复变量双曲余弦平方—高斯光束的束腰宽度及其位置

The beam waist width and its location of the elegant cosh-squared-Gaussian beams

本文引入了近轴近似下波动方程的解—复变量双曲余弦平方 -高斯光束 ,该光束与双曲余弦函数项相关的参数为复数。本文主要对复变量双曲余弦平方 -高斯光束的基本特性进行了研究。由Collins公式出发推导出了光束通过近轴ABCD光学系统传输时的场分布函数。基于二阶矩定义 ,导出了光斑尺寸的解析表达式 ,并得到了该光束在自由空间传输时束腰宽度及其位置的解析式。最后对所得结果进行了数值计算和分析。

We describe a class of closed-form solutions of the paraxial wave equation,the elegant cosh-squared-Gaussian(EchSG) beams whose parameter related with cosh function part is complex number.The basic properties of EchSG beams are studied.Starting from the Collins formula,the closed-form filed distribution of EchSG beams passing through a paraxial ABCD optical system is deriverd.Based on the second-order moment method,the general closed-form expression of the beam width is obtainde,the beam waist width and its location for the EchSG beams propagation in free space are also deduced.Numerical calculations are made to illustrate the properties of the EchSG beams.