Off-axis metasurface holographic imaging positions based on periodic modulation

GUO Wenhao; PU Xinxin; ZHANG Wei; LIANG Haifeng; ZHU Yechuan; HOU Jinyao; SUN Xueping; ZHOU Shun; LIU Weiguo

doi:10.7498/aps.74.20251068

Abstract

Metasurface holography based on planar optical devices has attracted considerable attention due to its potential for miniaturizing optical components and systems. However, traditional on-axis holography has inherent zeroth-order diffraction and twin-image effects, which significantly degrade image quality and limit its practical applications. Off-axis metasurface holography, in contrast, provides a promising solution to overcoming these limitations. In this work, we design a metasurface hologram composed of titanium dioxide (TiO₂) nanopillars on a silicon dioxide (SiO₂) substrate, by using the high refractive index and low optical loss of TiO₂ in the visible light range to achieve efficient phase control. The unit cell height is set to 600 nm to ensure sufficient phase accumulation, and the working wavelength is 635 nm. The hologram is constructed by mapping the continuous 0–2π phase distribution obtained from computational holography onto the unit cell array, and changing the nanopillar diameter to achieve full phase coverage. We systematically investigate the effect of the unit cell period on the imaging position in off-axis holography. Numerical simulations show that as the period increases from 280 nm to 350 nm, the center of the holographic image gradually shifts toward the center of the image plane. The optimal period is found to be 324 nm, at which the image is reconstructed precisely at the designed position. Further simulations using different off-axis angles (0°–45°) and nanopillar heights (600–2000 nm) confirm that the imaging position remains fixed at the target location, indicating that it is mainly determined by the unit cell period rather than other structural parameters. These results demonstrate that by carefully selecting the unit cell period, the holographic image can be accurately reconstructed at a predetermined positions with high image quality, providing theoretical guidance for designing high-precision off-axis metasurface holographic imaging systems.

Keywords:

Authors and contacts

1.
Shaanxi Province Key Laboratory of Thin Films Technology and Optical Test, Xi’an Technological University, Xi'an 710021, China
2.
Shenzhen Key Laboratory of Ultraintense Laser and Advanced Material Technology, Center for Intense Laser Application Technology, and College of Engineering Physics, Shenzhen Technology University, Shenzhen 518118, China

Corresponding author: ZHANG Wei, zhangwei0105@sztu.edu.cn ; ZHU Yechuan, zyc_xatu@126.com ; LIU Weiguo, wgliu@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 52075410), the Key Research and Development Program of Shaanxi Province, China (Grant No. 2025CY-YBXM-085), the Natural Science Basic Research Program of Shaanxi, China (Grant No. 2025JC-JCQN-093), the Innovation Capability Support Program of Shaanxi, China (Grant No. 2025ZY1-GNYZ-05), and the Science and Technology Program of Shenzhen, China (Grant No. JCYJ20220530153013030).

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References

[1]	Thureja P, Shirmanesh G K, Fountaine K T, Sokhoyan R, Grajower M, Atwater H A 2020 ACS Nano 14 15042 Google Scholar
[2]	Su D E, Wang X W, Shang G Y, Ding X M, Burokur S N, Liu J, Li H Y 2022 J. Phys. D: Appl. Phys. 23 5102 Google Scholar
[3]	High A A, Devlin R C, Dibos A, Polking M, Wild D S, Perczel J, Leon N P, Lukin M D, Park H 2015 Nature 522 192 Google Scholar
[4]	Wang Z H, Zhu Y C, Zhou S, Guo W H, Liu Y, He C, Bai M Y, Liu W G 2024 Infrared Phys. Techn. 142 105521 Google Scholar
[5]	Yuan Y Y, Sun S, Chen Y, Zhang K, Ding X M, Ratni B, Wu Q, Burokur S N, Qiu C W 2020 Adv. Sci. 7 2001437 Google Scholar
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[13]	Wang Q, Zhang X Q, Xu Y H, Gu J Q, Li Y F, Tian Z, Singh R , Zhang S , Han J G, Zhang W L 2016 Sci. Rep 6 32867 Google Scholar
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[15]	Zhao W Y, Liu B Y, Jiang H, Song J, Pei Y B, Jiang Y Y 2016 Opt. Lett. 41 147 Google Scholar
[16]	Li X, Chen L W, Li Y, Zhang X H, Pu M B, Zhao Z Y 2016 Sci. Adv. 2 e1600892 Google Scholar
[17]	Li X, Chen L W, Li Y, Zhang X H, Pu M B, Zhao Z Y, Ma X I, Wang Y Q, Hong M H, Luo X A 2016 Sci. Adv. 2 e1601102 Google Scholar
[18]	Malek S C, Ee H S, Agarwal R 2016 Nano Lett. 16 5053 Google Scholar
[19]	Li Z, Kim I, Zhang L, Mehmood M Q, Anwar M S, Saleem M, Lee D, Nam K T, Zhang S, Luk’yanchuk B S, Wang Y, Zheng G X, Rho J, Qiu C W 2017 ACS Nano 11 9382 Google Scholar
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[21]	Gao F, Zhou X, Lu L T, Deng J, Yan B 2023 Results Phys. 52 106925 Google Scholar
[22]	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
[23]	Noh J, Kim J, Rho J 2024 Nano Lett. 25 11398 Google Scholar
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图 1 超表面全息图示意图　(a) 基于超表面的全息成像示意图; (b) 单个周期内的单元结构示意图

Figure 1. Schematic diagram of metasurface hologram: (a) Schematic diagram of metasurface-based holographic imaging; (b) the unit cell diagram in one period.

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图 2 不同周期单元结构的相位调制和透射率随直径的变化　(a) 相位调制; (b) 透射率

Figure 2. Variation of phase shift and transmission with diameter for the unit cell with various period: (a) Phase shift; (b) transmission.

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图 3 离轴全息图模拟　(a) 目标图案; (b) 相位全息图; (c) 计算机生成的全息像

Figure 3. Simulation of off-axis hologram: (a) Target pattern; (b) phase-only hologram; (c) computer-generated hologram imaging.

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图 4 (a)—(h) 单元结构周期分别为280, 290, 300, 310, 320, 330, 340, 350 nm时的全息图数值模拟结果; (i) 不同周期对应的全息图像中心坐标; (j) 全息像中心坐标x和y与单元结构周期变化关系拟合曲线

Figure 4. (a)—(h) Numerical simulation results of holography images with the unit cell periods of 280, 290, 300, 310, 320, 330, 340, and 350 nm; (i) centre coordinates of holographic images corresponding to different periods; (j) fitted curves of the dependence of the holographic image center coordinates x and y on the unit cell period.

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图 5 (a)—(j) 单元结构周期分别为310, 312, 314, 316, 318, 320, 322, 324, 326, 328 nm时的全息图数值模拟结果; (k) 全息像中心坐标x和y与单元结构周期变化关系拟合曲线

Figure 5. (a)—(j) Numerical simulation results of holography images with the unit cell periods of 310, 312, 314, 316, 318, 320, 322, 324, 326 and 328 nm; (k) fitted curves of the dependence of the holographic image center coordinates x and y on the unit cell period.

DownLoad: Full-Size Img PowerPoint

图 6 不同周期下成像性能　(a) 理想情况下成像效果; (b) PSNR; (c) SSIM

Figure 6. Imaging performance under different periods: (a) Ideal imaging result; (b) PSNR; (c) SSIM.

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图 7 数值模拟单元结构周期P分别为310, 316, 324, 330 nm时的电场强度分布　(a)—(d) 纳米柱直径D = 100 nm; (e)—(h) 纳米柱满足2π相位时最大直径

Figure 7. Electric field intensity distributions from numerical simulations for unit cell periods P = 310, 316, 324, and 330 nm: (a)–(d) The nanopillar diameter D = 100 nm; (e)–(h) the maximum nanopillar diameter at 2π phase.

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图 8 (a)—(j)单元结构周期P为324 nm时, 离轴角分别为0°, 5°, 10°, 15°, 20°, 25°, 30°, 35°, 40°和45°时的数值模拟结果

Figure 8. (a)–(j) Numerical simulation results of holograms generated by the off-axis angle of 0°, 5°, 10°, 15°, 20°, 25°, 30°, 35°, 40° and 45°.

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图 9 不同高度单元结构的相位调制和透射率随直径的变化　(a)相位调制; (b)透射率

Figure 9. Variation of phase shift and transmission with diameter for the unit cell with various height: (a) Phase shift; (b) transmission.

DownLoad: Full-Size Img PowerPoint

图 10 (a)—(j) 单元结构高度分别为600, 700, 800, 900, 1000, 1200, 1400, 1600, 1800, 2000 nm时的全息图数值模拟结果

Figure 10. (a)–(j) Numerical simulation results of holograms with the unit structure height of 600, 700, 800, 900, 1000, 1200, 1400, 1600, 1800, and 2000 nm.

DownLoad: Full-Size Img PowerPoint

DownLoad: Full-Size Img PowerPoint

[1]	Thureja P, Shirmanesh G K, Fountaine K T, Sokhoyan R, Grajower M, Atwater H A 2020 ACS Nano 14 15042 Google Scholar
[2]	Su D E, Wang X W, Shang G Y, Ding X M, Burokur S N, Liu J, Li H Y 2022 J. Phys. D: Appl. Phys. 23 5102 Google Scholar
[3]	High A A, Devlin R C, Dibos A, Polking M, Wild D S, Perczel J, Leon N P, Lukin M D, Park H 2015 Nature 522 192 Google Scholar
[4]	Wang Z H, Zhu Y C, Zhou S, Guo W H, Liu Y, He C, Bai M Y, Liu W G 2024 Infrared Phys. Techn. 142 105521 Google Scholar
[5]	Yuan Y Y, Sun S, Chen Y, Zhang K, Ding X M, Ratni B, Wu Q, Burokur S N, Qiu C W 2020 Adv. Sci. 7 2001437 Google Scholar
[6]	Yue Z, Li J T, Zheng C L, Li J, Chen M Y, Hao X R, Xu H, Wang Q, Zhang Y T, Yao J Q 2022 Chin. Opt. Lett. 20 043601 Google Scholar
[7]	Yuan Y Y, Zhang K, Ratni B, Song Q H, Ding X M, Wu Q, Burokur S N, Genevet P 2020 Nat. Commun. 11 4186 Google Scholar
[8]	徐平, 肖钰斐, 黄海漩, 杨拓, 张旭琳, 袁霞, 李雄超, 王梦禹, 徐海东 2021 物理学报 70 084201 Google Scholar Xu P, Xiao Y F, Huang H X, Yang T, Zhang X L, Yuan X, Li X C, Wang M Y, Xu H D 2021 Acta Phys. Sin. 70 084201 Google Scholar
[9]	Ren H R, Fang X Y, Jang J, Bürger J, Rho J, Maier S A 2020 Nat. Nanotechnol. 15 948 Google Scholar
[10]	Ni X J, Kildishev A V, Shalaev V M 2013 Nat. Commun. 4 2807 Google Scholar
[11]	Ji R N, Zheng X R, Li Y L, Xie X, Lin F C, Liu C, Zheng Y W, Yu P Q, Li X R, Song K, Li Z F, Lu W, Zhang S, Wang S W, Wang D, Wang Q H 2025 Laser Photonics Rev. 19 e00398 Google Scholar
[12]	Pu X X, Sun X P, Ge S B, Cheng J, Zhou S, Liu W G 2022 Micromachines-Basel. 13 1956 Google Scholar
[13]	Wang Q, Zhang X Q, Xu Y H, Gu J Q, Li Y F, Tian Z, Singh R , Zhang S , Han J G, Zhang W L 2016 Sci. Rep 6 32867 Google Scholar
[14]	Liu K F, Chen Q M, Liu Y L, Song S C, Zhang H M, Shi L T, He M Y, Xiao S Q, Xiao S M, Zhang X H 2024 Appl. Phys. Lett. 125 041703 Google Scholar
[15]	Zhao W Y, Liu B Y, Jiang H, Song J, Pei Y B, Jiang Y Y 2016 Opt. Lett. 41 147 Google Scholar
[16]	Li X, Chen L W, Li Y, Zhang X H, Pu M B, Zhao Z Y 2016 Sci. Adv. 2 e1600892 Google Scholar
[17]	Li X, Chen L W, Li Y, Zhang X H, Pu M B, Zhao Z Y, Ma X I, Wang Y Q, Hong M H, Luo X A 2016 Sci. Adv. 2 e1601102 Google Scholar
[18]	Malek S C, Ee H S, Agarwal R 2016 Nano Lett. 16 5053 Google Scholar
[19]	Li Z, Kim I, Zhang L, Mehmood M Q, Anwar M S, Saleem M, Lee D, Nam K T, Zhang S, Luk’yanchuk B S, Wang Y, Zheng G X, Rho J, Qiu C W 2017 ACS Nano 11 9382 Google Scholar
[20]	Zheng G X, Mühlenbernd H, Kenney M, Li G X, Zentgraf T, Zhang S 2015 Nat. Nanotechnol. 10 308 Google Scholar
[21]	Gao F, Zhou X, Lu L T, Deng J, Yan B 2023 Results Phys. 52 106925 Google Scholar
[22]	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
[23]	Noh J, Kim J, Rho J 2024 Nano Lett. 25 11398 Google Scholar
[24]	Gopakumar M, Lee G Y, Choi S, Chao B, Peng Y F, Kim J, Wetzstein G 2024 Nature 629 791 Google Scholar
[25]	Guo W H, Pu X X, Zhu Y C, Wang Z H, Sun X P, Liu Y, Zhou S, Ge S B, Hang L Y, Liu W G 2025 Opt. Commun. 535 130015 Google Scholar

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