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摘要:
为深入研究在几何相位原理作用下的超构表面成像功能，本文利用超透镜的几何相位成像原理推导出任意曲线的成像公式，并利用标量衍射理论验证其可行性与正确性，同时将此理论应用于入射光偏振状态的检测中。结果表明，基于几何相位原理的超构表面相位调控能实现任意曲线的成像以及对入射光偏振状态检测的功能，这对于全息成像、光通信、量子科学等领域的研究都有一定的启发意义。
Abstract:In order to investigate the imaging function of metasurface based on geometric phase theory, this article deduces the imaging formulation of arbitrary curve with the theory of geometric phase imaging on metalens, and its feasibility and correctness is verified by scalar diffraction theory. The imaging formulation is further applied in polarization detection of the incident beam. The results show that phase manipulation of metasurface based on geometric phase can achieve the functions of arbitrary curve imaging and polarization detection of the incident beam, which is of great significance in the field of holographic imaging, optical communication and quantum science.
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图 1 不同几何相位设计实现不同成像功能的示意图。(a)在焦平面实现任意曲线成像；(b) 定性检测入射光偏振类型；(c) 定量检测线偏振光偏振方向，A为圆上的第j个点，AP为入射线偏振光的方向，AQ为点A处线偏振光的方向，AQ经过圆心
Figure 1. Schematic of different fuctions by phase design. (a) arbitrary curve imaging on focal plane; (b) detecting the polarization state of incident light qualitatively; (c) detecting the polarization direction of linearly polarized light quantitavely, A is the jth point on the circle, AP is the direction of incident linearly polarized light, AQ is the exact direction of linearly polarized light on point A, and AQ passes through the center of the circle
图 2 超构表面单元结构及其透射率。(a) 超构表面单元结构；(b) 同极化圆偏振光(虚线)和交叉极化圆偏振光(实线)的透射率
Figure 2. The unit cell of the metasurface and its transmittance. (a) The unit cell of the metasurface; (b) the transmittance of circularly co-polarized light (dashed line) and circularly cross-polarized light (solid line)
图 3 不同超构表面单元数下单个焦点的归一化强度图。(a) N =100; (b) N=250; (c) N=500; (d) N=
1000 Figure 3. Normalized intensity of single point under different numbers of meta-atoms. (a) N =100; (b) N=250; (c) N=500; (d) N=
1000 
图 4 焦平面处的光强分布。(a) 椭圆；(b) 圆；(c) 抛物线；(d) 三角形；(e) 正方形；(f) 字母“LZU”
Figure 4. The intensity distribution on focal plane. (a) an ellipse; (b) a circle; (c) a parabola; (d) a triangle; (e) a square; (f) the letters “LZU”
图 5 不同偏振的入射光及其对应的图像。(a)左旋圆偏振光入射；(b) 左旋椭圆偏振光入射；(c) 线偏振光入射；(d) 右旋椭圆偏振光入射；(b) 右旋圆偏振光入射。左侧表示入射的偏振状态，右侧表示相应偏振态入射时焦平面处的图像
Figure 5. Different polarization states of incident beam and their corresponding result figures. (a) incident with LCP light; (b) incident with left-handed elliptically polarized light; (c) incident with linear polarized light; (d) incident with right-handed elliptically polarized light; (e) incident with RCP light. The left denotes the incident polarized state and the right denotes corresponding result figures on focal plane
图 6 光强随极角变化的图像及其归一化强度分布曲线。入射偏振光的旋转角度分别是(a)
$ 0 $ ，(b)$ \dfrac{\mathrm{{\text{π}} }}{4} $ ，(c)$ \dfrac{\mathrm{{\text{π}} }}{2} $ ，(d)$ \dfrac{3\mathrm{{\text{π}} }}{4} $ 。图中第一行左侧箭头表示入射线偏振光的方向，右侧箭头表示焦平面前偏振片传输轴的方向Figure 6. Different figures of which the intensity varies with the polar angle and their normalized intensity distribution curves. The rotation angles of incident polarized light are (a)
$ 0 $ , (b)$ \dfrac{\mathrm{{\text{π}} }}{4} $ , (c)$ \dfrac{\mathrm{{\text{π}} }}{2} $ , (d)$ \dfrac{3\mathrm{{\text{π}} }}{4} $ ,respectively. The left arrow in the first row shows the direction of incident polarized light, while the right arrow shows the transmission axis of the analyzer before the focal plane -
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