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摘要:
矢量光场由于其独特的光场分布特性，在许多领域都得到了广泛且深入的研究与应用。传统光场调控手段受限于材料的光学特性及物理尺寸，难以实现灵活高效的动态操控功能。超表面凭借其亚波长结构设计所带来的额外自由度，突破了上述局限，使得对矢量光场的振幅、相位、偏振态乃至传播方向等的独立调控成为可能。本文结合国内外矢量光场领域的基础理论及最新进展，系统地阐述了矢量光场的基本原理及其数学模型，重点介绍了目前超表面生成矢量光场的方法，以及这种矢量光场在聚焦、轨道角动量检测、高精度定位等方面应用的具体案例与创新成果。
Abstract:Due to their unique field distribution properties, vectorial optical fields have been extensively researched and applied across various domains. However, traditional methods for controlling optical fields are limited by material properties and physical dimensions, which restrict flexible and efficient dynamic manipulation capabilities. In contrast, metasurfaces overcome these constraints with subwavelength structural designs that provide additional degrees of freedom for independent control over attributes such as amplitude, phase, polarization, and propagation direction of vectorial optical fields. This paper systematically combines foundational theories with recent advancements in domestic and international research on vectorial optical fields to elucidate the fundamental principles and mathematical models underlying them. It particularly focuses on current methodologies using metasurfaces to generate vectorial optical fields, along with specific case studies and innovative outcomes in applications including focusing, orbital angular momentum detection, and high-precision positioning.
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Key words:
- vectorial optical field /
- metasurfaces /
- light field control
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图 1 几种常规模式和柱对称矢量模式瞬时电场的空间分布[37]。(a) x偏振高斯基模；(b) x偏振HG10模式；(c) x偏振HG01模式；(d) y偏振HG01模式；(e) y极化HG01模式；(f) x偏振LG01模式；(g)径向极化模式；(h)角向偏振模式；(i)广义圆柱矢量光束
Figure 1. Spatial distribution of instantaneous electric vector field for several conventional modes and CV modes[37]. (a) x-polarized fundamental Gaussian mode; (b) x-polarized HG10 mode; (c) x-polarized HG01 mode; (d) y-polarized HG01 mode; (e) y-polarized HG01 mode; (f) x-polarized LG01 mode; (g) Radially polarized mode; (h) Azimuthally polarized mode; (i) Generalized CV beams
图 5 时空涡流管到涡流环的保角映射仿真[76]。时空涡旋管相位Ф1(x, y)在自由空间传播并转换，成为涡流环后，第二相位掩模Ф2(u, v)可以被应用于准直，颜色坐标表示展开相位的大小
Figure 5. Conformal mapping simulation of a spatiotemporal vortex tube transforming into a vortex ring[76]. The spatial-temporal vortex tube phase Ф1(x, y) propagates and evolves in free space to become a vortex ring, after which a second phase mask Ф2(u, v) can be applied for collimation, with color coding representing the magnitude of the expanded phase
图 6 基于狭缝结构的超表面矢量光束生成系统。He-Ne，He-Ne laser：氦氖激光器；DF：强度滤波器；QWP：四分之一波片；P1，P2：偏振片；S：样品；MO：显微镜物镜；CCD：电荷耦合器件；GLP1，GLP2：Glan激光偏振器；MS：超表面；Lens：透镜。(a)不同阶次的柱状矢量场生成装置[78]；(b) 基于超表面的光学针场生成系统配置示意图(光学针场用紫色箭头表示)[79]；(c)利用超表面的矢量涡旋光束生成装置[80]
Figure 6. System configuration for vector beam generation based on a slit-structured metasurface. He-Ne, He-Ne laser: Helium-neon laser; DF: Intensity filter; QWP: Quarter-wave plate; P1, P2: Polarizers; S: Sample; MO: Microscope objective lens; CCD: Charge-coupled device; GLP1, GLP2: Glan laser polarizers; MS: Metasurface; Lens: Lenses. (a) Apparatus for the generation of different orders of cylindrical vector fields[78]; (b) Schematic diagram of the optical needle field generation system configuration using a metasurface (the optical needle field is represented by purple arrows)[79]; (c) Setup for generating vector vortex beams utilizing a metasurface[80]
图 7 用于矢量光场生成的柱状纳米结构的超表面和级联超表面。(a)由六边形单元组成的超表面的侧视图(左)和俯视图(右)[81]；(b)六边形单元中的椭圆形非晶硅柱结构[81]；(c-e)是q = 0.5、1.0和1.5的级联超表面近光轴分布示意图[83]；(f-h) q = 0.5, 1.0和1.5的超表面的交叉偏振显微图像，这里q是由超表面单元结构的位置变化和慢轴取向决定的一个常数[83]；(i)生成三维柱状矢量光场的超表面纳米结构和SEM图像[87]
Figure 7. Cylindrical nanostuctured metasurfaces and cascaded metasurfaces for vector optical field generation. (a) Side view (left) and top view (right) of a metasurface composed of hexagonal units[81]; (b) Elliptical amorphous silicon pillar structure within the hexagonal unit cell[81]; (c-e) Schematic illustrations of near-axis distributions for cascaded metasurfaces with topological charges q = 0.5, 1.0, and 1.5, respectively[83]; (f-h) Cross-polarized microscopy images of metasurfaces with q values of 0.5, 1.0, and 1.5, where q is a constant determined by the positional variation and slow axis orientation of the metasurface unit structures[83]; (i) Nanoscale structure of the metasurface for generating three-dimensional cylindrical vector optical fields accompanied by SEM images[87]
图 8 流线型金属透镜的概念图[89]。通过圆偏振点光源辐射获得时间反转电场(蓝色箭头)源，并且可以由具有空间变化的各向异性轴的半波片产生。红色流线是由上述空间变化的各向异性轴形成的矢量场的轨迹(橙色箭头)获得的
Figure 8. Concept illustration of the streamlined metalens[89]. The time-reversed electric fields (blue arrows) are obtained by the radiation of a circularly polarized point source and could be generated by a half-wave plate with spatially variant anisotropic axes. The red streamline is obtained by the trajectory of the vectorial field (orange arrows) formed by spatially variant anisotropic axes mentioned above
图 10 MIM超表面结构[102]。(a) 超表面的结构，其中黄色环为双纳米棒结构，浅棕色环为单纳米棒结构。插图：结构放大图；(b) 第一个环中的一个扇区；(c) 双纳米棒结构；(d) 单纳米棒结构
Figure 10. MIM metasurface structure[102]. (a) The metasurface configuration, where yellow rings denote double-nanorod structures and light brown rings represent single-nanorod structures. Inset: Magnified view of the structure; (b) A sector within the first ring; (c) Detailed illustration of the double-nanorod structure; (d) Single-nanorod structure depicted explicitly
图 11 超表面的轨道角动量检测。(a)全息表面的结构[105]；(b)仿真生成的干涉图[105]；(c)仿真结果的二值化图像[105]；(d)全息表面的扫描电子显微镜照片，凹槽在等相位置[105]；(e) LCP入射时的OAM探测器[106]；(f-h) 携带不同拓扑荷的涡旋光束((f) l= 0，(g) l=−1，(h) l=−2) 入射时OAM探测器的模拟强度分布图[106]；(i) 左图为具有π/4相位步进的八段Si截止线螺旋相位板的光学显微图像，右图为该结构的SEM图像及相应的涡旋光束强度分布图[106]
Figure 11. Orbital angular momentum detection with a metasurface. (a) Structure of the holographic metasurface[105]; (b) Simulated interference pattern generated[105]; (c) Binary representation of the simulated results[105]; (d) Scanning electron microscope (SEM) image of the holographic surface, showing grooves at phase-matched positions[105]; (e) The OAM detector upon left-handed circularly polarized (LCP) incidence[106]; (f-h) Simulated intensity distributions of the OAM detector when illuminated by vortex beams carrying different topological charges: (f) l = 0, (g) l = −1, and (h) l = −2[106]; (i) Optical micrograph of an eight-segment silicon cutoff-line spiral phase plate with π/4 phase steps on the left, and on the right, the SEM image of this structure alongside its corresponding vortex beam intensity distribution map[106]
图 12 纳米颗粒定位[112]。(a) 显微镜物镜将径向偏振光束紧密聚焦在玻璃基板上的硅天线上，浸油物镜将NA在(0.95，1.3)之间的光收集并聚焦，CCD在后焦面上；(b) 光轴上的天线的远场强度分布图；(c) 横向位移为40 nm的远场强度分布图
Figure 12. Nanoparticle localization[112]. (a) A microscope objective tightly focuses a radially polarized light beam onto silicon antennas on a glass substrate, where an oil-immersion objective collects and focuses light with numerical aperture (NA) ranging between 0.95 to 1.3, and a CCD is positioned at the rear focal plane; (b) Far-field intensity distribution diagram of the antenna along the optical axis; (c) Far-field intensity distribution diagram for a lateral displacement of 40 nm
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