会聚厄米-双曲余弦高斯光束的光强分布和焦移

 基于厄米-双曲余弦高斯光束通过无光阑限制薄透镜聚焦的解析传输公式，研究了厄米-双曲余弦高斯光束聚焦区域的光强分布，并对光束的焦移进行了分析，讨论了偏心参数对光强主极大位置的影响。结果表明：TEM₁₁模厄米-双曲余弦高斯光束的相对焦移（绝对值）随偏心参数和菲涅尔数的减小而增大，菲涅尔数较大时相对焦移趋于零。TEM₂₂模光束在偏心参数小于0.54时，轴外与轴上光强极大值的比值大于1，此时光强主极大在轴外，偏心参数大于0.54时则相反；在偏心参数等于0.54时比值为1，此时光束有两个主极大，偏心参数愈大光强愈集中于轴上。使用LW法和GH法得到的TEM₂₂模光束的相对焦移（绝对值）随偏心参数和菲涅尔数的变化规律与TEM₁₁模光束一致，但相同参数下使用这两种方法得出的具体结果不同。

Intensity distributions and focal shifts of converging Hermite-cosh-Gaussian beams

Based on the closed-form propagation expression of Hermite-cosh-Gaussian beams passing through an unapertured thin lens, intensity distributions in focal region were studied. Focal shifts of the beams and dependences of maximal intensity position on decentered parameter were investigated. The results show that the relative focal shifts (absolute value) in TEM_(11)-mode Hermite-cosh-Gaussian beams increase with decreasing decentered parameter and Fresnel number, and tend zero with large Fresnel number. For TEM_(22)-mode Hermite-cosh-Gaussian beams the principal maximum intensity is located off the axis when the decentered parameter is smaller than 0.54 and on the axis when decentered parameter is greater than 0.54. When decentered parameter equals 0.54, the beam has double principal maximum intensity here. The intensity is more concentrated into the axis with greater decentered papameter. Dependences of the relative focal shifts in TEM_(22)-mode beam obtained using LW and GH methods on decentered parameter and Fresnel number coincide with that of TEM_(11)-mode beam. However, there is quantitative difference between the results obtained using the two different methods.