高斯涡旋光束的光束传输因子和峭度参数

The beam propagation factor and the kurtosis parameter of a Gaussian vortex beam

基于强度二阶矩定义,导出了高斯涡旋光束光束传输因子即M^2因子的解析表达式,高斯涡旋光束的M^2因子唯一取决于拓扑电荷数n.数值计算表明,高斯涡旋光束的M^2因子随着拓扑电荷数n的增大而增大.基于强度高阶矩,还导出了高斯涡旋光束经傍轴ABCD光学系统传输时峭度参数的解析表达式,高斯涡旋光束的峭度参数取决于拓扑电荷数n、参数δ、矩阵元A和矩阵元D.在自由空间传输时,高斯涡旋光束的峭度参数仅取决于拓扑电荷数n和参数δ.自由空间传输时,高斯涡旋光束峭度参数的变化规律为:峭度参数随参数δ的增大先减小而后趋向于一最小值,随拓扑电荷数n的增大而减小.这一研究有助于高斯涡旋光束的实际应用.

Based on the definition of the second-order moment of intensity, the analytical expression for the beam propagation factor, namely the M2 factor, of a Gaussian vortex beam is derived, which is uniquely determined by the topological charge n. The numerical result indicates that the M2 factor of a Gaussian vortex beam increases with the increase of topological charge n. By means of the higher-order moment of intensity, the analytical expression for the kurtosis parameter of a Gaussian vortex beam passing through a paraxial ABCD optical system is also presented, which depends on topological charge n, parameter δ, transfer matrix elements A and D. When propagating in free space, the kurtosis parameter of a Gaussian vortex beam is determined by topological charge n and parameter δ. With the increase of parameter δ, the kurtosis parameter of a Gaussian vortex beam in free space first decreases and finally tends to a minimal value. Moreover, the kurtosis parameter of a Gaussian vortex beam in free space decreases with the increase of topological charge n. This research is helpful for the practical application of the Gaussian vortex beam.