We theoretically show how, using a cylindrical lens, a Gaussian beam with a finite number of parallel zero-intensity lines (edge dislocations) is transformed into a vortex beam that carries orbital angular momentum (OAM) and topological charge (TC). Remarkably, while the original beam is assumed to carry a non-zero OAM and have no TC, the latter is shown to appear during free-space propagation. Considering two parallel center-symmetric zero-intensity lines located as an example, we look into the dynamics of generating two intensity nulls at the double focal length: with increasing distance between the vertical zero-intensity lines, two optical vortices are first generated on the horizontal axis before converging at the origin and then diverging along the vertical axis. Irrespective of the between-line distance, such an optical vortex has ${\rm TC} = - {2}$ at any distance from the optical axis, except for the original plane. With changing distance between the zero-intensity lines, the OAM that the beam carries is changing, taking positive and negative values, or a zero value at a certain between-line distance. We also show that if the number of zero-intensity lines is infinite, a vortex beam with finite OAM and infinite TC is generated.

中文翻译：

---

将边缘位错数组转换为多涡旋光束

我们从理论上说明了如何使用圆柱透镜将有限数量的平行零强度线（边缘错位）的高斯光束转换为携带轨道角动量（OAM）和拓扑电荷（TC）的涡旋光束。值得注意的是，虽然假定原始光束携带一个非零的OAM且没有TC，但后者显示为在自由空间传播期间出现。以两个平行的中心对称零强度线为例，我们研究了在双焦距下生成两个强度零点的动力学：随着垂直零强度线之间距离的增加，首先在光学零点上产生两个光学涡旋。水平轴，然后在原点收敛，然后沿垂直轴发散。不管线间距离如何，这种光学涡旋都具有$ {\ rm TC} =-{2} $距光轴的任何距离（原始平面除外）。随着零强度线之间距离的变化，光束所承载的OAM会发生变化，正值和负值或线之间的某个距离处的值为零。我们还表明，如果零强度线的数量是无限的，则会生成具有有限OAM和无限TC的涡旋束。