为了研究双曲正弦高斯光束在梯度折射率介质中的传输特性, 利用广义惠更斯-菲涅耳衍射积分法推导了光束强度分布解析表达式, 据此结合空间二阶矩定义得到了束腰宽度和位置的解析表达式, 并对光束强度分布、光斑尺寸、束腰宽度及其位置进行了数值计算和分析。结果表明, 轴向光强分布呈周期性变化, 横向光场分布受梯度折射系数和光束参量影响, 通过对这些参量的适当调整, 可以改变光斑尺寸和束腰位置。

In order to study the propagation characteristics of sinh-Gaussian beams in gradient-index medium, the analytical expression of the intensity was derived based on the general Huygens-Fresnel diffraction integral. Based on the second-order moment definition, the analytical expression for the beam width and the waist location were deduced. The intensity, facular size, beam waist and its position were calculated. The results show that the axial intensity changes periodically and the transverse intensity distribution are largely affected by the nonlinearity of the medium and the modulation parameter of the beams. The spot site and waist location can be changed by adjusting the parameter appropriately．