圆孔限制下有相位变化的高斯光束远场发散度的理论分析

Analysis of Far-field Divergence of a Gaussian Beam with Phase Variation Under Circular Aperture Diffraction

依据夫琅和费衍射理论,通过引入高斯变换,即把夫琅和费衍射积分中的贝赛尔函数用一高斯函数来近似,详细分析并推导出圆孔限制下具有相位变化的高斯光束远场发散度的近似计算公式.与传统数值积分求光束发散度相比,它避免了繁琐数值积分,其误差不超过3 %.

Based on the Fraunhofer diffraction,the formula of the Gaussian beam＇s divergence is deduced and analyzed in detail by using the Gaussian transform, such as using the Gaussian function instead of the Bessel function in the Fraunhofer diffraction formula. Compared with the direct numerical integration of the Fraunhofer diffraction,this formula avoids the troublesome integral,but the error is no more than 3%.