涡旋洛伦兹-高斯光束的远场矢量结构特征

利用矢量角谱法和稳相法，研究了涡旋洛伦兹-高斯光束的远场矢量结构特征，导出了横电项(TE项)和横磁项(TM项)远场电磁场和相应能流的解析表达式。通过相应的数值计算，分析了拓扑电荷数对涡旋洛伦兹-高斯光束及其矢量结构项远场能流分布的影响。TE项由位于竖直方向的2瓣或3瓣组成，TM项可由TE项旋转90得到。涡旋洛伦兹-高斯光束在拓扑电荷数小时内部中空，外部亮环均匀分布。增大拓扑电荷数，涡旋洛伦兹-高斯光束外部亮环上的能流呈起伏分布，内部变化相对复杂。涡旋洛伦兹-高斯光束及其矢量结构项的光斑尺寸随拓扑电荷数的增大而增大，但会饱和。研究显示，涡旋洛伦兹-高斯光束在实际应用时拓扑电荷数不宜过大。

Vectorial structure characteristics of vortex Lorentz-Gauss beam in far-field

Based on the method of vector angular spectrum representation and the method of stationary phase, the analytical expressions for the electromagnetic fields of the vectorial structure, namely the transverse electric (TE) and the transverse magnetic (TM) terms of a vortex Lorentz-Gauss beam, are derived in the far-field. Moreover, the analytical expressions of the energy flux of the TE and TM terms are also presented in the far-field. The influence of the topological charge on the energy flux distributions of the vortex Lorentz-Gauss beam and its vectorial structure are analyzed by numerical examples. The TE term is composed of two or three lobes which are located at the y-axis. The TM term can be viewed as the TE term rotating 90 degrees. When the topological charge is small, the vortex Lorentz-Gauss beam takes on dark hollow shape, and the brightly outer ring is uniform. With increasing the topological charge, the energy flux in the brightly outer ring of the vortex Lorentz-Gauss beam fluctuates, and the change in the central region is relative complicated. With increasing the topological charge, the beam sizes of the vortex Lorentz-Gauss beam and its vectorial structure also augment. However, the beam sizes of the vortex Lorentz-Gauss beam and its vectorial structure will saturate. In the practical application of the vortex Lorentz-Gauss beam, therefore, the topological charge should not be too large.