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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
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Orthogonal matrix of polarization combinations: concept and application to multichannel holographic recording
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Abstract
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. -
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References
[1] Lu CP, Hager GD, Mjolsness E. Fast and globally convergent pose estimation from video images. IEEE Trans Pattern Anal Mach Intell 22, 610–622 (2000). doi: 10.1109/34.862199 [2] Horadam KJ. Hadamard Matrices and Their Applications (Princeton University Press, 2012). [3] Trefethen LN, Bau III D. Numerical Linear Algebra: Twenty-Fifth Anniversary Edition (SIAM, Philadelphia, 2022). [4] Feynman RP, Hibbs AR, Styer DF. Quantum Mechanics and Path Integrals (Dover Publications, New York, 2010). [5] Wang R, Guo JB, Leung H. Orthogonal circulant structure and chaotic phase modulation based analog to information conversion. Signal Process 144, 104–117 (2018). doi: 10.1016/j.sigpro.2017.10.003 [6] Li JH, He MZ, Zheng TX, Cao LC, He QS et al. Two-dimensional shift-orthogonal random-interleaving phase-code multiplexing for holographic data storage. Opt Commun 284, 5562–5567 (2011). doi: 10.1016/j.optcom.2011.08.008 [7] Figueroa J, Cros J, Viarouge P. Generalized transformations for polyphase phase-modulation motors. IEEE Trans Energy Convers 21, 332–341 (2006). doi: 10.1109/TEC.2005.859965 [8] Xin Y, Wang ZD, Giannakis GB. Space-time diversity systems based on linear constellation precoding. IEEE Trans Wirel Commun 2, 294–309 (2003). doi: 10.1109/TWC.2003.808970 [9] Li JH, Cao LC, Gu HR, Tan XD, He QS et al. Orthogonal-reference-pattern-modulated shift multiplexing for collinear holographic data storage. Opt Lett 37, 936–938 (2012). doi: 10.1364/OL.37.000936 [10] Makey G, Yavuz Ö, Kesim DK, Turnalı A, Elahi P et al. Breaking crosstalk limits to dynamic holography using orthogonality of high-dimensional random vectors. Nat Photonics 13, 251–256 (2019). doi: 10.1038/s41566-019-0393-7 [11] Kinoshita N, Muroi T, Ishii N, Kamijo K, Shimidzu N. Control of angular intervals for angle-multiplexed holographic memory. Jpn J Appl Phys 48, 03A029 (2009). doi: 10.1143/JJAP.48.03A029 [12] Cao LC, Wang Z, Zhang H, Jin GF, Gu C. Volume holographic printing using unconventional angular multiplexing for three-dimensional display. Appl Opt 55, 6046–6051 (2016). doi: 10.1364/AO.55.006046 [13] Sherif H, Naydenova I, Martin S, McGinn C, Toal V. Characterization of an acrylamide-based photopolymer for data storage utilizing holographic angular multiplexing. J Opt A Pure Appl Opt 7, 255–260 (2005). doi: 10.1088/1464-4258/7/5/007 [14] Yoneda N, Saita Y, Nomura T. Binary computer-generated-hologram-based holographic data storage. Appl Opt 58, 3083–3090 (2019). doi: 10.1364/AO.58.003083 [15] Eto T, Takabayashi M, Okamoto A, Bunsen M, Okamoto T. Numerical simulations on inter-page crosstalk characteristics in three-dimensional shift multiplexed self-referential holographic data storage. Jpn J Appl Phys 55, 08RD01 (2016). doi: 10.7567/JJAP.55.08RD01 [16] Jin ZW, Janoschka D, Deng JH, Ge L, Dreher P et al. Phyllotaxis-inspired nanosieves with multiplexed orbital angular momentum. eLight 1, 5 (2021). doi: 10.1186/s43593-021-00005-9 [17] Ouyang X, Xu Y, Xian MC, Feng ZW, Zhu LW et al. Synthetic helical dichroism for six-dimensional optical orbital angular momentum multiplexing. Nat Photonics 15, 901–907 (2021). doi: 10.1038/s41566-021-00880-1 [18] Fang XY, Ren HR, Gu M. Orbital angular momentum holography for high-security encryption. Nat Photonics 14, 102–108 (2020). doi: 10.1038/s41566-019-0560-x [19] Zang JL, Kang GG, Li P, Liu Y, Fan FL et al. Dual-channel recording based on the null reconstruction effect of orthogonal linear polarization holography. Opt Lett 42, 1377–1380 (2017). doi: 10.1364/OL.42.001377 [20] Zang JL, Fan F, Liu Y, Wei R, Tan XD. Four-channel volume holographic recording with linear polarization holography. Opt Lett 44, 4107–4110 (2019). doi: 10.1364/OL.44.004107 [21] Guo JY, Wang T, Quan BG, Zhao H, Gu CZ et al. Polarization multiplexing for double images display. Opto-Electron Adv 2, 180029 (2019). [22] Koek WD, Bhattacharya N, Braat JJM, Chan VS, Westerweel J. Holographic simultaneous readout polarization multiplexing based on photoinduced anisotropy in bacteriorhodopsin. Opt Lett 29, 101–103 (2004). doi: 10.1364/OL.29.000101 [23] Wei HY, Cao LC, Xu ZF, He QS, Jin GF et al. Orthogonal polarization dual-channel holographic memory in cationic ring-opening photopolymer. Opt Express 14, 5135–5142 (2006). doi: 10.1364/OE.14.005135 [24] Barada D, Ochiai T, Fukuda T, Kawata S, Kuroda K et al. Dual-channel polarization holography: A technique for recording two complex amplitude components of a vector wave. Opt Lett 37, 4528–4530 (2012). doi: 10.1364/OL.37.004528 [25] Zhou SL, Liu L, Chen ZJ, Ansari MA, Chen XZ et al. Polarization-multiplexed metaholograms with erasable functionality. J Phys D Appl Phys 56, 155102 (2023). doi: 10.1088/1361-6463/acbf61 [26] Ilieva D, Nedelchev L, Petrova T, Tomova N, Dragostinova V et al. Holographic multiplexing using photoinduced anisotropy and surface relief in azopolymer films. J Opt A Pure Appl Opt 7, 35 (2005). doi: 10.1088/1464-4258/7/1/005 [27] Li X, Chen QM, Zhang X, Zhao RZ, Xiao SM et al. Time-sequential color code division multiplexing holographic display with metasurface. Opto-Electron Adv 6, 220060 (2023). doi: 10.29026/oea.2023.220060 [28] Xiong B, Liu Y, Xu YH, Deng L, Chen CW et al. Breaking the limitation of polarization multiplexing in optical metasurfaces with engineered noise. Science 379, 294–299 (2023). doi: 10.1126/science.ade5140 [29] Nikolova L, Ramanujam PS. Polarization Holography (Cambridge University Press, Cambridge, 2009). [30] Kuroda K, Matsuhashi Y, Fujimura R, Shimura T. Theory of polarization holography. Opt Rev 18, 374–382 (2011). doi: 10.1007/s10043-011-0072-5 [31] Wang JY, Tan XD, Qi PL, Wu CH, Huang L et al. Linear polarization holography. Opto-Electron Sci 1, 210009 (2022). doi: 10.29026/oes.2022.210009 [32] Kuroda K, Matsuhashi Y, Shimura T. Reconstruction characteristics of polarization holograms. In 2012 11th Euro-American Workshop on Information Optics 1–2 (IEEE, 2012);http://doi.org/10.1109/WIO.2012.6488904. [33] Yarlagadda RKR, Hershey EJ. Hadamard Matrix Analysis and Synthesis (Springer, New York, 1997). [34] Lin SH, Hsu KY, Chen WZ, Whang WT. Phenanthrenequinone-doped poly(methyl methacrylate) photopolymer bulk for volume holographic data storage. Opt Lett 25, 451–453 (2000). doi: 10.1364/OL.25.000451 [35] Chen YX, Hu P, Huang ZY, Wang JY, Song HY et al. Significant enhancement of the polarization holographic performance of photopolymeric materials by introducing graphene oxide. ACS Appl Mater Interfaces 13, 27500–27512 (2021). doi: 10.1021/acsami.1c07390 [36] Lin SH, Chen PL, Chuang CI, Chao YF, Hsu KY. Volume polarization holographic recording in thick phenanthrenequinone-doped poly(methyl methacrylate) photopolymer. Opt Lett 36, 3039–3041 (2011). doi: 10.1364/OL.36.003039 [37] Hao JY, Lin X, Lin YK, Chen MY, Chen RX et al. Lensless complex amplitude demodulation based on deep learning in holographic data storage. Opto-Electron Adv 6, 220157 (2023). doi: 10.29026/oea.2023.220157 -
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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
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Figure 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 OMPC2×4 in conjunction with Hadamard matrices enables the generation of additional OMPCs with dimensionalities of 4n, where n is any power of 2.
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Figure 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).
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Figure 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.
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Figure 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.
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Figure 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.
