离轴高斯涡旋光束的轨道角动量研究

Research on orbital angular momentum of off axial Gaussian vortex beam

由近轴光束理论,推导了离轴高斯涡旋光束在质心坐标中轨道角动量的解析表达式,在此基础上对离轴涡旋光束轨道角动量的分布及其传输进行了研究,数值研究表明,观测平面上离轴涡旋光束的轨道角动量的分布不再具备圆对称的特点,轨道角动量为0的等高线为封闭曲线,其内部区域轨道角动量数值为负,外部为正.随着传输距离的增加,远场区观测平面上轨道角动量的分布逐渐演变为近似左右对称的情形,拓扑荷数越大,演变的速度越快.另一方面,离轴距离也会影响到轨道角动量的分布,在确定的观测平面上,离轴距离越大,观测平面上轨道角动量极小值(负区域)的模值会越接近轨道角动量的极大值(正区域).该结论在研究离轴涡旋光束与微粒作用时能提供指导意见.

By the theory of paraxial approximation for optical beam, the analytical expression of orbital angular momentum （OAM） of off axial Gaussian vortex beam is derived in the coordinates of centroid, based on which distribution of OAM of off axial vortex beam and its propagation are investigated. Numerical calculations show that the OAM of off axial vortex beam is not circularly symmetric. The contour of zero OAM is a close curve, inside which the OAM is positive and outside which the OAM is negative. With the increment of propagation length, the distribution of OAM of off axial vortex beam tends to be approximately right and left symmetric, and the bigger the topological charge is, the faster the distribution of OAM tends to form the characteristic of symmetry. Besides, the off axial distance also has influence on the distribution of OAM. On a certain observation plane, the absolute value of the minimum OAM （in negative area） will become closer to the absolute value of the maximum OAM （in positive area） if the off axial distance increases. The conclusion can provide guidance during the research on the interaction between off axial vortex beam and particles.