# Multiplexing Perfect Optical Vortex for Holographic Data Storage
## 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, [PERSON] 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, [PERSON] 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. [PERSON] 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 \(\ell\) 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 \(\ell\) 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].