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胡金高娃; 赵尚男; 王灵杰; 叶昊坤; 张建萍; 张新

doi:10.37188/CO.2023-0039

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doi: 10.37188/CO.2023-0039

胡金高娃 ^{1, 2,},
赵尚男 ^{1, 2,,},
王灵杰 ¹,
叶昊坤 ^{1, 2},
张建萍 ¹,
张新 ^{1, 2}

1.
中国科学院长春光学精密机械与物理研究所, 吉林长春130033
2.
中国科学院大学, 北京100049

基金项目:国家自然科学基金项目（No. 62005271）

详细信息

作者简介:
胡金高娃（1999—），女，吉林长春人，硕士研究生，2021年于南京邮电大学获得学士学位，主要从事超构表面设计、光学设计仿真研究。E-mail：[email protected]

赵尚男（1993—），女，吉林长春人，博士研究生，分别于2015年和2018年于北京理工大学获得学士学位和硕士学位，主要从事光学设计仿真、超构表面设计的研究。E-mail：[email protected]

中图分类号:O436.1;TH74
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- 网络出版日期: 2023-07-13

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HU Jin-gao-wa ^{1, 2
,},
ZHAO Shang-nan ^{1, 2
,,},
WANG Ling-jie ¹,
YE Hao-kun ^{1, 2},
ZHANG Jian-ping ¹,
ZHANG Xin ^{1, 2}

1.
Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China
2.
University of Chinese Academy of Sciences, Beijing 100049, China

Funds:Supported by the National Natural Science Foundation of China (No. 62005271)

More Information

Corresponding author: [email protected]

摘要

摘要:
目的：超构透镜作为一种新型的平面光学元件，能够灵活操控光的相位、偏振、振幅，在器件轻量化和批量化制造等方面具有很大的发展和应用前景，目前受到了广泛关注。离轴超构透镜作为一种特殊的超构透镜且具有一定的色散作用，可作为分光元件，为实现微小型仪器提供了一种独特而可行的途径。本论文提出了一种离轴超构透镜的设计方法，并分析了不同数值孔径、离轴角度等参数对于离轴超构透镜的光谱分辨率、聚焦效率以及仿真结果的影响，为后续离轴超构透镜的研究与应用提供思路。方法：利用Lumerical软件分别仿真了参数为NA=0.408 α=13°、NA=0.180 α=13°、NA=0.408 α=20°等多个离轴超构透镜。结果：仿真结果表明：离轴角度与光谱分辨率大小成正相关，离轴角度越大，光谱分辨能力越强，但聚焦效率越低；当数值孔径越小时，相位分布的覆盖范围越小，会导致仿真与理论的聚焦位置偏差变大。结论：设计者需要根据需求合理平衡数值孔径、离轴角度等参数，最终实现理想效果。该研究结论对离轴超构透镜的理论分析和实际应用中的参数设计具有重要参考价值。
- 超构透镜 /
- 离轴超构透镜 /
- 设计 /
- 仿真分析
Abstract:
Objective
As a new type of planar optical element, meta-lens can flexibly control the phase, polarization and amplitude of light. They have great potential for device lightweighting and mass manufacturing, and have garnered widespread attention. Off-axis meta-lens, a special type of meta-lens with certain dispersion effect, can be used as a spectral element, providing a unique and feasible way to realize micro instruments. This paper proposes a design method for off-axis meta-lens and analyzes the effects of numerical aperture, off-axis angle, and incident wavelength on the simulation deviation, resolution and focusing efficiency of off-axis meta-lenses, which provides valuable insights for subsequent research and application of off-axis meta-lenses.

Methods
Several off-axis meta-lenses with parameters NA=0.408 α=13°, NA=0.18 α=13°, NA=0.408 α=20° were simulated by Lumerical, respectively.

Results
The simulation results indicate that the off-axis angle is directly proportional to the spectral resolution. As the angle increases, t the spectral resolution becomes larger, but the focusing efficiency decreases. A smaller numerical aperture result in a smaller coverage of the phase distribution, leading to a larger deviation between the simulation and theory.

Conclusion
Designers need to reasonably balance parameters such as numerical aperture and off-axis angle according to the requirements to finally achieve the desired effect. The conclusion of this study is an important reference value for theoretical analysis and parameter design of off-axis meta-lens in practical application.
- meta-lens /
- off-axis meta-lens /
- design /
- simulation analysis

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图 1 离轴超构透镜聚焦示意图

Figure 1. Diagram of focusing an off-axis meta-lens

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图 2 离轴超构透镜设计流程图

Figure 2. Design flowchart of off-axis mate-lens

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图 3 不同半径单元结构对应的相位分布

Figure 3. Phase distribution corresponding to unit structures of different radii

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图 4 仿真结构图

Figure 4. Simulation structure diagram

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图 5 仿真结果图

Figure 5. Simulation result of off-axis mate-lens

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图 6 D=30 μm，α=13°，λ ₀=1.550 μm，f=32.986 μm时的相位分布与仿真结果图

Figure 6. Phase distribution and simulation results for D=30 μm, α=13°, λ₀=1.550 μm, f=32.986 μm

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图 7 D=30 μm，α=13°，λ ₀=1.550 μm，f=80 μm时的相位分布与仿真结果图

Figure 7. Phase distribution and simulation results for D=30 μm, α=13°, λ₀=1.550 μm, f=80 μm

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图 8 $ |\Delta \vec{r}| $ 示意图

Figure 8. Schematic diagram of $ |\Delta \vec{r}| $

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图 9 不同α的离轴超构透镜相位分布图

Figure 9. Phase distribution of off-axis meta-lens with different α

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图 10 α=13°,不同λ入射时离轴超构透镜沿Z轴的光强分布图

Figure 10. The intensity distribution of the off-axis meta-lens along Z axis with different λ incident when α=13°

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图 11 α=20°,不同λ入射时离轴超构透镜沿Z轴光强分布图

Figure 11. Intensity distribution of the off-axis meta-lens along Z axis with different λ incident when α=20°

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图 12 NA=0.408时，不同离轴角度对应的聚焦效率曲线图

Figure 12. Curve plot of focusing efficiency corresponding to different off axis angles at NA=0.408

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表 1 离轴超构透镜设计参数(单位：μm)

Table 1. Main parameters of off-axis meta-lens (Unit: μm)

参数	数值
设计波长（μm）	1.550
焦距（μm）	32.986
离轴角度（°）	13
数值孔径	0.408

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表 2 不同NA的离轴超构透镜理论计算与仿真聚焦位置对比（单位：μm）

Table 2. Comparison of theoretical calculation and simulation focusing positions of off-axis meta-lens with different NA (Unit: μm)

NA	理论聚焦位置x-z	仿真聚焦位置x-z	相对偏差δx-δz
0.408	(7.420, 32.141)	(7.100, 31.200)	(0.320, 0.941)
0.180	(17.996, 77.950)	(14, 62)	(3.996, 15.950)

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表 3 不同NA的离轴超构透镜理论计算与仿真聚焦位置对比（单位：μm）

Table 3. Comparison of theoretical calculation and simulation focusing positions of off-axis meta-lens with different NA (Unit: μm)

NA	理论聚焦位置x-z	仿真聚焦位置x-z	相对偏差δx-δz
0.388	（14.975,29.391）	（14.322,28.416）	（0.653,0.975）
0.371	（18.446,27.347）	（17.638,26.300）	（0.808,1.047）

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表 4 离轴角度α=13°时不同工作波长对应的聚焦效率

Table 4. Focusing efficiency of different working wavelengths at the off-axis angle α=13°

工作波长 λ（μm）	聚焦效率
1.550	59.14％
2.022	29.32％
2.800	18.42％
3.000	17.65％

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