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光的轨道角动量自由度已被作为一种新的信息载体用于光全息信息处理技术之中. 然而, 目前关于轨道角动量全息技术的研究主要集中在二维轨道角动量全息, 即重构的二维全息图像位于三维空间中的某一个平面内. 如何进一步实现三维空间轨道角动量全息技术并将其用于增加全息通信的信息容量仍然是一个空白. 本文基于轨道角动量自由度和重构的二维图像在三维空间中的位置自由度, 实现了三维空间轨道角动量全息技术. 换言之, 在我们实现的三维空间轨道角动量全息中, 目标物体图像的获得不仅要求使用正确的解码轨道角动量态, 还要求在正确的空间位置来探测物体的图像. 此外, 还进一步研究了三维空间轨道角动量全息复用技术, 并指出该复用技术可用于信息加密. 与传统的二维轨道角动量全息技术相比, 三维空间轨道角动量全息技术使用了额外的自由度, 即成像的空间位置. 因此, 基于三维空间轨道角动量全息技术的加密方案可以进一步提高信息的安全等级. 我们的理论模拟结果和实验结果验证了三维空间轨道角动量全息技术以及三维空间轨道角动量全息加密技术的可行性.The degree of freedom of orbital angular momentum of light has been used as a new information carrier in optical holographic information processing technology. However, current research on orbital angular momentum holography mainly focuses on two-dimensional orbital angular momentum holography, where the reconstructed two-dimensional holographic image is located in a certain plane in three-dimensional space. How to further implement three-dimensional spatial orbital angular momentum holographic technology and use it to increase the information capacity of holographic communication is still a blank. Here, we implement three-dimensional spatial orbital angular momentum holographic technology based on the degrees of freedom of orbital angular momentum and the positional degrees of freedom of reconstructed two-dimensional images in three-dimensional space. In other words, in the three-dimensional spatial orbital angular momentum holography, the acquisition of the target object image requires not only the correct orbital angular momentum state used for decoding, but also the correct spatial position where the object’s image is detected. In addition, we further investigate the three-dimensional spatial orbit angular momentum holographic multiplexing technology and point out that this multiplexing technology can be used for information encryption. Compared with traditional two-dimensional orbital angular momentum holography, three-dimensional spatial orbital angular momentum holography uses an additional degree of freedom. Therefore, the encryption scheme based on three-dimensional spatial orbital angular momentum holographic technology can further improve the security level of information. Our simulation results and experimental results have verified the feasibility of three-dimensional spatial orbit angular momentum holographic technology and three-dimensional spatial orbit angular momentum holographic encryption technology.
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Keywords:
- orbital angular momentum /
- optical holography /
- optical encryption
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图 1 用于实现三维空间OAM全息的全息图设计方案. 通过将目标图像与二维Dirac梳状采样阵列相乘即可获得能够保留OAM特征的全息图; 然后通过在保留OAM全息图上添加OAM态的螺旋相位分布, 生成具有OAM特征选择性的全息图; 最后, 使用FZP对OAM选择性全息图进行编码, 即可获得用于三维空间OAM全息的全息图. 这里, FZP的“焦距”($ {f_{{\text{FZP}}}} $)控制着重构出的全息图像在三维空间中的位置
Fig. 1. Design of the holograms of three-dimensional (3D) spatial OAM holography. The OAM-preserved holograms are obtained by multiplying the target images with the two-dimensional Dirac comb sampling array. Then, the OAM-selective holograms are generated by adding a phase function of OAM modes onto the OAM-preserved hologram. 3D spatial OAM-selective holograms are obtained by encoding the OAM-selective holograms with the Fresnel zone plates (FZP). The positions of the reconstructed holographic images are controlled by the focal lengths of FZP ($ {f_{{\text{FZP}}}} $).
图 2 三维空间OAM全息的理论模拟结果 (a) 理论模拟中选用的6个目标图像; (b) 6个目标图像的三维空间OAM全息图; (c)三维空间OAM全息中, 6个图像重构的理论模拟结果.
Fig. 2. Simulation results of the reconstructed images of 3D spatial OAM holography: (a) The six target images; (b) holograms of 3D spatial OAM holography of six target images; (c) simulation results of reconstructed images in 3D spatial OAM holography.
图 3 三维空间OAM全息的实验装置及其重构结果 (a) 实验装置. 波长633 nm、输出功率10 mW线偏振连续激光经过SLM-1调制后携带OAM态; 由透镜L1和L2组成的4f系统将SLM-1成像到SLM-2上; 三维空间 OAM全息的全息图加载于SLM-2上. 携带OAM态的光场经SLM-2衍射后, 在三维空间中重构出的目标物体的全息图像; (b) 与图2(c)中一一对应的三维空间OAM全息图像重构的实验结果
Fig. 3. Experiments and results of 3D spatial OAM hologram reconstruction. (a) Experimental setup. The light source is a continuous-wave laser operating at 633 nm with an output power of ~10 mW. The incident light, after modulated by SLM-1, carries the desired OAM state. A 4f system consisted of lenses L1 and L2 images SLM-1 onto the SLM-2. The holographic images of objects will be reconstructed in 3D space after the light field carrying OAM state is diffracted by SLM-2. (b) The experimental results of 3D spatial OAM holographic image reconstruction, which corresponds to the simulation results in Fig. 2 (c).
图 4 三维空间OAM多路复用全息 (a) 三维空间OAM多路复用全息的全息图设计; (b) 三维空间OAM多路复用全息的重构的实验结果. 只有当入射光束具备正确的OAM态, 且在正确的全息图像重构平面内时, 才会出现清晰的图像. 这里, 每一行的三个实验数据已做了归一化处理
Fig. 4. 3D spatial OAM holographic multiplexing technology. (a) Design of the holograms for 3D spatial OAM holographic multiplexing technology. (b) The experimental results for the 3D spatial OAM holographic multiplexing technology. Only when the incident beam has the correct OAM state and is in the correct holographic image reconstruction plane, will a clear image appear. Here, the three experimental data in each row have been normalized.
图 5 在三维空间OAM全息中, 全息重构图像的间距对串扰的影响. 第一行表示用于编码的三个FZP的“焦距”$ {f_{{\text{FZP}}}} $= z1, $ {f_{{\text{FZP}}}} $= z2和$ {f_{{\text{FZP}}}} $=z3的大小. 在重构的结果中, 每一个重构图像的左上角的数字为该图像对应的参数$ R = {{{{\bar I}_{{\text{pigeon}}}}} \mathord{\left/ {\vphantom {{{{\bar I}_{{\text{pigeon}}}}} {{{\bar I}_{{\text{non - pigeon}}}}}}} \right. } {{{\bar I}_{{\text{non - pigeon}}}}}} $的值. $ {\bar I_{{\text{pigeon}}}} $和$ {\bar I_{{\text{non - pigeon}}}} $分别代表鸽子区域和非鸽子区域的强度分布的平均值
Fig. 5. Influence of the distances among the holographic reconstructed images on crosstalk in 3D spatial OAM holography. The first line represents the values of the “focal length” of the three FZPs used for encoding, $ {f_{{\text{FZP}}}} $= z1, $ {f_{{\text{FZP}}}} $= z2, and $ {f_{{\text{FZP}}}} $= z3. In the reconstructed results, the number in the upper left corner of each image represents its value of the parameter $ R = {{{{\bar I}_{{\text{pigeon}}}}} \mathord{\left/ {\vphantom {{{{\bar I}_{{\text{pigeon}}}}} {{{\bar I}_{{\text{non - pigeon}}}}}}} \right. } {{{\bar I}_{{\text{non - pigeon}}}}}} $, where among them, $ {\bar I_{{\text{pigeon}}}} $represents the average intensity value in the pigeon areas and $ {\bar I_{{\text{non - pigeon}}}} $ represents the average intensity distribution in non-pigeon areas.
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[1] Gabor D 1948 Nature 161 777
Google Scholar
[2] Blanche P A, Bablumian A, Voorakaranam R, et al. 2010 Nature 468 80
Google Scholar
[3] Huang L, Chen X, Mühlenbernd H, et al. 2013 Nat. Commun. 4 2808
Google Scholar
[4] Li X, Ren H, Chen X, et al. 2015 Nat. Commun. 6 6984
Google Scholar
[5] Wakunami K, Hsieh P Y, Oi R, et al. 2016 Nat. Commun. 7 12954
Google Scholar
[6] Pégard N C, Mardinly A R, Oldenburg I A, Sridharan S, Waller L, Adesnik H 2017 Nat. Commun. 8 1228
Google Scholar
[7] Yu H, Lee K, Park J, Park Y 2017 Nat. Photon. 11 186
Google Scholar
[8] Makey G, Yavuz Ö, Kesim D K, Turnalı A, Elahi P, Ilday S, Tokel O, Ilday F Ö 2019 Nat. Photonics 13 251
Google Scholar
[9] Marquet P, Rappaz B, Magistretti P J, Cuche E, Emery Y, Colomb T, Depeursinge C 2005 Opt. Lett. 30 468
Google Scholar
[10] Rosen J, Brooker G 2008 Nat. Photonics 2 190
Google Scholar
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Google Scholar
Zhao Y C, Zhang X Y, Yuan C J, Nie S P, Zhu Z Q, Wang L, Li Y, Gong L P, Feng S T 2014 Acta Phys. Sin. 63 224202
Google Scholar
[12] Refregier P, Javidi B 1995 Opt. Lett. 20 767
Google Scholar
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Google Scholar
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Wang R D, Zhang Y P, Zhu X F, Wang F, Li C G, Zhang Y A, Xu W 2019 Acta Phys. Sin. 68 114202
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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