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根据径向电场分量与角向电场分量所满足的二阶微分方程分析简单柱面坐标偏振光束本征模场的特性。根据坐标变换公式将瑞利-索末菲标量衍射积分公式转化为简单柱面坐标偏振光束衍射远场径向电场分量与角向电场分量的计算公式。根据衍射源电场振幅分布与空间频谱分布的关系,给出简单柱面坐标偏振光束微分算子衍射源光斑半径和径向空间频率半径的计算公式,它可用于计算简单柱面坐标偏振光束的光束传输因子。并以计算LG10模柱面坐标偏振拉盖尔-高斯光束的光束参量为例说明了该公式的实用性。
The properties of the eigenmode field of a simple cylindrical coordinate polarized beam are analyzed according to the second order differential equations which are satisfied by the radial electric field component and the angular electric field component. According to the coordinate transformation formula, Rayleigh-Sommerfeld scalar diffraction integral formula is transformed into the formula for calculating the far-field radial electric field component and the angular electric field component of a simple cylindrical coordinate polarized beam. According to the relationship between the amplitude distribution of the electric field of the diffraction source and the spatial spectrum distribution, the formula for calculating the radius of the spot radius and the radial space frequency of the diffractive operator for a simple cylindrical coordinate polarized beam is given. It can be used to calculate the beam of a simple cylindrical coordinate polarized beam Transfer factor. The practicality of this formula is illustrated by taking the beam parameter of LG10 mode cylindrical Laguerre-Gaussian beam as an example.