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基于单层超表面结构, 设计并制作了一种具有大焦深的离轴超透镜. 利用相位叠加的设计方法, 将偏转与聚焦这两个功能合二为一以实现离轴聚焦, 并通过优化入射孔径和离轴偏转角来增大焦深. 实验结果表明: 当入射电磁波的频率为9 GHz时, 离轴偏转角为27.5°, 焦距为335.4 mm, 这与30° 和350 mm 的预设值比较符合. 在8, 9和10 GHz三个频率下的焦深分别为263.2, 278.5和298.2 mm, 分别对应波长的7.02倍、8.36倍和9.98倍. 该离轴超透镜结构简单, 具有良好的离轴聚焦能力和较大的焦深, 这在小型化、平面化的大焦深成像系统以及离轴光学系统中具有潜在的应用前景 .
A kind of off-axis meta-lens with large focal depth based on a single-layer metasurface is designed and fabricated. Our proposed off-axis focus is realized by combining the two functions of deflection and focus through phase superposition method, and the focal depth can be increased by optimizing the input aperture and off-axis deflection angle. Three-dimensional finite difference time domain (FDTD) method is used for numerical simulation to construct the off-axis meta-lens, then the off-axis meta-lens is fabricated and its focus performance is tested in a microwave anechoic chamber. Experimental results indicate that at the designed electromagnetic wave frequency (9 GHz), the measured off-axis deflection angle is 27.5° and the focal length is 335.4 mm, which agree with the designed values of 30° and 350 mm. The measured full-wave half-maximum (FWHM) at the focal point is 48.2 mm, however, the simulated FWHM is 40.2 mm, which means that the imaging quality of the measured focus spot is slightly worse than the simulated one. This is mainly due to the fact that the actual parameters of the fabricated meta-lens are inconsistent with simulated parameters. In addition, during the measurement, the large sampling interval in the x- direction also leads to experimental errors. The focusing efficiency of the off-axis meta-lens at the working frequency of 9 GHz is calculated to be 16.9%. The main reason for the low focusing efficiency is that the plasmonic metasurface works in the transmission mode, which can manipulate only the cross-polarized component of the incident wave, and the maximum efficiency will not exceed 25%. Moreover, the focal depths at 8 GHz, 9 GHz and 10 GHz are 263.2 mm, 278.5 mm and 298.2 mm, respectively, which are 7.02 times, 8.36 times and 9.98 times the corresponding wavelengths, indicating that a larger focal depth off-focus meta-lens is achieved. This kind of off-axis meta-lens has a simple structure, good off-axis focus ability and large focal depth, which has potential applications in a compact and planar off-axis optical system and large focal depth imaging system. Although the working waveband in this article is the microwave band, according to the size scaling effect of the metasurface, it is also possible to design a large focal depth off-axis meta-lens in other bands such as visible light and terahertz bands by using the same method. -
Keywords:
- metasurface /
- meta-lens /
- large focal depth /
- phase superposition
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图 1 (a)基于超表面的波束偏转器; (b)常规的共轴超透镜; (c)离轴超透镜
Fig. 1. (a) Beam deflector based on metasurface; (b) conventional on-axis meta-lens; (c) off-axis meta-lens.
图 2 (a)离轴超透镜的天线单元; (b)当频率为9 GHz的x偏振波垂直入射到天线单元时, 正交偏振波的透射率和透射相位随lx的变化关系; (c)满足(3)式的相位分布
Fig. 2. (a) Antenna unit of the off-axis meta-lens; (b) when an x-polarized wave with frequency of 9 GHz is incident perpendicularly onto the antenna units, transmittance and transmission phase of the orthogonal polarized wave vary with lx; (c) phase distributions satisfying Eq. (3).
图 3 (a)制备的超表面样品的正面结构照片, 矩形红色虚线为局部放大图; (b)实验装置
Fig. 3. (a) Image of the fabricated metasurface sample, and the rectangular red dotted line is a zoom view; (b) experimental set-up.
图 4 测试得到的不同频率处正交偏振波的电场强度分布 (a) 8 GHz; (b) 9 GHz; (c) 10 GHz. 红色点划线代表聚焦平面所在的位置, 倾斜的白色虚线代表u1轴、u2轴和u3轴
Fig. 4. Measured electric field intensity distributions of the orthogonal polarized waves at different frequencies: (a) 8 GHz; (b) 9 GHz; (c) 10 GHz. The red dotted lines represent the position of the focal planes, and the white dashed lines represent the u1 axis, u2 axis and u3 axis.
图 5 工作频率9 GHz处, 透镜焦点处归一化电场强度分布 (a)仿真结果; (b)实验结果
Fig. 5. At the working frequency of 9 GHz, the normalized electric field intensity distribution at the focal point of the metalens: (a) Simulation result; (b) experimental result.
图 6 测试得到的不同频率处的焦深 (a) 8 GHz; (b) 9 GHz; (c) 10 GHz
Fig. 6. Depth of focus at different frequencies: (a) 8 GHz; (b) 9 GHz; (c) 10 GHz.
表 1 离轴超透镜的仿真结果和实验结果比较
Table 1. Simulation and experimental results of the off-axis metalens.
入射波频
率/GHz仿真结果 实验结果 α/(°) F0/mm DOF/mm α/(°) F0/mm DOF/mm 8 33.2 302.5 223.6 30.5 278.9 263.2 9 30.0 350.0 241.9 27.5 335.4 278.5 10 26.8 385.3 254.3 23.6 400.2 298.2 
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[1] Yu N F, Capasso F 2014 Nat. Mater. 13 139
Google Scholar
[2] Sun S L, H Q, Hao J M, Xiao S Y, Zhou L 2019 Adv. Opt. Photonics 11 380
Google Scholar
[3] Bi Y, Huang L L, Li X W, Wang Y T 2021 Front. Optoelectron 14 154
[4] Wan Lei Pan D P, Feng T H, Liu W P, Potapov A A 2021 Front. Optoelectron. 14 1
Google Scholar
[5] Scheuer J 2017 Nanophotonics 6 137
Google Scholar
[6] Chen S Q, Li Z C, Liu W W, Cheng H, Tian J G 2019 Adv. Mater. 31 16
[7] Liu T J, Huang L R, Hong W, Ling Y H, Luan J, Sun Y L, Sun W H 2017 Opt. Express 25 16332
Google Scholar
[8] Ding J F, Huang L R, Liu W B, Ling Y H, Wu W, Li H H 2020 Opt. Express 28 32721
Google Scholar
[9] Pan W, Wang X Y, Chen Q, Ren X Y, Ma Y 2020 Front. Optoelectron. 16 6
[10] Ji C, Song J K, Huang C, Wu X Y, Luo X G 2019 Opt. Express 27 34
Google Scholar
[11] Ling Y H, Huang L R, Hong W, Liu T J, Luan J, Liu W B, Wang Z Y 2017 Opt. Express 25 29812
Google Scholar
[12] Khorasaninejad M, Zhu A Y, Roques-Carmes C, Chen W T, Oh J, Mishra I, Devlin R C, Capasso F 2016 Nano Lett. 16 7229
Google Scholar
[13] Zhuang Z P, Chen R, Fan Z B, Pang X N, Dong J W 2019 Nanophotonics 8 1279
Google Scholar
[14] Chen W T, Zhu A Y, Sisler J, Bharwani Z, Capasso F 2019 Nat. Commun. 10 1
Google Scholar
[15] Wang S M, Wu P C, Su V C, Lai Y C, Chu C H, Chen J W, Lu S H, Chen L, Xu B B, Kuan C H, Li T, Zhu S, Tsai D P 2017 Nat. Commun. 8 187
Google Scholar
[16] Fan Z B, Qiu H Y, Zhang H L, Pang X N, Zhou L D, Liu L, Ren H, Wang Q H, Dong J W 2019 Light Sci. Appl. 8 67
Google Scholar
[17] Groever B, Chen W T, Capasso F 2017 Nano Lett. 17 4902
Google Scholar
[18] Chen Q M, Li Y, Han Y H, Deng D, Yang D H, Zhang Y, Liu Y, Gao J M 2018 Appl. Opt. 57 7891
Google Scholar
[19] Paniagua-Dominguez R, Yu Y F, Khaidarow E, Choi S, Leong V, R, Bakker M, Liang X N, Fu Y H, Valuckas V, Krivitsky L A, Kuznetsov A I 2018 Nano Lett. 18 2124
Google Scholar
[20] 范庆斌, 徐挺 2017 物理学报 66 144208
Google Scholar
Fan Q B, Xu T 2017 Acta Phys. Sin. 66 144208
Google Scholar
[21] 杨皓明 2008 博士学位论文(天津: 南开大学)
Yang H M 2008 Ph. D. Dissertation (Tianjin: Nankai University) (in Chinese)
[22] Khorasaninejad M, Chen W T, Oh J, Capasso F 2016 Nano Lett. 16 3732
Google Scholar
[23] Zhu A Y, Chen W T, Khorasaninejad M, Oh J, Zaidi A, Mishra I, Devlin R C, Capasso F 2017 APL Photonics 2 036103
Google Scholar
[24] Zhou Y, Chen R, Ma Y G 2017 Opt. Lett. 42 4716
Google Scholar
[25] Zhu A Y, Chen W T, Sisler J, Yousef K M A, Lee E, Huang Y W, Qiu C W, Capasso F 2019 Adv. Opt. Mater. 7 1801144
Google Scholar
[26] Ou K, Li G H, Li T X, Yang H, Yu F L, Chen J, Zhao Z Y, Cao G T, Chen X S, Lu W 2018 Nanoscale 10 19154
Google Scholar
[27] Zhao H, Quan B G, Wang X K, Gu C Z, Li J J, Zhang Y 2018 ACS Photonics 5 5
[28] Chen W T, Khhorasaninejad M, Zhu A Y, Oh J, Devlin R C, Zaidi A, Capasso F 2017 Light Sci. Appl. 6 e16259
Google Scholar
[29] Chen C, Song W, Chen J W, Wang J H, Chen Y H, Xu B B, Chen M K, Li H M, Fang B, Chen J, Kuo H Y, Wang S M, Tsai D P, Zhu S, Li T 2019 Light Sci. Appl. 8 99
Google Scholar
[30] Zhou Y, Chen R, Ma Y G 2018 Appl. Sci. 8 3
[31] Banerji S, Meem M, Majumder A, Vasquez F G, Sensale-Rodriguez B, Menon R 2019 Optica 6 6
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