We demonstrate a type of singular beam that accelerates along a parabolic trajectory and has a cross-section intensity pattern exhibiting a dark central region surrounded by multiple rings with the innermost (main) ring resembling an equilateral triangle. The key to creating such beams is to replace the standard triangle with a rounded one, made up of six circular arcs connected end to end. The individual input phase mask for each arc can be analytically computed, and the whole input phase mask for the beam is thus obtained by piecing together these individual phases. Furthermore, the continuity of field forces of these triangle-like modes is discrete; that is, an index similar to the topological charge of vortex beams arises. Numerical results show that the energy flow in the beam’s cross section circulates around the dark center along the triangle-like main ring, suggesting a possible application in orbiting particles along an irregular path.

中文翻译：

---

加速三角形奇异光束

我们演示了一种奇异光束，它沿着抛物线轨迹加速，并具有横截面强度模式，该强度模式展示出一个黑暗的中央区域，该区域被多个环包围，其中最里面的（主）环类似于等边三角形。创建此类梁的关键是用一个圆角的三角形代替标准三角形，该三角形由首尾相连的六个圆弧组成。可以分析地计算出每个电弧的单独的输入相位掩模，从而通过将这些单独的相位拼接在一起来获得光束的整个输入相位掩模。此外，这些三角形模式的场力的连续性是离散的。即，产生类似于涡旋束的拓扑电荷的指数。