从傍轴波动方程出发, 给出了啁啾双曲正割脉冲光束在自由空间中的传输方程, 研究了啁啾对双曲正割脉冲光束空间强度分布的影响。结果表明, 在初始位置初始时刻啁啾对双曲正割脉冲光束空间强度的分布没有任何影响, 但会影响脉冲前后沿的空间强度分布。当双曲正割脉冲光束传输以后, 啁啾对双曲正割脉冲光束空间强度的分布影响很大, 只要啁啾系数足够大, 对于脉冲宽度大于一个甚至是几十个光波振荡周期的双曲正割脉冲光束同样存在空间奇异性。啁啾系数的大小和符号对双曲正割脉冲光束空间强度的分布有不同的影响。

The propagation expression for the ultrashort chirped hyperbolic secant pulsed beams in free space is deduced analytically. The influence of chirp on the spatial intensity distributions of the hyperbolic secant pulsed beams is studied. The results show that, at the initial distance and the initial time the chirp has no influence on the spatial intensity distributions, but it affects the pulse front edge or back edge. When the pulsed beams propagate in free space, the chirp affects the spatial intensity distributions of the hyperbolic secant pulsed beams seriously. The spatial singularity appears as long as the chirp is enough large for the hyperbolic secant pulsed beams whose pulse duration is longer than one even few cycle optical oscillation period. The sign of the chirp also affects the spatial intensity distribution of the ultrashort hyperbolic secant pulsed beams.