拉盖尔高斯光束矢量远场特性的角谱法分析

Analysis of Vectorial Far-Field Characteristics of Laguerre-Gaussian Beams by Angular-Spectrum Method

基于非傍轴矢量光束传输理论,研究了拉盖尔高斯光束的远场特性。运用角谱衍射公式以及稳相法,得到了初始为线偏振态的拉盖尔高斯光束传输一段距离后的矢量电场分布的解析表示式。数值计算了初始为x方向偏振的拉盖尔高斯光束沿z轴传播时各方向的电场分量及等相面空间分布。结果表明,传输一段距离后,出现了平行于传播方向的电场分量,其强度分布呈双峰结构,且其值远小于垂直电场方向的分量值;随着拓扑荷数的增加,该平行分量增加,光斑发散程度也相应增强。该光束等相面呈螺旋状分布。

Based on the nonparaxial vectorial beam propagation theory, the far-field characteristics of Laguerre Gaussian beams are studied. By using the angular spectrum diffraction formula and the stationary-phase method, the analytic expression of the vectorial electrical field distribution for a Laguerre-Gaussian beam with an initial linear polarization state after some propagation distances is obtained. The electric field components along different directions and the spatial distribution of the equiphase surface are numerically calculated for a Laguerre-Gaussian beam which propagates along the z axis and is initially polarized in the x direction. The results show that, after some propagation distances, the electric field component which is parallel to the propagation direction appears and its intensity distribution shows a double-peak pattern. The value of this component is much lesser than that of the perpendicular component. With the increase of the topological charge, this parallel component increases and the light spot divergence degree enhances. This beam has a helical equiphase surface.