A new publication from Opto-Electronic Advances; DOI 10.29026/oea.2024.230180, discusses orthogonal matrix of polarization combinations: concept and application to multichannel holographic recording.

Orthogonal matrices are a fundamental mathematical concept with widespread applications in various scientific and engineering fields. Formed by rows and columns, an orthogonal matrix is a square matrix where the rows and columns consist of mutually orthogonal unit vectors. These vectors are normalized to a size of 1 and are mutually perpendicular. Common types of orthogonal matrices include rotation matrices and Hadamard matrices. Orthogonal matrices serve as powerful tools with unique properties, making them indispensable in a variety of applications. Representing rigid transformations, they possess the ability to maintain important properties during operations, rendering them valuable in diverse mathematical and computational contexts.

While existing orthogonal matrices are applicable to modulating the amplitude or phase degrees of freedom, they fall short when it comes to modulating polarization. This limitation hinders the application of orthogonal matrices in the polarization modulation dimension to some extent. Therefore, there is an urgent need for a new type of orthogonal matrix specifically designed for polarization combinations. This matrix should extend the control over the degrees of freedom of orthogonal matrices and offer a fresh perspective for applications in polarization modulation.

Multiplexing techniques offer an ideal approach to enhance the vast information storage capacity of holographic technology, encompassing angle, shift, orbital angular momentum, and polarization multiplexing. Among these multiplexing techniques, polarization multiplexing stands out as an attractive method due to its ability to selectively reconstruct holograms based on polarization, effectively retaining storage information for each polarization. In the realm of polarization holography, the characteristics of r reconstruction play a crucial role in achieving polarization multiplexing. However, traditional polarization multiplexing methods are limited to supporting two orthogonal states for signal light or recording reference light. Despite the introduction of four-channel holographic multiplexing, additional orthogonal state separation of the reconstruction light is still required within two orthogonal channels to facilitate the reconstruction of four holograms. It is noteworthy that the four holograms generated using this method cannot be distinguished solely based on the illumination of the reference light. Therefore, proposing a matrix not constrained by the number of orthogonal polarizations can significantly enhance the capabilities of polarization multiplexing in polarization holography.

Addressing the aforementioned issue, a collaborative effort between Prof. Xiaodi Tan's group from Fujian Normal University, China, and Prof. Takanori Nomura's group from Wakayama University, Japan, has proposed a comprehensive method for constructing multidimensional non-square matrix-type Orthogonal Matrix of Polarization Combinations (OMPC). By transforming from a three-dimensional coordinate system to an orthogonal polarization basis coordinate system, this method provides a compilation of polarization combinations that adhere to orthogonal relationships in different coordinate systems. The dimensionality of polarization combinations satisfying orthogonal relationships is significantly enhanced through the infinite expansion of polarization elements.

To demonstrate the advantages and effectiveness of the proposed OMPC, the research introduces an experiment using OMPC_2×4 (a four-dimensional OMPC with mutually orthogonal dual-component polarization combinations). OMPC is capable of recording and reconstructing multiple polarized holograms at a single location either individually or simultaneously. During the recording process, various polarization combination vectors from OMPC serve as the reference light for the polarization channels, enabling the polarization interference system to record multiple holograms carrying different information. Under the conditions satisfying the Bragg condition, during the reconstruction process, illuminating the hologram with a beam containing different polarization combination vectors in the polarization channels allows the individual or simultaneous reconstruction of the information stored in the hologram.

To validate the feasibility of the proposed method, a four-channel experiment using OMPC_2×4 was conducted, followed by a comprehensive analysis. The results indicate that the method exhibits robustness and effectiveness when applied to phenanthrenequinone-doped polymethyl methacrylate (PQ/PMMA) materials. Only the reference light adhering to the OMPC_2×4 conditions can achieve autonomous and high-contrast reconstruction of stored information. Deviation from this standard would result in concurrent reconstruction of multiple data items. Therefore, this method ensures the security of information storage. The approach demonstrates promising potential in significantly improving the multiplexing capability of multi-channel holograms.

The proposed OMPC introduces new ideas, tools, and means for polarization modulation, enabling the enhancement of holographic storage capacity through polarization modulation strategies. This advancement broadens the application scope of polarization holography, particularly in the fields of optical storage and information security. Therefore, this efficient and scalable method presents a novel and unprecedented opportunity for the multiplexing of multiple polarization-selective holograms using polarization-sensitive materials. The research results provide a basis for speculation, suggesting that with an increase in the dimensionality of OMPC, it becomes possible to record and reconstruct multiple images at a single location within the material using reference light with more polarization modulation components. Combining this method with multi-dimensional modulation of signal light (phase and amplitude) will significantly elevate the storage density of optical information.

Keywords: orthogonal matrix of polarization combinations / polarization-modulated multiplexing / multichannel recording / polarization holography / dynamical information modulation
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Xiaodi Tan, a professor of Fujian Normal University, is a Fellow of the International Society for Optics and Photonics (SPIE) and a Fellow of the Optical Society of America (OPTICA). He serves as a director of The Chinese Optical Society and the Chinese Society for Optical Engineering. His research focuses on collinear holographic data storage technology, polarization holography theory and applications, high-performance holographic recording materials, and information display technology and applications. Prof. Tan has published over 300 papers, delivered more than 70 invited presentations at international conferences, co-authored 2 books, and holds more than 30 granted patents. He has received Gold Medal of the 48^th International Exhibition of Inventions of Geneva, the Third Prize of National Scientific and Technological Progress Award and one SONY R&D Headquarters Department Chief Award. Currently, he is presiding over a National Key Research and Development Program of China and a Key Projects of the Regional Cooperation Fund of the National Natural Science Foundation of China. Professor Tan has presided over a project fund of the National Natural Science Foundation, 3 projects under the 863 Program, and several other horizontal projects. The "Information Photonics Research Center" was established in the summer of 2018, formerly known as the "Information Optics Research Lab" (established in September 2012 at Beijing Institute of Technology). Its mission is to achieve the spatiotemporal transformation of information using photonic methods. The team currently comprises 12 staff members, 11 Ph.D. students, and 32 master's students.
Official website of the Information Photonics Research Center: http://www.iprc.ac.cn/
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Zheng SJ, Tan JR, Liu HJ et al. Orthogonal matrix of polarization combinations: concept and application to multichannel holographic recording. Opto-Electron Adv 7, 230180 (2024). doi: 10.29026/oea.2024.230180