ cells ($p=q=9$) in each point-data page. It is illuminated by the POV reading beam. The reflected beam from SLM2 carries the information of the kth data page. To obtain the reconstructed image, the reflected beam undergoes Fourier transformation using a Fourier lens with a wavelength of 150 mm. The resulting reconstructed image is captured using a charge-coupled device (CCD) as depicted in Figure 4. The pixel size of CCD is 6.45 $\mathsf{\mu }$m × 6.45 $\mathsf{\mu }$m.

3.2. Experimental Reconstructed Process in Holographic Data Storage

To validate the selectivity of the POV and assess the confidentiality of the data storage method, the correctly matched reading beam and a mismatched reading beam were employed to retrieve the stored information. The results of these two scenarios are depicted in Figure 4. When the matched reading beam with a topological charge of $\ell =-5$ illuminates the POV-multiplexing hologram, the reconstructed image is captured by the CCD. As seen in Figure 4, the reconstructed image exhibits multiple Gaussian points and some useless optical spots. To mitigate the useless optical spots, a mode-selective aperture array is used to effectively eliminate the optical spots and filter out the Gaussian points present in the reconstructed image. Subsequently, each point in the reconstructed point-data page is transformed into a 2-bit data representation by utilizing different intensity thresholds. Specifically, the intensity thresholds were set as $T_1=25$, $T_2=120$, and $T_3=200$. The determination of these thresholds is based on the gray-scale values ($T_1,T_2,$ and $T_3$) of the data page. The intensity levels of the reconstructed point-data page are represented by $I_1^2,I_2^2,I_3^2,$ and $I_4^2$. Therefore, the relationship between the threshold values and intensity levels can be expressed as $I_1^2<T_1<I_2^2<T_2<I_3^2<T_3<I_4^2$. It should be noted that the specific values of the thresholds can be adjusted and fixed based on prior experiments. Once determined, these threshold values remain unchanged throughout the experiment. Lastly, by comparing the intensity levels of each point with these thresholds, the data are decoded simultaneously, enabling efficient data storage and retrieval. For example, the first row of the reconstructed point-data page is magnified, and the intensity of the red line is extracted. Based on the extracted results, it is evident that the four intensity levels exhibit distinct differences, making them easily distinguishable.

However, in our proposed approach, we employed a mismatched reading beam with a topological charge of $\ell =0$ to retrieve the stored information. As depicted in Figure 4, the reconstructed image shows the presence of optical spots, while the Gaussian points are notably absent. Moreover, when attempting to extract the intensity of the first row, no discernible information can be obtained. This intriguing observation highlights the selectivity and secrecy of the proposed method based on perfect optical vortices (POV). The absence of Gaussian points in the reconstructed image suggests that the stored information is effectively encoded and protected within the holographic data. The utilization of a mismatched reading beam with a topological charge different from that of the stored data pages ensures that only the intended information can be accessed and deciphered. This enhances the security of the holographic data storage system, making it less vulnerable to unauthorized access or data leakage.

Based on the proof-of-principle experiments conducted, our approach achieves a high level of selectivity in retrieving the stored information. Only when the reading beam precisely matches the topological charge of the stored data pages can the desired information be successfully reconstructed. This selectivity adds an additional layer of security to the system, making it challenging for unauthorized users to access or interpret the stored data. Our proposed approach based on perfect optical vortices (POV) offers enhanced selectivity and secrecy in holographic data storage. The utilization of a mismatched reading beam and the absence of Gaussian points in the reconstructed image attest to the effectiveness of our method in protecting and safeguarding the stored information. This contributes to the development of more secure and reliable data storage systems, ensuring the privacy and confidentiality of sensitive data.

3.3. Experimental Multiplexing Process in Holographic Data Storage

To further demonstrate the effectiveness of multiplexing, six different data pages were stored within the single POV-multiplexing hologram. These data pages correspond to topological charges of 5, 10, 15, −5, −10, and −15. Then, the POV-multiplexing hologram was illuminated by the corresponding inverse POV beams with ${\ell }_{\mathrm{reading}}$ = −5, −10, −15, 5, 10, and 15, and the resulting reconstructed images were captured using CCD. These reconstructed images are presented in Figure 5.

In Figure 5, the six point-data pages can be accurately reconstructed from the POV-multiplexing hologram by utilizing the corresponding POV reading beam. The reconstructed images showcase well-preserved POV intensity characteristics at each data point, indicating the successful retrieval of the stored information. It is important to note that each point in the point-data page has the capacity to store 2 bits of information. With a data page size of $(9\times 9)$ cells, the total storage capacity per data page amounts to $(9\times 9\times 2)$ bits. Therefore, a single data page can store a significant amount of data. In the case of the POV-multiplexing hologram, which incorporates six data pages, the total storage capacity is greatly increased. Each data page contributes $(9\times 9\times 2)$ bits, so the overall storage capacity reaches $(162\times 6)$ bits. This demonstrates a substantial enhancement in storage capacity achieved through the multiplexing of data using POV beams. Overall, the successful reconstruction of the six point-data pages and the significant increase in storage capacity validate the effectiveness of the POV-multiplexing hologram approach for high-density holographic data storage applications.

4. Discussion

To quantitatively assess the quality of data page reconstruction, the bit error rate (BER) is employed as a metric. The BER is calculated by dividing the number of erroneous symbols by the total number of symbols, providing a measure of the accuracy of the reconstructed data, that is,

$$\mathrm{BER}=\frac{{\sum }_{i=1}^K{E}_i}{{\sum }_{i=1}^K{M}_i},$$

(12)

where $E_i$ is the number of error bits in one point-data page, and $M_i$ is the total number of recorded bits in one point-data page.

4.1. Effect of Axicon Periods on Reconstructed Data Quality and BER

The impact of varying the axicon periods ($d_{POV}$) on the quality of the reconstructed data is illustrated in Figure 6; Figure 6a shows the POV of array the image with different axicon periods ($d_{POV}$). Figure 6b shows the BER with different axicon periods ($d_{POV}$). Figure 6c shows the minimum sampling distance ($d_{min}$) of OV and POV, respectively. As seen in Figure 6a, when the wavelength and the focal length of the lens are fixed, there exists an inverse relationship between the diameter of the POVs and the axicon period ($d_{POV}$). In other words, the storage density can be increased by increasing the axicon periods. However, increasing the axicon periods leads to an increase in crosstalk among POVs, resulting in a weakening of the properties of the POVs and, consequently, an increase in BER. As depicted in Figure 6b, the reconstructed data are found to be error-free when $d_{POV}$ is set to 0.2 and 0.4. However, as $d_{POV}$ increases, the BER of the reconstructed data exhibits an increasing trend. Therefore, in the experiment, the selection of axicon periods needs to strike a balance between storage density and BER.

From the analysis of Figure 6c, it can be observed that the minimum sampling distance ($d_{\min }$) of the optical vortex (OV) increases with the topological charge (ℓ). In contrast, the minimum sampling distance of the perfect optical vortex (POV) remains independent of its topological charge. For topological charges lower than 8, OV exhibits a better minimum sampling distance compared to POV. However, when the topological charge exceeds 8, POV outperforms OV in terms of the minimum sampling distance, showcasing the advantages of POV. In simpler terms, when using larger topological charges, the advantage of the storage density offered by POV becomes more pronounced. This means that POV can achieve a higher storage density compared to OV when employing larger topological charges.

4.2. Effect of Multiplexing Number on BER

Figure 7a demonstrates the influence of varying the multiplexing number (K) on the quality of the reconstructed data. As the multiplexing number increases, there is a slight enhancement in the quality of the reconstructed data when utilizing perfect optical vortex (POV) compared to conventional optical vortex (OV). However, it should be noted that both POV and OV are subject to the effects of the multiplexing number.

Furthermore, the relationship between the multiplexing number and storage capacity is investigated. An experiment was conducted under the same experimental conditions, and the receiving area of the CCD camera remained constant. Figure 7b presents the results of this experiment, illustrating the relationship between the multiplexing number and the storage capacity of both conventional OV and POV methods. At the initial stage of the experiment, with a small multiplexing number, OV has an advantage in terms of storage capacity. This is because OV can utilize smaller topological charges to encode data, allowing for a higher density of data storage. However, as the multiplexing number increases, the storage capacity of OV reaches its limit, requiring the use of larger topological charges to maintain the data density. On the other hand, POV demonstrates its advantage in increasing storage capacity as the multiplexing number increases. With the ability to efficiently use topological charges, POV can store more data within the same storage area compared to OV. For instance, when the multiplexing number is set to 14 ($K=14$), the storage capacity of OV is 480 bits, while the storage capacity of POV is 780 bits. This demonstrates that POV achieves a significant increase of up to $50\%$ compared to OV in terms of storage capacity. This significant improvement implies that employing POV in multiplexing holographic data storage enables a larger number of data pages to be stored within a given storage area. As a result, the utilization of POV offers the potential to enhance storage capacity and efficiency, offering a more compact and efficient solution for data storage.

5. Conclusions

In conclusion, we have presented a novel approach for holographic data storage using the multiplexing of perfect optical vortex (POV). In our proposed method, the topological charge (ℓ) of the POV serves as the label for different point-data pages, while the intensity levels of individual points within the data pages are utilized for data storage.

Through our proof-of-principle experiments, we have demonstrated the successful reconstruction of point-data pages from the POV-multiplexing hologram when illuminated by the corresponding POV reading beam. The reconstructed images exhibit accurate representation of the stored data, and the information contained within can be easily extracted by setting appropriate intensity thresholds. One of the key advantages of our approach is the high storage density offered by POV. Compared to traditional optical vortex methods, POV enables the design of more storage cells within the same storage area. This results in improved storage capacity and allows for the storage of larger volumes of data in a single hologram. We have also conducted investigations into the impact of two important parameters, namely, axicon periods and multiplexing numbers, on the storage performance. The selection of these parameters plays a crucial role in achieving a balance between storage density and bit error rate (BER). By carefully optimizing these parameters, we can achieve the desired storage density while minimizing data retrieval errors. Furthermore, our proposed method offers enhanced data security in holographic data storage. The selective nature of the POV reading beam, which is specific to the helical mode indexes, enhances the security of stored data and prevents unauthorized access.

Our proposed multiplexing approach utilizing perfect optical vortex beams offers a valuable and practical solution for achieving high-density and secure holographic data storage systems. The increased storage density, coupled with the potential for improved data retrieval accuracy through parameter optimization, opens up new possibilities for advanced holographic data storage technologies. With further advancements and optimizations, the multiplexing of perfect optical vortex beams holds great promise for the development of next-generation holographic data storage systems.