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摘要:偏振成像技术在目标探测、生物医学等领域具有重要应用价值，基于超构表面设计的偏振成像系统可以有效避免传统偏振成像系统存在的结构复杂、体积和质量大等问题，有利于实现光学系统微型化、轻量化和集成化。然而，传统超构表面设计方法忽略了超构表面结构的局部非周期性引起的近场电磁耦合，在大数值孔径的条件下会严重影响器件的衍射效率。为了解决这个问题，本文提出了一种基于边界优化的偏振复用超构透镜设计方法，并由此设计了一种能对 x和 y偏振光独立调控的大数值孔径(~0.94)偏振成像超构透镜。在基于人工择优初始结构的优化设计中，通过参数扫描、人工择优的传统设计方法得到超构透镜初始结构，然后通过边界优化方法对超构透镜进行进一步的优化，其衍射效率相比于优化前可以提高20%左右；在基于均匀阵列初始结构的优化设计中，通过20次左右的迭代，超构透镜衍射效率可以达到92%左右。本文提出的优化设计方法可有效提高偏振复用超构表面器件效率，并且能够简化多功能超构表面的设计步骤，在偏振成像、光通信等领域具有应用前景。Abstract:Polarization imaging technology has important application value in target detection, biomedicine, and other fields, but traditional polarization imaging systems suffer from complex structures, large volume, and heavy weight. The polarization imaging system based on metasurfaces can avoid these problems effectively, which is conducive to the development of miniaturized, lighter and easily-integrated optical systems. However, the traditional design method for metasurfaces ignores near-field electromagnetic coupling caused by the local aperiodicity, which will seriously affect the diffraction efficiency of metalenses, especially if they have a large numerical aperture. To solve this problem, a general method for designing polarization-multiplexed metalenses based on boundary optimization is proposed in this paper, and a polarization imaging metalens with a large numerical aperture (~0.94) is designed, which can independently control x- and y-polarized light. For the optimization design with artificially optimal initial structures, the traditional design method of parameter scanning and manual selection was used to obtain the initial structure of the metalens, and then it was further optimized by the boundary optimization, resulting in about 20% improvement of the diffraction efficiency compared with that before optimization. For the optimization design with a uniform array as the initial structure, the diffraction efficiency can reach about 92% after about 20 iterations. The optimized design method proposed in this paper can effectively improve the efficiency of polarization-multiplexed metasurfaces, showing promising applications in polarization imaging, optical communication, and other fields.
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图 1边界优化原理及流程示意图。(a) 正向仿真；（b）伴随仿真；(c) 优化算法流程图
Figure 1.Schematic diagram of boundary optimization principle and process. (a) Forward simulation. (b) Adjoint simulation. (c) Flow chart of the optimization algorithm
图 2(a)单元结构示意图；(b)64个单元结构的传输相位响应
Figure 2.(a) Schematic diagram of a unit cell; (b) propagation phase responses of 64 unit cells
图 3优化前后纳米柱沿(a)x方向和(b)y方向的宽度变化；(c)部分纳米柱优化前后对比图
Figure 3.Width changes of nanofins along the (a)x-direction and (b)y-direction before and after optimization. (c) Comparison of part of nanofins before and after optimization
图 4优化前(a)x偏振光和(b)y偏振光入射下的xz平面光强分布；优化后(c)x偏振光和(d)y偏振光入射下的xz平面光强分布；(e)~(h)沿着(a)~(d)中虚线绘制的归一化强度分布
Figure 4.Intensity distributions in thexzplane before optimization under the illumination of (a)x-polarized light and (b)y-polarized light. Intensity distributions in thexzplane after optimization under the illumination of (c)x-polarized light and (d)y-polarized light. (e)~(h) Normalized intensity profiles along the dashed lines are shown in (a)~(d)
图 5x偏振光入射时，(a)优化前和(b)优化后的相位分布；y偏振光入射时，(c)优化前和(d)优化后的相位分布
Figure 5.The phase distributions (a) before and (b) after optimization for the incident ofx-polarized light. The phase distributions (c) before and (d) after optimization for the incident ofy-polarized light
图 6优化过程中超构透镜的(a)绝对效率和(b)衍射效率
Figure 6.(a) Absolute efficiency and (b) diffraction efficiency of the optimized metalens during optimization
图 7(a)x偏振光和(b)y偏振光入射下，不同初始结构的超构透镜的绝对效率；(c)x偏振光和(d)y偏振光入射下，不同初始结构的超构透镜的衍射效率
Figure 7.Absolute efficiency of five metalenses with different initial structures during optimization under illumination of (a)x-polarized light and (b)y-polarized light. Diffraction efficiency of five metalenses with different initial structures during optimization under illumination of (c)x-polarized light and (d)y-polarized light
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