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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。
Based on the paraxial wave equation, the transmission equation of the chirped hyperbolic secant secant pulse beam in free space is given and the effect of chirp on the spatial intensity distribution of the hyperbolic secant secant pulse beam is studied. The results show that the initial chirp at initial position has no effect on the spatial distribution of the hyperbolic quasi- pulsed beam, but affects the spatial distribution of the front and back edges of the pulse. After the transmission of the hyperbolic secant pulse beam, the chirp has a great influence on the spatial intensity distribution of the hyperbolic secant pulse beam. As long as the chirp coefficient is large enough, for a hyperbolic curve whose pulse width is larger than one or even tens of optical oscillation periods, Quasi-pulsed beams also have spatial singularity. The size and sign of the chirp coefficient have different effects on the spatial intensity distribution of the hyperbolic secant pulse beam.