Multiplexing technology, as a means to effectively enhance information storage and transmission capabilities, has always been of great interest. Traditional multiplexing techniques, such as angular multiplexing, positional multiplexing, orbital angular momentum multiplexing, and polarization multiplexing, hold significant importance in information storage and transmission. However, when exploring multiplexing technologies across various dimensions, the polarization dimension faces challenges due to the limitations of its finite orthogonal combinations. Given that only two mutually orthogonal polarization states can be identified on the basic Poincaré sphere, this undoubtedly poses a significant obstacle to polarization modulation. To overcome this challenge, Professor Xiaodi Tan's team from Fujian Normal University has proposed a construction method for an Optical Polarized Orthogonal Matrix (OPOM), which successfully breaks through the limitation on the number of orthogonal combinations. Additionally, the team experimentally verified the application effect of this method in high-dimensional multiplexing for polarization holography. Relevant research results were recently published in Photonics Research, Volume 13, Issue 2, 2025. [Shujun Zheng, Jiaren Tan, Xianmiao Xu, Hongjie Liu, Yi Yang, Xiao Lin, Xiaodi Tan, "Optical polarized orthogonal matrix," Photonics Res. 13, 373 (2025)]
The OPOM constructed by the research team is a non-square matrix composed of polarization unit vectors, capable of achieving arbitrary numbers of orthogonal polarization combinations, thereby breaking through the limitation on the number of orthogonal combinations in traditional polarization multiplexing. By combining Jones vectors with Hadamard matrices, the team constructed minimum-order and higher-order OPOMs, significantly improving the multiplexing capacity and stability of the system. Prior to constructing any OPOM, the team first derived the minimum OPOM, namely OPOM2×4. As shown in Figure 1, when constructing the basic OPOM2×4 expansion layer, OPOM2×4 was used as the minimum unit, and the expansion layer was generated by replicating rectangles with a side length of m. Simultaneously, a Hadamard layer was constructed, which was formed by arranging the elements of the Hadamard matrix. The element modules in the Hadamard layer correspond one-to-one with and are multiplied by the elements in the basic OPOM2×4 expansion layer, thereby generating any 2m×4m OPOM.
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Figure 1 Construction of OPOM
Polarization holography technology is capable of simultaneously recording amplitude, phase, and polarization information, aiming to achieve the recording and selective reconstruction of polarization multi-channels. Leveraging the orthogonal null-reconstruction characteristic of polarization holography at a 90-degree interference angle, eight sets of column vectors of OPOM4×8 were used as polarization keys to sequentially record eight holograms. The research results showed that although the holograms shared the same polarization state, due to the orthogonal selectivity among the information, multiple images could still be independently manipulated within different polarization channels through orthogonal polarization combinations. By selecting the required combinations of input polarization states, the reconstructed images could be switched with almost no crosstalk. The research team successfully achieved the retrieval of multi-channel digital information (Figure 2) and the dynamic display of images (Figure 3) using OPOM4×8.
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Figure 2 Experimental results of digital information retrieval using OPOM4×8
Figure 3 Experimental results of image dynamic display using OPOM4×8
Professor Xiaodi Tan commented that, "The introduction of the OPOM concept is not only innovative but also opens up new possibilities for multi-channel broadcasting applications such as optical communication, multi-dimensional optical storage, optical logic devices, anti-counterfeiting, and ultra-high-security optical encryption. This work makes a significant contribution to the field of orthogonal matrices and is expected to drive further research and development in these areas."
