摘要:
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.
Abstract:
A new approach to designing planar, high numerical aperture, low loss, focusing reflectors using circular subwave-length high contrast gratings is presented. Through analyzing particular physical scene, a mathematical transformation from existing “focus line” convergent beam, which can be achieved by bar grating reflector, to the convergent beam with a“focus point”, is obtained. By changing the shape of the bar grating reflector with the mathematical transforma-tion obtained, a circular grating reflector, which can achieve “focus point” convergent beam, is obtained. The focusing properties and reflection characteristic of the circular grating reflector are numerically studied with the finite element method. After the radially polarized light reflected from circular grating reflector with a diameter of 29.788 μm, the beam will focus at 10 μm away from the reflector, resulting in a numerical aperture of 0.8302 and a reflectivity of 0.9163. In the focal plane, the numerical simulation results present a field distribution with a full width half maximum value of 1.5548 μm, which is extremely close to diffraction limit.
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