平顶光束K参数的解析传输方程
Analytical propagation expressions for kurtosis parameter of flat-topped beams
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摘要: 从Li提出的平顶光束模型和Collins公式出发，推导出平顶光束通过近轴ABCD光学系统K参数的解析传输公式。平顶光束的K参数与光束阶数M、瑞利长度zR和传输矩阵元A/B有关。另一方面，基于强度矩的传输方程，通过繁冗的积分，也推导出K参数的解析传输方程。大量数值计算结果证明二者所得结果相同。对平顶光束K参数的传输特性用数值计算例作了说明。Abstract: From the flat-topped beam model proposed recently by Li and the Collins formula, an analytical propagation expression for the kurtosis parameter (K parameter) of flat-topped beams through a paraxial ABCD system is derived. The K parameter depends on the beam order, Rayleigh length and ratio A/B of transfer matrix elements. Based on the propagation equation of intensity moments, a closed-form propagation equation of the K parameter is deduced. The two expressions are shown to be numerically equivalent. The propagation properties of the K parameter of flat-topped beams are illustrated with the caculated results.
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