从Wigner分布函数定义和菲涅耳衍射积分出发，导出了洛伦兹光束在束腰参考面、自由空间任一参考面以及ABCD系统出射参考面的Wigner分布函数的解析表达式。作为其典型应用，导出了洛伦兹光束二阶矩的解析表达式。数值模拟了束宽、发散角的变化规律并与相应的高斯光束参数的变化规律进行比较。结果表明洛伦兹光束比高斯型光束更适合作为二极管激光光束模型。

Based on the definition of Wigner distribution function and Fresnel diffraction integral, the analytical expressions of Wigner distribution function of Lorentz beam on the waist plane, and on a plane in free space as well as on the exit reference plane of an ABCD system are derived. As their typical applications, the analytical expressions of the second-order moments of Lorentz beam are derived. The transformation rules of beam width and divergence angle of Lorentz beam are simulated and compared with those of the corresponding Gaussian beam. It is shown that Lorentz beam is a more appropriate model than Gaussian beam for diode laser beams.