Orbital angular momentum multiplexing three-dimensionalencrypted hologram
Authors: FANG Guoquan , LIN Han , WANG Siyue , PENG Pu , FANG Zheyu ,   School of Physics, State Key Lab for Mesoscopic Physics, Peking University, Beijing100871, China
Published: February 2025

<sec>After decades of development, holography has evolved into a sophisticated optical technology for information display. Traditional holographic techniques, which rely solely on the wavelength and polarization of light as information carriers, are limited in both security and capacity of information. The introduction of orbital angular momentum (OAM) as an additional optical dimension into holography effectively addresses these challenges. In order to maintain the OAM mode characteristics of the original image, spatial discrete sampling must be performed first. The sampled image undergoes Fourier transform to generate a discrete hologram. An OAM-selective hologram is then constructed by multiplying the discrete hologram with a spiral phase factor. By superimposing multiple selective holograms with varying topological charges, an OAM-multiplexing hologram is generated.</sec><sec>Using this approach, computer simulations of OAM-based holography demonstrate the encryption of multiple two-dimensional images with different topological charges (<inline-formula><tex-math id="M1">\begin{document}$ {l}_{i} $\end{document}</tex-math></inline-formula>) into an OAM-multiplexing hologram for storage. Decryption is achieved by illuminating the multiplexing hologram with a reproduction beam of a specific topological charge. When the condition (<inline-formula><tex-math id="M2">\begin{document}$ l'_{i}+{l}_{i}= 0 $\end{document}</tex-math></inline-formula>) is satisfied, the original image associated with the corresponding topological charge is successfully reproduced.</sec><sec>Furthermore, a three-dimensional object, such as a rose in the article, can be decomposed into multiple two-dimensional planes by using a layering method. Holograms for each layer are generated based on their spatial positions and a custom function <inline-formula><tex-math id="M3">\begin{document}$ f $\end{document}</tex-math></inline-formula> that assigns topological charges (<inline-formula><tex-math id="M4">\begin{document}$ {l}_{j} $\end{document}</tex-math></inline-formula>). These holograms are stored in a phase array through OAM-multiplexing holography, effectively reducing the dimensionality of information storage. By setting different reproduction charges (<inline-formula><tex-math id="M5">\begin{document}$ l'_{j} $\end{document}</tex-math></inline-formula>), the holograms are successfully reconstructed.The spatial position of each layer is determined by the function <inline-formula><tex-math id="M6">\begin{document}$ f $\end{document}</tex-math></inline-formula>, enabling the replicating and stacking of layers to achieve a three-dimensional reconstruction of the rose, including its petals, from different perspectives. This process realizes three-dimensional holography. Notably, the combination of topological charge and the function <inline-formula><tex-math id="M7">\begin{document}$ f $\end{document}</tex-math></inline-formula>servesacts as a cryptographic key, significantly enhancing the security of information transmission. This OAM-selective holography technology not only improves security, but also achieves higher information throughput, indicating its enormous potential in various applications.</sec>