Gao Yang, Liu Jianlong, Zhang Xueru, Wang Yuxiao, Song Yinglin, Liu Shutian, Zhang Yan
Department of Physics, Harbin Institute of Technology, Harbin, China.
Opt Express. 2012 Jan 16;20(2):1320-9. doi: 10.1364/OE.20.001320.
A theoretical analysis based on scalar diffraction theory about the recently reported focal-shift phenomena in planar metallic nanoslit lenses is presented. Under Fresnel approximation, an axial intensity formula is obtained, which is used to analyze the focal performance in the far field zone of lens. The relative focal shift is totally dependent on the Fresnel number only. The influences of the lens size, preset focal length and incident wavelength can be attributed to the change of Fresnel number. The total phase difference of the lens is approximately equal to the Fresnel number multiplied by π. Numerical simulations performed using finite-difference time-domain (FDTD) and near-far field transformation method are in agreement with the theoretical analysis. Using the theoretical formula assisted by simple numerical method, we provide predictions on the focal shift for the previous literatures.
本文基于标量衍射理论，对平面金属纳米狭缝透镜中最近报道的焦移现象进行了理论分析。在菲涅耳近似下，得到了轴向强度公式，用于分析透镜远场区域的聚焦性能。相对焦移完全仅取决于菲涅耳数。透镜尺寸、预设焦距和入射波长的影响可归因于菲涅耳数的变化。透镜的总相位差近似等于菲涅耳数乘以π。使用时域有限差分法（FDTD）和近远场变换方法进行的数值模拟与理论分析一致。利用理论公式并辅以简单的数值方法，我们对先前文献中的焦移进行了预测。
