“叉形”全息光栅产生的光涡旋结构：库默光束
Structure of optical vortices produced by holographic gratings with "fork" geometry: Kummer beams
摘要：
具有拓扑缺陷（一个或多个条纹的分支）的全息光栅被广泛用于产生具有光学涡旋（OV）的光束。本文分析了以条纹分叉点为中心的高斯光束照射二元计算全息图产生的OV光束。通常，这样的光束被认为是傍轴波动方程的标准解的类似物-拉盖尔-高斯（LG）模式代表OV的经典示例。然而，强度分布和空间演化的整个过程显示出与LG原型的重要差异。在整数拓扑电荷的情况下，所产生的OV光束可以由特殊的库默函数描述，其允许将这些光束称为“库默光束”。对Kummer梁的性质进行了数值和解析研究。与相应的LG模式的主要区别是在光束外围的强度衰减慢得多，光束发散度高得多;库默尔和LG光束之间的差异随着OV拓扑电荷的增加而增加。
英文摘要：
Holographic gratings with topological defects (branching of one or more fringes) are widely used for generating light beams with optical vortices (OV). This work presents an analysis of OV beams produced by binary computer-generated holograms enlightened by Gaussian beams centered at the fringe bifurcation point. Usually such beams are considered as analogs of the standard solutions of paraxial wave equation - Laguerre-Gaussian (LG) modes representing classical examples of OVs. However, the intensity profile and the whole process of their spatial evolution show important differences from the LG prototypes. In the case of integer topological charge, a created OV beam can be described by the special Kummer function, which allows referring to these beams as to "Kummer beams". Properties of Kummer beams are studied numerically and analytically. Main distinctions from the corresponding LG modes are much slower intensity decay at the beam periphery and much higher beam divergence; differences between the Kummer and LG beams grow with the OV topological charge.
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