Focusing characteristics of Riemann-Silberstein vortices of edge-dislocation Gaussian beam passing through a bifocal lens
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摘要: 基于时间平均复标量场的零值点，推导出寄居于高斯光束中的刃型位错线形成的Riemann-Silberstein (RS)涡旋通过双焦透镜传输时的复标量场。详细研究了刃型位错高斯光束形成的RS涡旋通过双焦透镜的聚焦特性，分析了传输距离和双焦透镜在x方向的焦距对RS涡旋的影响。研究发现RS涡旋通过双焦透镜后会出现RS涡旋的移动、新产生一对含有相反拓扑电荷的RS涡旋、两个含有相反拓扑电荷的RS涡旋逐渐靠近至湮灭，但是，在整个聚焦传输变化过程中，RS涡旋的总拓扑电荷守恒。特别地，当RS涡旋通过理想透镜时，复标量场中始终只有4个位于x轴上的RS涡旋。随着传输距离增加，这4个RS涡旋先逐渐靠近原点(0, 0)，又逐渐远离原点(0, 0)，但每个RS涡旋的拓扑电荷一直保持不变，因此，总拓扑电荷守恒。
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关键词:
- Riemann-Silberstein涡旋 /
- 双焦透镜 /
- 传输距离 /
- 拓扑电荷
Abstract: Based on the zeros of the time-averaged complex scalar field, the complex scalar field of Riemann-Silberstein (RS) vortices generated by the edge dislocation line embedded in the Gaussian beam propagating through the bifocal lens is derived. The focal characteristics of the RS vortices are studied in detail, and the influence of the propagation distance and the focal length of the bifocal lens on the RS vortices is nalyzed. It is found that the RS vortices will move after passing through the bifocal lens, a new pair of RS vortices with opposite topological charge will be generated, and two RS vortices with opposite topological charge will gradually approach each other to annihilation. However, during the entire focusing process, the total topological charge of the RS vortices is conserved. In particular, when the RS vortices pass through an ideal lens, there are always only four RS vortices on the x-axis in the complex scalar field. As the propagation distance increases, these four RS vortices gradually approach the origin (0, 0), and then gradually move away from the origin (0,0), but the topological charge of each RS vortex has remained unchanged, thus the total topological charge is conserved.-
Key words:
- Riemann-Silberstein vortices /
- bifocal lens /
- propagation distance /
- topological charge
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图 2 不同传输距离时Ψ(r)的等位相线图
Figure 2. Contour lines of phase of Ψ(r) for different values of the propagation distance
图 3 不同焦距fx时Ψ(r)的等位相线图
Figure 3. Contour lines of phase of Ψ(r) for different values of the focal length fx
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