Fig. 1. Construction schematic of arbitrary orthogonal matrix of polarization combinations (OMPC). Within the x–y–z coordinate system, only two mutually orthogonal polarized lights, namely s- and p-polarized lights, are available. Using these two orthogonal polarized lights as the bases for a new coordinate system, we can identify four mutually orthogonal 2-dimensional polarization combinations, forming the fundamental OMPC of the smallest dimensionality. Leveraging OMPC_2×4 in conjunction with Hadamard matrices enables the generation of additional OMPCs with dimensionalities of 4n, where n is any power of 2.

Fig. 2. Reconstruction schematic of the designed 4-channel polarization holographic material. When the material is illuminated with incident reference waves modulated by a combination of two different polarizations, vector superposition of reconstructed wave units allows for the independent reconstruction of four holograms. (a–d) By selectively choosing the linear polarizations (LP) of incident reference waves, we can reconstruct holograms in specific polarization-combination channels while simultaneously concealing holograms in other channels. (e–f) Except for the special incident reference waves, the four stored images within the material can be simultaneously reconstructed under other incident reference waves, such as (s, s), (s, −s), (p, p), or (p, −p).

Fig. 3. Simulated results for the four-channel polarization multiplexing holograms illuminated by reference waves with different linear polarizations for reading. (a) The state of polarization (SOP) of the partial reference waves for reading is depicted under either p- or s-polarization in the first component as the polarization angle in the second component gradually increases from the initial polarization angle of s- or p-polarization, respectively. (b) and (c) The reference waves employed for reading in the four-channel polarization multiplexing holograms comprise a first component that is p-polarized (or s-polarized) as well as a second component that starts from s-polarized (or p-polarized) and increases in polarization angle. The total increase in polarization angle is 360 degrees.

Fig. 4. Experimental setup and specific preparation process for polarization holograms in the four-channel configurations. (a) Experimental setup for recording the multiplexing polarization holograms. (b) Recording conditions for 4-channel polarization holograms. Four exposure recordings were carried out consecutively; each exposure employed its respective polarization-combination channel to record the corresponding image. For instance, in the reference optical path, reference arms 1 and 2 were respectively modulated to be p- and s-polarized, respectively. Simultaneously, the amplitude-modulated spatial light modulator (A-SLM) on the signal optical path uploaded the image of the letter “A”. Subsequently, the two beams mutually interfered in the phenanthrenequinone-doped poly (methyl methacrylate) (PQ/PMMA) material. L1–L2: lenses; BE: beam expander system composed of L1 and L2 (5× overall beam expansion); HWP1–HWP4: half-wave plates; PBS1–PBS2: polarization beam splitters; M1–M3: mirrors; BS: beam splitter; CCD: charge-coupled device.

Fig. 5. Reconstructed experimental results for the four-channel polarization multiplexing holograms, with a specific focus on the outcomes achieved when 16 different polarization combinations of reference waves were used to illuminate the holograms for reading. (a) State of polarization (SOP) of partial reading reference waves as a function of the rotational angle of half-wave plate 4 (HWP4) as it increased from any of its initial positions. (b, e) The reference waves employed for reading in the four-channel polarization multiplexing holograms reconstruction consisted of a first component that was (b) p-polarized or (e) s-polarized as well as a second component that transitioned from (b) s-polarized or (e) p-polarized to other linear polarizations as the rotational angle of HWP4 increased by increments of 22.5°. (c, d) Five reconstruction results showcased from the experimental datasets depicted in (b) and (e), respectively, highlighting the outcomes achieved under different reading reference waves.