Optical polarized orthogonal matrix

Abstract Orthogonal matrices have become indispensable tools in various fields, including coding, signal processing, and light field regulation. Traditionally, it has been assumed that orthogonal matrices consist of one-dimensional elements capable of modulating only amplitude or phase information. However, light waves have another critical dimension-polarization. Existing polarization orthogonal combinations have faced limitations, with a maximum pairwise orthogonal combination of 2 mapped to the basic Poincaré Sphere, hindering the regulation of polarization. Despite these challenges, we demonstrate the feasibility of constructing Optical Polarized Orthogonal Matrices (OPOMs) without restricted orthogonal numbers. This non-square matrix composed of polarization unit vectors, shows promise for multi-channel information retrieval and dynamic image display. The versatility of OPOM can be extended to various fields such as optical communication, optical storage, logic devices, anti-counterfeiting, and optical encryption.