研究了横向分布为平顶高斯模式的宽带激光在自由空间的传输特性，分析了频带宽度对其强度分布的影响。首先推导了平顶高斯模式宽带激光的每一频率分量在自由空间的传输公式，然后将频率域的传输公式通过傅里叶变换得到时间域的传输公式。基于推导的公式通过数值算例给出了不同频带宽度激光光束的强度分布结果，详细分析了空间模式的变化和时空耦合现象。研究结果表明：随着传输距离增大，平顶高斯空间模式趋于高斯分布。同时随着带宽增大，平顶高斯模式宽带激光表现出更强的时空耦合现象，并导致其空间横向分布发生明显变化。变化的主要特征为波前的强度分布随带宽增大而变窄，波后的强度分布则随带宽增大而远离轴中心向外扩展。

The propagation properties of broadband laser with flattened-Gaussian transverse modes are studied and the influences of the laser bandwidth on intensity distributions are analyzed. The propagation expression of each frequency component of the broadband laser with flattened-Gaussian transverse modes is deduced and then the propagation expression in spatial domain is obtained by Fourier transform. Numerical examples are illustrated to show intensity distributions with different distance and bandwidth. Variations of spatial modes and spatiotemporal effect are investigated and discussed in detail. The results show that the intensity distributions tend to Gaussian mode with increasing of distance. Also, the laser presents stronger spatiotemporal effect when the bandwidth increases and the transverse distributions change evidently. The characteristic of the changes is that the intensity distributions of the wave front are narrowing and those of the wave rear are spreading with decreasing bandwidth.