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提出了一种利用数学变换来快速设计环形汇聚光栅反射镜的方法.通过分析具体的物理场景,抽象出已有条形汇聚光栅的“线”汇聚特性与所要设计的“点”汇聚特性在数学上对应的变换关系,然后用该数学变换对条形汇聚光栅进行外形上的变换,外形变换后的条形光栅即为可以实现“点”汇聚的环形光栅.用有限元算法对设计的环形汇聚光栅进行仿真,仿真证明采用该方法设计的环形光栅可以很好地实现高反、高汇聚.采用这一方法,设计了直径为29.788μm的环形光栅反射镜,当垂直入射的径向偏振光从设计的环形光栅表面反射回来后将发生汇聚,汇聚焦点位于环形光栅表面10μm处.经计算,反射镜的数值孔径为0.8302,反射率为0.9163,在焦点所在的汇聚面上,汇聚光栅电场分布的半高宽为1.5548μm.
A method of using the mathematical transformation to design a circular convergent grating mirror is proposed in this paper.By analyzing the specific physical scene, the “” “convergence The convergent characteristics are mathematically related to the transformation relations, and then the mathematical transformation is used to transform the shape of the bar-shaped convergent grating. The transformed bar-shaped grating is a ring grating capable of realizing ”dot" convergence. The simulation results show that the ring grating designed by this method can achieve high reflection and high convergence.An annular grating mirror with a diameter of 29.788μm is designed by this method.When the vertical incidence Of the radial polarized light from the design of the ring grating surface will be reflected after the convergence will focus on the surface of the ring grating located 10μm.After calculation, the mirror numerical aperture of 0.8302, the reflectivity of 0.9163, in the focus of the convergence surface , The half width of the convergent grating electric field distribution is 1.5548 μm.