The propagation of a partially Lorentz–Gauss beam in a uniform-intensity diffractive axicon is studied according to the Huygens–Fresnel principle, the Hermite–Gaussian expansion of a Lorentz function, and using the stationary phase method. We have derived the intensity equation of a partially coherent Lorentz-Gauss beams propagating through uniform-intensity diffractive axicon, and we proved mathematically that it is the superposition of Bessel beams of various orders after emerging from axicon, using Hermite’s function series and the Bessel function integral formulas. The results show that the intensity distribution of the diffracted beam is the intensity pattern evolved from a Lorentz–Gauss shaped spot into a Gaussian-shaped spot at any position on the focal length of the axicon, and the intensity distribution of a partially Lorentz–Gauss beam generated by an axicon becomes uniform by increasing the beam width and more uniform and constant with the larger coherence width.

中文翻译：

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来自轴棱镜的部分相干洛伦兹-高斯光束的相干特性和强度分布

根据惠更斯-菲涅耳原理、洛伦兹函数的厄米-高斯展开并使用固定相方法研究了部分洛伦兹-高斯光束在均匀强度衍射轴棱锥中的传播。我们推导出了部分相干洛伦兹-高斯光束通过均匀强度衍射轴棱镜传播的强度方程，并利用厄米特函数级数和贝塞尔函数，从数学上证明了它是从轴棱镜出来后各种阶的贝塞尔光束的叠加积分公式。结果表明，衍射光束的强度分布是在展棱锥焦距上的任意位置处由洛伦兹-高斯形光斑演变为高斯形光斑的强度图案，