Orthogonal matrix of polarization combinations: concept and application to multichannel holographic recording

Orthogonal matrices have become a vital means for coding and signal processing owing to their unique distributional properties. Although orthogonal matrices based on amplitude or phase combinations have been extensively explored, the orthogonal matrix of polarization combinations (OMPC) is a novel, relatively unexplored concept. Herein, we propose a method for constructing OMPCs of any dimension encompassing 4n (where n is 1, 2, 4, 8, ...) mutually orthogonal 2n- component polarization combinations. In the field of holography, the integration of polarization multiplexing techniques with polarization-sensitive materials is expected to emerge as a groundbreaking approach for multichannel hologram multiplexing, offering considerable enhancements in data storage capacity and security. A multidimensional OMPC enables the realization of multichannel multiplexing and dynamical modulation of information in polarization holographic recording. Despite consolidating all information into a single position within the material, we effectively avoided extraneous crosstalk during the reconstruction process. Our results show that achieving four distinct holographic images individually and simultaneously depends on the polarization combination represented by the incident wave. This discovery opens up a new avenue for achieving highly holographic information storage and dynamically displayed information, harnessing the potential of OMPC to expand the heretofore limited dimensionality of orthogonal polarization.