从近轴波动方程出发推导了窄带和宽带双曲正割脉冲光束的解析传输公式。通过数值计算比较了分别采用复振幅包络(CAE)表示式和复解析信号(CAS)表示式得到的脉冲光束,得出了选择脉冲光束研究方法的条件。结果表明复振幅包络表示式得到的解会存在空间奇异性,使光束出现不符合物理意义的非光束行为。对于宽带光束,复振幅包络解的奇异点的位置距离轴中心较近,使复包络解不能正确表示脉冲光束,而对于奇异点位置远离轴中心的窄带光束,对脉冲光束产生的影响可以忽略。因此,窄带脉冲光束可以采用复振幅包络和复解析信号两种表示式来研究,而对于宽带脉冲光束,必须采用严格的复解析信号表示式。

Starting from paraxial wave equation, analytical propagation expressions of hyperbolic secant pulsed beams with narrowband and broadband are derived. By the use of numerical calculations, pulsed beams obtained by means of complex amplitude envelope representation and complex analytical signal representation are compared. The condition to determine what representation should be chosen is also given. It is found that pulsed beam obtained by using complex amplitude envelope representation has singularity, which is anti-beam behavior and loses physical meaning. In the case of pulsed beams with broadband, singularity of complex amplitude envelope solution locates near axis, which causes that the solution failed to describe pulsed beam. But for the case of pulsed beam with narrowband, singularity locates far from axis, which can be neglected in the study of pulsed beam. It is concluded that both of the representations are applicable to study narrowband pulse, but for broadband pulse only rigorous complex analytical signal representation should be adopted.