Hollow vortex Gaussian beams

A kind of hollow vortex Gaussian beam is introduced. Based on the Collins integral, an analytical propagation formula of a hollow vortex Gaussian beam through a paraxial ABCD optical system is derived. Due to the special distribution of the optical field, which is caused by the initial vortex phase, the dark region of a hollow vortex Gaussian beam will not disappear upon propagation. The analytical expressions for the beam propagation factor, the kurtosis parameter, and the orbital angular mo- mentum density of a hollow vortex Gaussian beam passing through a paraxial ABCD optical system are also derived, respec- tively. The beam propagation factor is determined by the beam order and the topological charge. The kurtosis parameter and the orbital angular momentum density depend on beam order n, topological charge m, parameter y, and transfer matrix ele- ments A and D. As a numerical example, the propagation properties of a hollow vortex Gaussian beam in free space are demonstrated. The hollow vortex Gaussian beam has eminent propagation stability and has crucial application prospects in op- tical micromanipulation.

空心高斯涡旋光束的远场特性

基于角谱法和稳相法,推导出了空心高斯涡旋光束的TE波和TM波在自由空间远场传输和能流密度的解析表达式,研究了其相位奇点和能流密度分布。结果表明,空心高斯涡旋光束的远场特性主要跟控制参数有关。改变光束中的涡旋离轴量,光涡旋和能流密度黑核会发生移动。圆刃型位错线的半径和能流密度暗环位置跟束腰宽度有关,而能流密度的对称性主要受涡旋离轴量的影响。

空心高斯涡旋光束在各向异性non-Kolmogorov大气湍流的光强分布

为了分析大气湍流对空心涡旋光束传输光强的影响,基于广义惠更斯-菲涅尔原理和Rytov相位结构函数近似,利用各向异性大气non-Kolmogorov湍流谱模型,推导出空心高斯涡旋(HGV)光束在各向异性大气湍流中的传输光强解析式,数值模拟分析了传输距离、湍流参数和光束参数对光强分布的影响。研究结果表明:随着传输距离增大,HGV光束的传输光强将由空心分布逐步演化为高斯分布,且拓扑荷数越大、束腰半径越小、波长越长的HGV光束的光强受各向异性大气湍流影响越小;当湍流的各向异性系数、广义指数和内尺度越大,以及外尺度与结构常数越小时,HGV光束的传输光强随传输距离的演化会减慢,表明HGV光束在较弱的各向异性non-Kolmogorov大气湍流中传输时光强分布受到湍流的影响较小。