为了研究超短啁啾脉冲复宗量拉盖尔-高斯光束合理的物理模型和光束参量对物理模型的影响,采用复振幅包络表示式和复解析信号表示式推导了这类脉冲光束的复振幅包络解和复解析信号解。对复振幅包络解奇异性的产生进行了详细分析,讨论了脉冲啁啾、脉冲宽度和模式对复振幅包络解奇异性的影响。计算结果表明,当脉冲光束存在啁啾时,啁啾量越大,复振幅包络解的奇异点位置离光束中心越近,而复解析信号解在任意大小啁啾的情况下都不存在奇异性;对于啁啾量相同的脉冲,脉冲宽度越小或模指数越大其奇异性位置离光束中心越近。因而要建立激光光束合理的物理模型必须根据光束参量采用合适的研究方法。

In order to study the physical model of the ultrashort pulses with spatial profiles of elegant Laguerre-Gaussian transverse modes and the effect of beam parameters on the model,complex amplitude envelope(CAE) solution and complex analytical signal(CAS) solution of pulsed beams were derived according to CAE and CAS representations.Generation of the singularity in the CAE solution and effect of the chirp,the pulse duration and the mode on it were analyzed.The results indicate that singularity of the CAE solution closer to the central with larger chirp and the CAS solution doesn't present singularity with any chirp.The singularity is located nearer to the central axis for the pulses with higher order transverse modes and shorter pulse duration.Thus,to obtain reasonable physical model of the laser beams,appropriate method should be adopted according to the beam parameters.