高斯涡旋光束的动量及轨道角动量与拓扑电荷数的关系及其在自由空间中的传输

将近轴光束理论应用于光束的动量及轨道角动量研究,推导了涡旋光束动量以及轨道角动量的解析表达式,在此基础上,对高斯涡旋光束的动量及轨道角动量的分布及其在自由空间中的传输进行了研究.理论分析及数值计算表明,动量的径向分量和角向分量在数值上比较接近,远小于动量的纵向分量,随着传输距离的增大,动量的三个分量在观测平面上的分布会逐渐沿径向拓展,其在观测平面上的极大值位置各不相同,都与源平面上光束的拓扑电荷数和束腰半径有关,观测平面上的整体积分表明,动量的三个分量在传输中都保持守恒;另外,观测平面上高斯涡旋光束轨道角动量的分布在传输中也会沿径向拓展,其在观测平面上的极大值位置与动量的纵向分量相同.观测平面上的整体积分证实了高斯涡旋光束在传输中轨道角动量保持守恒.

Relation of momentum and orbital angular momentum of Gaussian vortex beam with topological charge and their propagation in free space

While the theory of paraxial approximation is applied to the research of momentum and orbital angular momentum （OAM）, the analytical expressions of momentum and OAM of vortex beam are derived. Based on the analytical expression, the distribution and propagation of the momentum and OAM of the Gaussian vortex beam is investigated in free space. Theoretical analysis and numerical simulation show that the values of the radial and angular components of momentum are close to each other, and they are far smaller that the value of the longitudinal component of momentum. The three components of momentum of the beam will expand along the radial direction during propagation in the cross section. The maximum positions of the three components are different, which problem is dependent on the topological charge and the beam width of the source beam. The whole integration results of the three components on the cross section shows the conservation of the momentum of the beam. Besides, the OAM of the Gaussian vortex beam will also expand along the radial direction during propagation. The maximum position of the OAM is the same as that of longitudinal component of the momentum. The whole integration result on the cross section confirms the conservation of the OAM of the Gaussian vortex beam while propagating.