Design of broadband achromatic far-infrared metalens based on chalcogenide glass using parameterized topology optimization
doi: 10.37188/CO.EN-2025-0003
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摘要:
超透镜技术在小型化、集成化红外成像系统中有着广泛的应用。然而，由于单元结构的较高色散，超透镜经常出现色差，使得宽带消色差红外成像难以实现。该文章构建了基于硫系玻璃的6种不同单元结构，并对其相位色散参数进行分析，建立数据库。在此基础上，采用色差补偿和参数化伴随拓扑优化的方法，在远红外波段将这6种单元结构排列组合，设计出数值孔径为0.5的宽带消色差超透镜。仿真结果表明，该超透镜在9~11µm的工作波长范围内实现了近衍射极限聚焦，具有良好的消色差性能，全波长具有为54%~58%的平坦的聚焦效率。
Abstract:Metalens technology has been applied extensively in miniaturized and integrated infrared imaging systems. However, due to the high phase dispersion of unit structures, metalens often exhibits chromatic aberration, making broadband achromatic infrared imaging challenging to achieve. In this paper, six different unit structures based on chalcogenide glass are constructed, and their phase-dispersion parameters are analyzed to establish a database. On this basis, using chromatic aberration compensation and parameterized adjoint topology optimization, a broadband achromatic metalens with a numerical aperture of 0.5 is designed by arranging these six unit structures in the far-infrared band. Simulation results show that the metalens achieves near diffraction-limited focusing within the operating wavelength range of 9−11 µm, demonstrating the good performance of achromatic aberration with flat focusing efficiency of 54%−58% across all wavelengths.
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Key words:
- metalens /
- chalcogenide glass /
- topology optimization /
- high efficiency /
- long wave infrared /
- broadband operation
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图 1 (a) 消色差超透镜示意图；(b) 消色差超透镜的相位轮廓示意图
Figure 1. (a) Schematic for achromatic metalens; (b) Schematic for Phase profile of an achromatic metalens
图 2 六种不同单元结构的侧面和顶部视图
Figure 2. The side and top views of the six different unit structures
图 3 (a) 单元结构相位模拟结果；(b) 实心方柱结构相位-色散参数分布，其中红叉和蓝点分别代表实际方柱结构和理论结构的相位-色散参数；(c) 所有单元结构的相位-色散参数数据库；(d) 每个位置上最接近理论结构的初始结构的相位-色散参数分布
Figure 3. (a) Phase simulation results of unit structure; (b) Distributions of the phase-dispersion parameters for the solid square column structure, where red cross and blue point represent the phase-dispersion parameters of an actual square column structure and the theoretical structure, respectively; (c) Database of the phase-dispersion parameters for all unit structures; (d) Distributions of the phase-dispersion parameters of the initial structure closest to theoretical structures for each position
图 4 参数化伴随拓扑优化的工作流程图
Figure 4. The workflow of the parameterized adjoint topology optimization process
图 5 (a) 前向模拟光路；(b) 伴随模拟光路
Figure 5. (a) Forward simulation light path; (b) Adjoint simulation light path
图 6 (a) 单元结构变化示意图；(b) 迭代步长为0和40次后超透镜的归一化相位分布；(c) 不同入射波长对应的聚焦效率随优化迭代步长的变化
Figure 6. (a) Schematic diagram of the unit structures changes; (b) The normalized phase distribution of the metalens after the iteration step of 0 and 40; (c) Variation of focusing efficiency corresponding to different incident wavelengths concerning the step of optimization iterations
图 7 (a) x-z平面归一化光强分布，白色虚线表示180 µm位置；(b) 在x-y平面上焦点处的归一化光强分布
Figure 7. (a) Distribution of normalized light intensity on the x-z plane, with the white dashed line indicating the position at 180 µm; (b) Distribution of normalized light intensity at the focal point on the x-y plane
图 8 (a) 不同波长对应的焦距；(b) 不同波长对应的FWHM，以及满足衍射极限的相应FWHM
Figure 8. (a) Focal lengths at different wavelengths; (b) FWHM values at different wavelengths, and corresponding FWHM values that meet the diffraction limit
图 9 超透镜在不同波长下的聚焦效率
Figure 9. Focusing efficiency of the metalens at different wavelengths
图 10 (a) 原始图像；(b) 在9~11µm波长范围的模拟图像
Figure 10. (a) The original image; (b) The simulated image in the wavelength range of 9-11 µm
表 1 Summary of performances for broadband achromatic metalens
Table 1. Summary of performances for broadband achromatic metalens
NA Operating wavelength (µm) Diameter (µm) Average focusing efficiency Polarization Ref. 0.6 0.45−0.75 6 45% Insensitive [11] 0.6 0.63 20 65% Circular [10] 0.11 0.62 112 45% Circular [24] 0.38 3−5 30 46.5% Insensitive [8] 0.56 0.64 10.2 50% Circular [25] 0.82 15.5 50 72% Circular [26] 0.54 8.6−11.4 191.4 38.2% Circular [27] 0.5 9−11 204 56% (54−58%) Insensitive This paper 
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