采用柯林斯公式研究了一阶时空耦合高斯脉冲光束在自由空间的传输特性。推导出了输出面上光束的解析表达式。定义了等相位面旋转角度来衡量相位耦合的严重程度。分析了关联因子和等相位面旋转角度随传输距离的变化。数值模拟了一阶时空耦合高斯脉冲光束在自由空间传输时，空间频率域中脉冲光束强度分布和相位分布的演化情况。研究结果表明，一阶时空耦合高斯脉冲光束在自由空间传输一段距离后仍然是一阶时空耦合高斯脉冲光束；但其时空耦合程度、脉冲光束强度分布和相位分布都会随着传输距离而改变。

The propagation characteristics of Gaussian pulsed beams with first-order spatio-temporal coupling (FSTC) are investigated by means of Collins formula, and the analytical expression for the FSTC beam on the output plane is derived. The rotation angle of equiphase surface is defined to estimate the severity of phase couplings. The correlation coefficient and the rotation angle of equiphase surface are analyzed with the variation of propagation distance. The intensity distribution and phase distribution for different propagation distances are simulated. It is found that after passing a distance in the free space, the FSTC beam keeps the form, but the severity of spatio-temporal couplings, the intensity distribution and phase distribution of the FSTC beam vary with the propagation distance.