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摘要: 传统光学透镜及光学系统基于光传播效应实现电磁波调控功能，其体积较大、不易集成。而超表面是由人工亚波长尺度单元构成的二维平面结构，由于其相对于传统透镜具有超薄的优势，并且可以实现对光场的任意调控，近年来在光学成像领域得到广泛研究和应用。本文阐述了超表面透镜的工作原理，分析了超表面成像透镜的单色像差和色像差成因以及对应的像质评价方法，之后综述了超表面成像透镜的研究现状及应用，最后总结了超表面在成像领域尚且存在的问题及其未来发展方向。超表面透镜便于集成、设计自由度高，有望在诸多应用领域取代传统成像器件，基于超表面的高效率、大视场、宽带、可重构可调谐成像器件将成为其未来重要发展方向。Abstract: Traditional optical lenses and optical systems implement electromagnetic wave control based on the light propagation effect. So they usually suffer from the bulky size. Recently, metasurfaces comprised of artificial subwavelength structures have been widely studied, since they take great advantages of their subwavelength thickness and provide arbitrary control of electromagnetic waves. Here, the electromagnetic wave control mechanism is introduced. Then, we analyze the monochromatic aberrations and chromatic aberrations of the metalens and the corresponding image quality evaluation methods. Also, we discuss the research progress and applications of metalens for imaging. The exist problems and future goals are pointed out at the end of the review. Based on the advantages of portability and a high degree of design freedom, metalens are expected to replace the traditional imaging devices in many applications. High efficiency, large field of view, broadband, reconfigurable and tunable imaging devices based on metasurfaces will help in important future development directions.
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Key words:
- metasurface /
- imaging /
- electromagnetic wave manipulation /
- aberration /
- image evaluation
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图 1 超表面透镜像差分析。（a）聚焦效率计算示意图。（b）超表面透镜焦平面电场分布图，其中蓝色、红色曲线分别代表衍射极限下的焦平面电场分布和超表面会聚透镜焦平面电场分布。（c）双曲相位分布衍射平面（上）和传统球面单透镜（下）的光学系统示意图及其对应的点列图。（d）消轴外像差超表面透镜结构。（e）衍射光学元件的斯特列尔比分布及不同入射角下的调制传递函数（MTF）。
Figure 1. The aberration analysis of metalens. (a) The schematic of focusing efficiency calculation. (b) The vertical cut of the focal spot of the metalens. The blue line and the red line represent the diffraction-limited intensity profile and the intensity profile of focusing metalens, respectively. (c) The schematics optical system and spot diagrams of metalens with hyperbolic phase profile (top) and traditional spherical lens (bottom). (d) The schematic of metalens designed for off-axis aberration correction. (e) The Strehl ratio and the Modulation Transfer Function (MTF) of the diffractive optical elements at different incidence angles.
图 2 消轴外像差超表面透镜设计。（a）平面超表面透镜（左）和弯曲基板超表面透镜（右）示意图及二者在中心波长1.55 μm、入射角10°条件下的点列图（PSF）[46]。（b）级联透镜校正剩余球差原理示意图（上）及不同角度入射光下级联透镜聚焦光斑的FWHM测量值（下）[58]。（c）超大视场角单层平面超表面透镜示意图（左上）、用于测量不同入射角下聚焦光斑的实验装置示意图（右上）和不同角度入射光下的聚焦光斑测量结果（下）[59]。
Figure 2. Metalens designs for monochromatic aberration correction. (a) Schematics and Point Spread Function (PSF) of a flat lens (left) and an aplanatic metasurface (right) illuminated with parallel monochromatic light at λ=1.55 μm and incident at an angle α=10°[46]. [Reprinted/Adapted] with permission from [ref. 46] © The Optical Society. (b) The operation of the metalens doublet in terms of the correction of spherical aberration (top) and measured FWHM of focal spot intensity profiles at different incident angle θ (bottom)[58]. Reprinted (adapted) with permission from (GROEVER B, CHEN W T, CAPASSO F. Meta-Lens Doublet in the Visible Region[J]. Nano Letters, 2017, 17(8):4902-4907.). Copyright (2017) American Chemical Society. (c) Schematic of a single-layer planar metalens with an ultra-wide FOV (top-left), schematic of experimental setup for imaging a focal spot produced by metasurface at various incident angles (top-right) and measured focusing spots at all incident angles (bottom)[59]. Reprinted (adapted) with permission from (SHALAGINOV M Y, AN S, YANG F, et al.. Single-Element Diffraction-Limited Fisheye Metalens[J]. Nano Letters, 2020, 20(10):7429-7437.). Copyright (2020) American Chemical Society.
图 3 消色差超表面透镜设计。（a）将两个不同波长的光聚焦在同一位置的超表面级联透镜示意图。每层超表面的相位共同提供了两个不同波长下所需的双曲线相位分布[62]。（b）反射式消色差超表面透镜示意图（左）以及工作波长500 nm和550 nm下反射光附加相位与纳米柱宽度的关系（右）[64]。（c）两种集成谐振单元的偏振转换效率（红色）和相位分布（蓝色）图[42]。（d）不同色散特性超表面透镜所需的相对群延迟和相对群延迟色散分布。（e）由超表面校正透镜和传统球面镜构成的光学系统示意图[67]。（f）分区消色差超表面透镜示意图[69]。
Figure 3. Metalens designs for chromatic aberration correction. (a) Schematic diagram of a metasurface cascade lens that focuses two different wavelengths of light at the same position. The phases at each layer together to provide the required hyperbolic phase profiles at the two different wavelengths[62]. Reprinted (adapted) with permission from (ZHOU Y, KRAVCHENKO I I, WANG H, et al.. Multilayer Noninteracting Dielectric Metasurfaces for Multiwavelength Metaoptics[J]. Nano Letters, 2018, 18(12):7529-7537.). Copyright (2018) American Chemical Society. (b) Schematic of an achromatic metalens working in reflection mode (left). Computed reflection phase shift as a function of the nanopillar width at two different wavelength of 500 and 550 nm (right)[64]. Reprinted (adapted) with permission from (KHORASANINEJAD M, SHI Z, ZHU A Y, et al.. Achromatic Metalens over 60 nm Bandwidth in the Visible and Metalens with Reverse Chromatic Dispersion[J]. Nano Letters, 2017, 17(3):1819-1824.). Copyright (2017) American Chemical Society. (c) Polarization conversion efficiency (red curves) and phase profile (blue curves) for integrated-resonant unit elements (IRUEs)[42]. Reprinted (adapted) with permission from (WANG S, WU P C, SU V-C, et al.. A broadband achromatic metalens in the visible[J]. Nature Nanotechnology, 2018, 13(3):227-232.). Copyright (2017) Shuming Wang et al. (d) Required relative group delays (left) and relative group delay dispersion (right) as a function of metalens coordinate. (e) Schematic of a hybrid lens consisting of a metacorrector and a spherical lens[67]. Reprinted (adapted) with permission from (CHEN W T, ZHU A Y, SISLER J, et al.. Broadband Achromatic Metasurface-Refractive Optics[J]. Nano Letters, 2018, 18(12):7801-7808.). Copyright (2018) American Chemical Society. (f) Schematic drawing of a multizone RGB-achromatic metalens showing achromatic focusing of RGB light coming from different lens locations[69]. From [LI Z, LIN P, HUANG Y-W, et al.. Meta-optics achieves RGB-achromatic focusing for virtual reality[J]. Science Advances, 2021, 7(5):eabe4458.]. Reprinted with permission from AAAS.
图 4 可调及可重构超表面透镜设计。（a）氢化反应前后超表面透镜的相位分布以及对应的电场强度分布[89]。（b）可拉伸PDMS衬底超表面示意图（上），纳米棒的长、宽、高以及埋入深度分别为l=240 nm, w=100 nm, h=70 nm, and d=200 nm。不同拉伸比s对应的透射圆偏振光沿光轴的强度分布（左下）以及焦距测量值和计算值（右下）[91]。（c）可调级联超表面透镜示意图。该超表面透镜由一片固定透镜和一片可移动透镜构成[93]。（d）超表面级联透镜成像装置示意图（上）及不同外加电压和成像距离p对应的成像效果（下）[93]
Figure 4. Tunable metalens and reconfigurable metalens. (a) The calculated phase discontinuity profiles and the corresponding full-field intensities of the metalens before and after hydrogenation, respectively[89]. Reprinted (adapted) with permission from (YU P, LI J, ZHANG S, et al.. Dynamic Janus Metasurfaces in the Visible Spectral Region[J]. Nano Letters, 2018, 18(7):4584-4589.). Copyright (2018) American Chemical Society. (b) Schematic illustrations of a metasurface on stretched PDMS (top). Length, width, height and embedded depth of each nanorod is l=240 nm, w=100 nm, h=70 nm, and d=200 nm, respectively. Intensity distributions of transmitted cross-polarized light with different s along the optical axis (left-bottom). Measured (black dots) and calculated (red line) focal length of the lens as a function of s (right-bottom). The error bars represent ranges where intensity is larger than 90% of peak intensity. Inset shows transverse intensity profiles of the focused beam with different s[91]. Reprinted (adapted) with permission from (EE H-S, AGARWAL R. Tunable Metasurface and Flat Optical Zoom Lens on a Stretchable Substrate[J]. Nano Letters, 2016, 16(4):2818-2823.). Copyright (2016) American Chemical Society. (c) Schematic illustration of the proposed tunable lens, comprised of a stationary lens on a substrate, and a moving lens on a membrane[93]. Reprinted (adapted) with permission from (ARBABI E, ARBABI A, KAMALI S M, et al.. MEMS-tunable dielectric metasurface lens[J]. Nature Communications, 2018, 9(1):812.). Copyright (2018) Ehsan Arbabi et al. (d) Schematic illustration of the imaging setup using a regular glass lens and the tunable doublet (top). Imaging results (bottom), showing the tuning of the imaging distance of the doublet and glass lens combination with applied voltage[93]. Reprinted (adapted) with permission from (ARBABI E, ARBABI A, KAMALI S M, et al.. MEMS-tunable dielectric metasurface lens[J]. Nature Communications, 2018, 9(1):812.). Copyright (2018) Ehsan Arbabi et al
表 1 传统透镜和超表面透镜热分析结果
Table 1. Thermal analysis results of conventional optical lens and metalens
工作温度 −40 ℃ 20 ℃ 80 ℃ Ge折射率 3.9797396 4.0047928 4.0297544 Ge热膨胀系数/（℃） 5.70×10−6 Si折射率 3.4083457 3.4179176 3.4274101 Si热膨胀系数/（℃） 2.62×10−6 传统透镜焦距/μm 252.016 250.000 248.025 Si超表面透镜焦距/μm 251.682 251.742 251.762 Ge超表面透镜焦距/μm 248.612 248.753 248.913 
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