焦斑二阶矩半径与光束近场分布的关系

为分析光束振幅畸变和相位畸变对其焦斑二阶矩半径的影响，以光波标量衍射理论中的夫琅和费衍射公式为基础，根据光斑二阶矩半径的定义，推导了直接依赖于光束近场复振幅分布的焦斑二阶矩半径的一般表达式,并进一步推导了直接依赖于光束近场强度分布和相位分布的焦斑二阶矩半径和焦斑二阶矩角半径的表达式。结果表明：畸变光束的焦斑二阶矩角半径由光束近场波前相位梯度的强度加权均方根值和对数强度梯度的强度加权均方根值决定。利用焦斑二阶矩半径表达式，可直接分析并计算光束近场分布由于振幅调制和相位畸变导致的焦斑二阶矩半径的变化及焦斑发散角的变化。利用焦斑发散角表达式，直接推出了理想高斯光束和像散高斯光束的远场发散角，得到了与文献一致的结果，验证了表达式的正确性。

Relation between second-order moment radius of focal spot and near field distribution of laser beam

In order to analyze the effect of aberration of amplitude and phase of laser beam on second-order moment radius of focal spot, based on the Fraunhofer formula for light wave scalar diffraction theory and the definition of second-order moment radius, the general expression for focal spot second-order moment radius depending on the complex amplitude of near field is derived. The second-order moment radius of the focal spot depending on intensity distribution and phase distribution of near field is derived, and its clear physical meaning is described. The second-order moment radius and the divergence angle of focal spot may be easily calculated with the second-order moment radius expression of focal spot. At last, the divergence angles of focal spots of several kinds of Gaussian laser beams a