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光学加密技术因其并行处理、大容量和低功耗等优势在信息安全领域发挥着巨大的应用潜力. 其中, 偏振作为光的一个重要自由度, 基于偏振操控和复用的光学加密技术受到广泛研究. 然而当前基于像素化或交错式超表面设计的偏振操控方法, 仍面临制备难度大及相邻单元结构间耦合引起串扰等问题, 复用通道数量受限. 本文提出了一种基于矢量焦点超构透镜的纵向可变、级联偏振结构加密新方法. 该方法采用几何相位调控原理, 通过相同结构尺寸但不同旋向的TiO2纳米柱的定制和排列, 实现超构透镜所需的单相位轮廓, 在纵向多个焦平面上生成多个矢量焦点, 并重构级联的偏振结构. 这里任意两个级联的偏振结构被编码相互正交的偏振旋转角, 随着入射线偏振光的偏振方向发生变化, 偏振结构上的偏振分布随之动态变化, 因此, 不同偏振方向的透射光强度分布也被动态调制, 可实现十通道信息加密. 只有通过正确的密钥(入射波长、入射偏振态、出射光偏振态和观察位置)才能解码加密信息. 该方法结合了超构透镜的多焦点偏振旋转、偏振结构设计及纵向、级联控制, 提升了信息容量和安全性, 在光学信息显示、加密和防伪等领域具有重要的应用潜力.Optical encryption technologies show significant potential applications in information security due to their advantages of parallel processing, large capacity, and low power consumption. Polarization, as an important degree of freedom of light, has attracted extensive research interest in optical encryption through polarization manipulation and multiplexing. However, current polarization control methods based on pixelated or interleaved metasurfaces still face significant challenges, including fabrication complexity and inevitable crosstalk caused by coupling between the neighboring structures, which limits the number of achievable multiplexing channels. A novel encryption method featuring longitudinal variability and cascaded polarization structures realized by metalenses with vectorial foci is proposed in this work. The intensity distributions on different observation planes are simulated using the Fresnel–Kirchhoff diffraction integral. Based on the geometric phase principle, the designed metalens consisting of TiO2 nanopillars with identical dimensions but spatially variant orientation angles, can generate multiple vectorial foci in different observation planes, reconstructing cascaded polarization structures. Here, any two cascaded polarization structures are encoded with mutually orthogonal polarization rotation angles. As the polarization direction of incident linearly polarized light changes, the polarization distribution encoded on the polarization structures can be dynamically modulated, consequently enabling ten-channel information encryption through polarization-dependent intensity redistribution. The encrypted information can only be decoded using the correct keys (incident wavelength, incident polarization state, output light polarization state, and observation position). This method integrates polarization rotation, polarization structure design, and longitudinal/cascaded control, significantly enhancing information capacity and security. It offers promising applications across various fields, such as optical display, encryption, and anti-counterfeiting.
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Keywords:
- metalens /
- dielectric metasurface /
- polarization manipulation /
- optical encryption
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图 1 (a) 多焦点超构透镜生成纵向可变、单波长(λ = 530 nm)且级联的偏振结构(图像或字母)示意图; (b) TiO2纳米柱单元结构示意图, 其中P, L, W 和 θ分别代表纳米柱的长、宽、高和旋转角, 周期固定为Px = Py = 300 nm; (c) 固定纳米柱长L = 205 nm、宽W = 100 nm, 不同高度H情况下的交叉极化(转换部分)和共极化(非转换部分)圆偏振光的仿真透射效率; (d) 固定高度H = 1000 nm, 不同长L和宽W的纳米棒阵列情况下的转换效率; 星号标示了所选最大转换效率对应的纳米柱尺寸(L = 205 nm, W = 100 nm); (e) 所选纳米柱阵列在圆交叉极化和同极化情况下的透射谱; (f) 所选纳米棒的旋转角度θ与附加相位Φ 和偏振转换效率之间的关系
Fig. 1. (a) Schematic diagram of multifocal metalens generating longitudinally varying, single-wavelength, and cascaded polarization structures (images or letters); (b) schematic diagram of the TiO2 nanorod unit cell, the parameters P, L, W and θ denote the period, length, width, and the rotation angle of the TiO2 nanorod, respectively, the period is fixed at Px = Py = 300 nm; (c) simulated cross-polarization (converted part) and co-polarization (non-converted part) transmission efficiency with different height H = 530 nm at λ = 530 nm with fixed length L = 205 nm and width W = 100 nm; (d) simulated conversion efficiency with different lengths and widths at λ = 530 nm with fixed height H = 1000 nm, the TiO2 nanorods with length L = 205 nm and width W = 100 nm are chosen for the maximum conversion efficiency, as shown in the star-mark; (e) calculated converted and non-converted efficiency spectra of the chosen TiO2 nanorod array; (f) dependence of phase Φ and polarization conversion efficiency on the rotation angle θ of the chosen TiO2 nanorods.
图 2 (a) 在焦平面z = f = 20 μm生成7个矢量焦点的超构透镜示意图, 每个焦点在水平LP光入射时的偏振方向如黄色箭头所示; (b) 超构透镜相位分布Φ(x, y)(上)和依照θ = Φ(x, y) /2的旋向进行排列的纳米棒(下); (c) 不同偏振光入射(第1列为RCP, 第2, 3列为LP)情况下, 分别利用FDTD(上)和F-K integral(下)方法在焦平面上计算得到的强度分布图
Fig. 2. (a) A metalens for generating seven vectorial foci along a semicircle at focal plane z = f = 20 μm, the polarization distribution for the foci upon the illumination of a horizontal LP light beam; (b) the phase profile (top) and the details of arrangement of each TiO2 nanorods (θ = Φ(x, y) /2, bottom) of the metalens; (c) intensity distributions at focal plane under different incident polarization states (RCP for the 1st column and LP for other columns), simulated by FDTD (top) and F-K integral (bottom).
图 3 不同焦点数和不同焦距的24个超构透镜在其对应焦平面上的强度分布
Fig. 3. Intensity distributions of 24 metalenses with different numbers of foci and focal lengths at their respective focal planes.
图 4 (a) 在纵向空间三个焦平面生成三个偏振数字的超构透镜; (b) 超构透镜的相位分布; (c) 圆偏振光入射, 在纵向三个焦平面生成的强度图; (d) 水平方向的线偏振光入射, 在纵向三个平面生成的偏振结构; (e) 设计的数字“8”由七条焦线组成; (f) 为生成偏振数字“2”而设计的每条焦线的偏振方向
Fig. 4. (a) A metalens generating three different polarization-encoded numbers at three focal planes along the longitudinal direction; (b) phase profile of the metalens. (c) Intensity distributions at three focal planes under circularly polarized light illumination; (d) polarization patterns generated at three focal planes under horizontally polarized light illumination; (e) designed number “8” composed of seven focal lines; (f) designed polarization distributions of each focal line for generating the number “2”.
图 5 (a) 在纵向2个观察平面上创建5对级联偏振结构的超构透镜; (b) 圆偏振光入射时, 在纵向2个焦平面生成的强度图; (c) 线偏振光偏振方向角为$ \beta=0 $时, 在纵向2个平面生成的偏振结构; (d) 线偏振光偏振方向角为$ \beta=\pi/4 $时, 在纵向2个平面生成的偏振结构
Fig. 5. (a) Metalens for creating five pairs of cascaded polarization structures at two focal planes; (b) intensity distributions at two focal planes under circularly polarized light illumination; (c) polarization distributions at two focal planes when illuminated by horizontally polarized light with β = 0; (d) polarization distributions at two focal planes when illuminated by diagonally polarized light with β = $ \pi/4 $
图 6 (a) 在沿纵向5个观察平面上创建五对级联偏振结构的超构透镜; (b) 圆偏振光入射情况下, 在5个观察平面生成的强度图; (c) 线偏振光偏振方向角为0°时在纵向5个平面生成的偏振结果; (d) 线偏振光偏振方向角为$ \pi/4 $时在纵向5个平面生成的偏振结果
Fig. 6. (a) Metalens creating five pairs of cascaded polarization structures at five focal planes along longitudinal direction; (b) intensity distributions at five focal planes under circularly polarized light illumination; (c) polarization distributions at five focal planes when illuminated by horizontally polarized light with β = 0; (d) polarization distributions at five focal planes when illuminated by diagonally polarized light with β = $ \pi/4 $
表 1 几种超表面信息加密技术在信息容量、安全性方面的对比
Table 1. Comparison of metasurface-based information encryption techniques in terms of information capacity and security
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[1] Matoba O, Nomura T, Perez C E, Millan M S, Javidi B 2009 Proc. IEEE 97 1128
Google Scholar
[2] Chen W, Javidi B, Chen X D 2014 Adv. Opt. Photonics 6 120
[3] Liu S, Guo C L, Sheridan J T 2014 Opt. Laser Technol. 57 327
Google Scholar
[4] Jiao S M, Zhou C Y, Shi Y S, Zou W B, Li X 2019 Opt. Laser Technol. 109 370
Google Scholar
[5] Liu S Y, Liu X H, Yuan J Y, Bao J 2021 Res. (Wash D C) 2021 7897849
[6] Yue F Y, Zhang C M, Zang X F, Wen D D, Gerardot B, Zhang S, Chen X Z 2018 Light Sci. Appl. 7 17129
[7] Zhang C M, Dong F L, Intaravanne Y, Zang X F, Xu L H, Song Z W, Zheng G X, Wang W, Chu W G, Chen X Z 2019 Phys. Rev. Appl. 12 034028
[8] Intaravanne Y, Chen X Z 2020 Nanophotonics 9 1003
Google Scholar
[9] Zhao R Z, Li X, Geng G Z, Li X W, Li J J, Wang Y T, Huang L L 2023 Nanophotonics 12 155
Google Scholar
[10] Yu N F, Patrice G, Mikhail A K, Aieta F, Tetienne J P, Capasso F, Gaburro Z 2011 Science 334 333
[11] Yu N F, Capasso F 2014 Nat. Rev. Mater. 13 139
Google Scholar
[12] Chen W T, Alexander Y Zhu, Capasso F 2020 Nat. Rev. Mater. 5 604-620
Google Scholar
[13] Yang R, Yu Q Q, Pan Y, Chen S, Li Z Y 2022 Opto-Electronic Eng. 49 220177
[14] Zheludev N I, Kivshar Y S 2012 Nat. Mater. 11 917
Google Scholar
[15] Minovich A E, Miroshnichenko A E, Bykov A Y, Murzina T V, Neshev D N, Kivshar Y S 2015 Laser Photonic Rev. 9 195
Google Scholar
[16] Fan Q B, Liu M Z, Zhang C, Zhu W Q, Wang Y L, Lin P C,Yan F, Chen L, Lezec H J, Lu Y Q, Agrawal A, Xu T 2020 Phys. Rev. Lett. 125 267402
Google Scholar
[17] Li Z, Liu W, Cheng H, Choi D Y, Chen S, Tian J 2019 Adv. Opt. Mater. 7 1900260
Google Scholar
[18] Bao Y J, Yu Y, Xu H F, Guo C, Li J T, Sun S, Zhou Z K, Qiu C W, Wang X H 2019 Light. Sci. Appl. 8 95
Google Scholar
[19] Li Z F, Premaratne M, Zhu W R 2020 Nanophotonics 9 3687
Google Scholar
[20] Overvig A, Alù A 2021 Adv. Photonics 3 026002
[21] Schlickriede C, Waterman N, Reineke B, Georgi P, Li G, Zhang S, Zentgraf 2018 Adv. Mater. 30 1703843
Google Scholar
[22] Mueller J B, Rubin N A, Devlin R C, Devlin, Groever B, Capasso Federico 2017 Phys. Rev. Lett. 118 113901
Google Scholar
[23] Ding F, Chang B D, Wei Q S, Huang L L, Guan X W, Sergey B I 2020 Laser Photon. Rev. 14 2000116
Google Scholar
[24] Intaravanne Y, Ansari M A, Ahmed H, Chen X Z 2023 Adv. Opt. Mater. 12 2203097
[25] Song Q, Khadir S, Vézian S, Vézian X, Damilano B, Mierry P D, Chenot S, Brandli V, Genevet P 2021 Sci. Adv. 7 1112
Google Scholar
[26] Zang X, Ding H, Intaravanne Y, Chen L, Peng Y, Xie J, Ke Q H, Balakin A V, Shkurinov A P, Chen X, Zhu Y, Zhuang S 2019 Laser Photon. Rev. 13 1900182
Google Scholar
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Google Scholar
[28] Sun P Z, Liu B H, Liu X, Zhang S Y, Shen D, Zhang Z G 2023 Opt. Lett. 48 3083
Google Scholar
[29] Kim I, Jang J, Kim G, Lee J, Badloe T, Mun J, Rho J 2021 Nat. Commun. 12 3614
Google Scholar
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Google Scholar
[31] Ahmed H, Ansari M A, Li Y, Zentgraf T, Mehmood M Q, Chen X 2023 Nat. Commun. 14 3915
Google Scholar
[32] Lin D M, Fan P Y, Hasman E, Brongersma M L, Bron G 2014 Science 345 298
Google Scholar
[33] Li H, Xu W H, Xu H, Song C Y, Tan Q, Yao J Q 2024 J. Opt. 26 035102
Google Scholar
[34] Xu Y, Xu Q, Zhang X, Feng X, Lu Y, Zhang X, Kang M, Han J, Zhang W 2022 Adv. Funct. Mater. 32 2207269
Google Scholar
[35] Yan L B, Zhu W M, Karim M F, Cai H, Gu A Y, Shen Z X, Chong P H J, Tsai D P, Kwong D L, Qiu C W, Liu A Q 2018 Adv. Opt. Mater. 6 1800728
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
[43] Song Q H, Baroni A, Sawant R, Peinan N, Brandli V, Chenot S, Vézian S, Damilano B, Mierry P, Khadi S, Ferrand P 2020 Nat. Commun. 11 2651
Google Scholar
[44] Guo X, Zhong J, Li B, Qi S, Li Y, Li P, Wen D, Liu S, Wei B, Zhao J 2020 Adv. Mater. 34 2103192
[45] Wen D D, Cadusch J J, Meng J, Crozier K B 2021 Nano Lett. 21 1735
Google Scholar
[46] Ning M H, Zhong H Z, Gu Z, Zhang L E, Qu N, Jun D, Li T, Li L 2025 Nanophotonics 14 495
Google Scholar
[47] Cao Y, Tang L L, Li Q, Lee C K, Dong Z G 2023 Small 19 2206319
Google Scholar
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Google Scholar
[49] Wang R X, Han J, Liu J L, Tian H, Sun W M, Li L, Chen X Z 2020 Opt. Express 45 3506
[50] Zhang Y, Liu W, Gao J, Yang X 2018 Adv. Opt. Mater. 6 1701228
Google Scholar
[51] 夏天, 谢振威, 袁小聪 2023 中国激光 50 212
Xia T, Xie Z W, Yuan X C J 2023 Chin. J. Lasers 50 212
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