论文标题
快速算法以计算激光束的紧密聚焦：循环极化涡流梁系列的有效性作为数学基础
Fast-speed algorithm to compute tight focusing of laser beams: The effectiveness of circularly polarized vortex beam series as a mathematical basis
论文作者
论文摘要
我们建议一种时间效率的算法，以通过高姿势显微镜物镜将直接连续波激光束的紧密聚焦计算为具有任意横截面的光线矢量分布。该算法是基于数学事实，即任何光束都可以分解为圆形极化涡流矢量梁的叠加 - 有限或无限的叠加，这使一个允许一个部分将焦点分解为两个部分，其中一个仅取决于距离的$ρ$和$ρ$和$ Z $，而另一个仅在azimuth $ cylind $ cylind cylind cylind cylind cylind cylind上。我们将建议的算法与该算法进行了比较，该算法是基于双综合理查兹 - 狼狼法的直接使用，并证明对单点计算的速度至少要快5倍，并且对于典型的焦距区域计算，前者至少要更快。
We suggest a time-effective algorithm to calculate tight focusing of a collimated continuous-wave laser beam with an arbitrary cross-section light vector distribution by a high-aperture microscope objective into a planar microcavity. This algorithm is based on the mathematical fact that any beam can be decomposed into a superposition -- either finite or infinite -- of circularly polarized vortex vector beams, which allows one to factorize focal field into two parts, one of which depends only on distance coordinates $ρ$ and $z$ and the other one only on an azimuth $φ$ in cylindrical coordinates. We compare the suggested algorithm with that based on the direct use of the double-integral Richards-Wolf method and demonstrate that the former is at least 5 times faster for single-point computations and at least two orders faster for typical focal-region computations.
