边缘衍射圆涡旋光束的奇异骨架演化和拓扑反应
Singular skeleton evolution and topological reactions in edge-diffracted circular optical-vortex beams
摘要：
圆形光学涡旋（OV）光束的边缘衍射改变了其奇异结构：多电荷轴向OV分裂成一组单电荷，形成衍射光束的“奇异骨架”。束截面中的OV位置取决于传播距离以及相对于入射束轴的边缘位置，并且当这些参数中的一个或两个改变时，OV芯描述规则的轨迹。然而，轨道并不总是连续的;它们可能伴随着拓扑反应，包括新奇点的出现，它们的相互作用和湮灭。基于Kirchhoff-Fresnel积分，研究了拓扑荷|m| =2和3的衍射库默尔光束和拉盖尔-高斯光束的奇异骨架行为。我们揭示的轨迹的不连续性和其他拓扑事件的奇异骨架的演变，似乎是高度敏感的入射光束的属性和衍射条件的性质。OV轨迹变得不连续的条件和实现这一点的机制进行了讨论。基于数值计算的结论得到了OV光束衍射的渐近解析模型的支持。所得结果可用于光学参量的测量和光学参量的诊断。
英文摘要：
Edge diffraction of a circular optical vortex (OV) beam transforms its singular structure: a multicharged axial OV splits into the set of single-charged ones that form the 'singular skeleton' of the diffracted beam. The OV positions in the beam cross section depend on the propagation distance as well as on the edge position with respect to the incident beam axis, and the OV cores describe regular trajectories when one or both of these parameters change. However, the trajectories are not always continuous; they may be accompanied with topological reactions, including emergence of new singularities, their interaction and annihilation. Based on the Kirchhoff-Fresnel integral, we consider the singular skeleton behavior in diffracted Kummer beams and Laguerre-Gaussian beams with topological charge |m|=2 and 3. We reveal the nature of the trajectories' discontinuities and other topological events in the singular skeleton evolution that appear to be highly sensitive to the incident beam properties and to the diffraction conditions. Conditions at which the OV trajectory becomes discontinuous and mechanisms by which this is realized are discussed. The conclusions based on the numerical calculations are supported by the asymptotic analytical model of the OV beam diffraction. The results can be useful in the OV metrology and for the OV beam's diagnostics.
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