高斯光束经圆形光阑衍射的远场发散特性

线偏振高斯光束经圆形光阑衍射后,其远场可表示成互相正交的横电(TE)项和横磁(TM)项之和。利用TE项和TM项的远场能流分布，导出了高斯衍射光束的TE项和TM项远场功率的解析表达式，由此可度量TE项和TM项在远场占总功率的比例。基于能流二阶矩的定义，给出了高斯衍射光束、TE项和TM项远场发散角的解析式以及三者远场发散角间的关系通式，重点分析了f参数和截取参数对远场发散角的影响。结果表明:随着f参数的增大，远场发散角先增大后趋向于各自的饱和值。截取参数对远场发散角的影响与f参数相关，当f参数较大时，截取参数对远场发散角的影响不明显；当f参数适中时，随着截取参数的增大，远场发散角先减小后趋向于各自的最小值；但当f参数较小时，高斯衍射光束和TM项二者的远场发散角出现一定的波动性。

Far-field divergent properties of linearly polarized Gaussian beam diffracted at circular aperture

The far-field of the linearly polarized Gaussian beams diffracted at a circular aperture can be expressed as a sum of two orthogonal transversal electric (TE) and transversal magnetic (TM) terms. According to the far-field energy flux distributions of the TE and TM terms, the analytical expressions of the power of the TE and TM terms for the Gaussian diffracted beam are derived, which allow one to examine the ratios of the power of the TE and TM terms to the whole beam power. Based on the definition of the second-order moment of the far-field energy flux distributions, the analytical formulae of the far-field divergence angles of the Gaussian diffracted beam and its TE and TM terms are obtained, as well as the relationship among those far-field divergence angles. The influences of the f-parameter and the truncation parameter on the far-field divergence angles are analyzed. With the increase of the f-parameter, the far-field divergence angles first increase and finally tend to their respective saturated values. The influence of the truncation parameter on the far-field divergence angles is related to the f-parameter. When the f-parameter is relatively large, the effect of the truncation parameter on the far-field divergence angles is not distinct. When the f-parameter is moderate, the far-field divergence angles first decrease and finally tend to their respective minimum values with increasing the truncation parameter. When the f-parameter is relatively small, the far-field divergence angles of the Gaussian diffracted beam and its TM term fluctuate in a certain degree with varying the truncation parameter.