推导了空心高斯光束经过傍轴光学系统的传输模型；利用导出的公式计算分析了空心高斯光束在自由空间的传输特性；最后利用Matlab对传输方程进行模拟仿真。结果表明：高斯光束的阶数n和沿傍轴的传输距离z是控制空心光束的主要参数。随着阶数n的增大，高斯光束逐渐变为空心高斯光束，且中心暗斑和亮环的半径也相应增加；当传输距离z 增大时，空心高斯光束的光斑发散，同时黑斑面积占总光斑面积的比率减小，而在远场“黑心”区域消失了，此时轴上的光强变为最大。

A propagation model for hollow Gaussian beams (HGBs) through the paraxial optical system is derived, the propagation properties of HGBs in free space are analyzed using the derived propagation formula, and the propagation equation is simulated by using Matlab software. The results show that the ordern and propagation distancez are the importance parameters for controlling hollow beams. With the increase of ordern , Gaussian beams are gradually become HGBs, and the center of dark and bright radius of the bright ring are correspondingly increased. With the increase of propagation distancez , HGBs are divergent, and black spot area is reduced in the ratio of the total spot area, but in the far-field the black spot is disappeared, and light intensity becomes the maximum on the axis.