Luo Mengdi, Wang Zhaoying
Opt Express. 2019 Dec 9;27(25):36259-36268. doi: 10.1364/OE.27.036259.
In most papers about the fractional vortex continuous beams (FVCBs), the relationship between the total vortex strength S and the propagation distance is not analyzed since the vortex structure is not stable in the near field. In this paper, we theoretically study the fractional vortex ultrashort pulsed beams (FVUPBs) possessing non-integer topological charges α at arbitrary plane and find that the vortex structure is propagation-distance-dependent. Both the intensity and phase distributions are calculated to analyze the vortex structure. To evaluate the propagation properties of FVUPBs, we focus on the total vortex strength (TVS) of FVUPBs to investigate the number of vortex, and demonstrate that the birth of a vortex is at α = m + ɛ, where m is an integer, ɛ is a changing fraction depending on the pulse durations, peak wavelengths and propagation distances. Furthermore, we discover that the FVUPBs carry decreasing TVS along the propagation axis in free space. This special vortex structure for FVUPBs appears due to the mixture weight of vortex pulsed beam with different integer topological charges (TCs) n. However, the total orbital angular momentum is invariant during propagation. The above phenomenon presented in our paper are totally particular and intriguing compared with the FVCBs.
在大多数关于分数涡旋连续光束（FVCBs）的论文中，由于涡旋结构在近场不稳定，因此未分析总涡旋强度S与传播距离之间的关系。在本文中，我们从理论上研究了在任意平面具有非整数拓扑电荷α的分数涡旋超短脉冲光束（FVUPBs），发现涡旋结构与传播距离有关。计算强度和相位分布以分析涡旋结构。为了评估FVUPBs的传播特性，我们专注于FVUPBs的总涡旋强度（TVS）来研究涡旋数量，并证明涡旋产生于α = m + ɛ，其中m为整数，ɛ是一个取决于脉冲持续时间、峰值波长和传播距离的变化分数。此外，我们发现FVUPBs在自由空间中沿传播轴携带的TVS会减小。FVUPBs这种特殊的涡旋结构是由于具有不同整数拓扑电荷（TCs）n的涡旋脉冲光束的混合权重所致。然而，总轨道角动量在传播过程中是不变的。与FVCBs相比，我们论文中呈现的上述现象完全独特且引人入胜。
