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摘要:
本文提出了一种离轴超构透镜的设计方法，并分析了不同数值孔径、离轴角度等参数对于离轴超构透镜的光谱分辨率、聚焦效率以及仿真结果的影响。利用Lumerical软件分别仿真了参数为
NA =0.408、α =13°；NA =0.180、α =13°及NA =0.408α =20°等多个离轴超构透镜。仿真结果表明：离轴角度与光谱分辨率大小成正相关，离轴角度越大，光谱分辨能力越强，但聚焦效率越低；数值孔径越小，相位分布的覆盖范围越小，会导致仿真聚焦位置与理论值偏差变大。设计者需要根据需求合理平衡数值孔径、离轴角度等参数，最终实现理想效果。本文得出的结论对离轴超构透镜的理论分析和实际应用中的参数设计具有重要参考价值。Abstract:We propose a design method for off-axis meta-lens and analyze the effects of numerical aperture, off-axis angle, and incident wavelength on the simulation deviation, resolution and focusing efficiency of off-axis meta-lenses. Several off-axis meta-lenses with parameters
NA =0.408α =13°,NA =0.180α =13°,NA =0.408α =20° were simulated by Lumerical, respectively. The simulation results indicate that the off-axis angle is directly proportional to the spectral resolution. As the angle increases, the spectral resolution becomes better, but the focusing efficiency decreases. A smaller numerical aperture result in a smaller coverage of the phase distribution, leading to a larger deviation between the simulation and theory. Designers need to reasonably balance parameters such as numerical aperture and off-axis angle according to the requirements to finally achieve the desired effect. This study has an important reference value for theoretical analysis and parameter design of off-axis meta-lens in practical application.-
Key words:
- meta-lens /
- off-axis meta-lens /
- simulation analysis
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图 3 不同半径单元结构对应的相位分布
Figure 3. Phase distribution corresponding to unit structure with different radii
图 4 离轴超构透镜的（a）单元结构仿真示意图 及（b）仿真结构图
Figure 4. (a) Schematic diagram of unit structure simulation and (b) simulated structure diagram of off-axis mate-lens
图 5 离轴超构透镜的Lumerical仿真结果图
Figure 5. Simulation results of off-axis mate-lens by Lumerical
图 6 D=30 μm，α=13°，λ0=1.550 μm，f=32.986 μm时的相位分布与仿真结果图
Figure 6. Phase distributions and simulation results for D=30 μm, α=13°, λ0=1.550 μm, f=32.986 μm
图 7 D=30 μm，α=13°，λ0=1.550 μm，f=80 μm时的相位分布与仿真结果图
Figure 7. Phase distribution and simulation results for D=30 μm, α=13°, λ0=1.550 μm, f=80 μm
图 9 不同α的离轴超构透镜相位分布图
Figure 9. Phase distributions of off-axis meta-lens with different α
图 10 α=13°,不同λ入射时离轴超构透镜沿Z轴的光强分布图
Figure 10. The intensity distributions of the off-axis meta-lens along Z axis with different incident wavelengths when α=13°
图 11 α=20°,不同λ入射时离轴超构透镜沿Z轴光强分布图
Figure 11. Intensity distribution of the off-axis meta-lens along Z axis with different incident wavelengths when α=20°
图 12 NA=0.408时，不同离轴角度对应的聚焦效率曲线图
Figure 12. Curve of focusing efficiency corresponding to different off axis angles at NA=0.408
表 1 离轴超构透镜设计参数
Table 1. Designed parameters of off-axis meta-lens
参数 数值 设计波长/μm 1.550 焦距/μm 32.986 离轴角度/（°） 13 数值孔径 0.408 
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表 2 不同NA（不同焦距f）的离轴超构透镜理论计算与仿真聚焦位置对比
Table 2. Comparison of the focusing positions of off-axis meta-lens with different NA and different focal lengths obtained by theoretical calculation and simulation
(Unit: μm) NA 理论聚焦位置x-z 仿真聚焦位置x-z 相对偏差δx-δz 0.408 (7.420, 32.141) (7.100, 31.200) (0.320, 0.941) 0.180 (17.996, 77.950) (14, 62) (3.996, 15.950)
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表 3 不同NA（不同离轴角度d）的离轴超构透镜理论计算与仿真聚焦位置对比
Table 3. Comparison of the focusing positions of off-axis meta-lens with different NA and different off-axis angles obtained by theoretical calculation and simulation
(Unit: μm) NA 理论聚焦位置x-z 仿真聚焦位置x-z 相对偏差δx-δz 0.388 （14.975,29.391） （14.322,28.416） （0.653,0.975） 0.371 （18.446,27.347） （17.638,26.300） （0.808,1.047）
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表 4 离轴角度α=13°时不同工作波长对应的聚焦效率
Table 4. Focusing efficiencies at different working wavelength at the off-axis angle α=13°
工作波长 λ（μm） 聚焦效率 1.550 59.14％ 2.022 29.32％ 2.800 18.42％ 3.000 17.65％
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