基于广义惠更斯菲涅耳衍射积分和相干偏振统一理论，研究了有振幅和相位调制的部分相干方形平顶脉冲电磁光束在自由空间的传输特性，推导出了有振幅和相位调制的部分相干方形平顶脉冲电磁光束在自由空间传输的交叉谱密度矩阵解析式，通过数值计算分析了有振幅和相位调制的部分相干方形平顶脉冲电磁光束在自由空间传输的光谱强度分布。研究结果表明振幅和相位调制半径、调制深度都会对部分相干方形平顶脉冲电磁光束的光谱强度分布产生影响，有振幅和相位调制的部分相干方形平顶脉冲电磁光束在自由空间传输的光谱强度分布与相干长度、脉冲时间相干长度和传输距离有关。

Based on the generalized Huygens-Fresnel diffraction integral and the unified theory of coherence and polarization, propagation properties of partially coherent electromagnetic square flat-topped pulsed beams with amplitude and phase modulations in free space are analyzed. The analytical expressions for the cross-spectral density matrix of partially coherent electromagnetic square flat-topped pulsed beams with amplitude and phase modulations in free space are derived, and the numerical calculations are also given. It is shown that the spectral intensity distribution of partially coherent electromagnetic square flat-topped pulsed beams is influenced by size of the modulation zone, the depth of amplitude and phase modulations, the coherence length and temporal coherence length of the beams, and transmission distance.