Radially polarized beams' phase filtering focal properties based on path integral analysis.

This paper introduces the path integral (PI) to the analysis of radially polarized (RP) beams' tight focusing problem. The PI makes the contribution of each incident ray on the focal region visible and then makes it possible to choose the filter's parameters more intuitively and precisely. Based on the PI, a zero point construction (ZPC) phase filtering method is realized intuitively. With ZPC, the focal properties of RP solid and annular beams before and after filtering were analyzed. The results show that the combination of a large NA annular beam and phase filtering can result in superior focus properties.