推导了高斯谢尔模光束通过 ABCD光学系统的交叉谱密度矩阵，研究了该条件下光谱偏振度的变化情况。比较研究了高斯谢尔模光束通过自由空间和聚焦光学系统的情况。研究表明，在自由空间中传输足够远的距离后光谱偏振度将达到稳定，在聚焦光学系统中光谱偏振度在焦面位置附近有明显的起伏变化，两者都与光源参量的选择有关。特别指出，位于焦面上的光谱偏振度等于其远场的光谱偏振度稳定值。

The cross-spectral density matrix of Gaussian Schell-model beams through the ABCD optical system is derived，and the variation of the spectral degree of polarization under this condition is given. A comparison between the cases of Gaussian Schell-model beams through the free space and focal optical system is studied. The study shows that the spectral degree of polarization will tend to the stable value after a long-propagation distance in free space，and the spectral degree of polarization has a sharp fluctuation at the position of focal plane in focal optical system. Both are related to the selection of light source parameters. In particular，the spectral degree of polarization at the position of focal plane equals the stable value of the spectral degree of polarization at the far field.