洛仑兹脉冲光束的复振幅包络解和复解析信号解的比较研究

使用复振幅包络表示式和复解析信号表示式推导了洛仑兹脉冲光束的传输公式．通过具体数值计算对脉冲光束的复振幅包络解和复解析信号解在不同带宽时的传输进行了对比研究．数值结果表明脉冲光束为窄带时，在传输方向轴中心的一定范围内两种解是一致的，而对于宽带脉冲光束，复振幅包络解在轴中心较近的距离即表现出奇异性，复解析信号解才是符合物理意义的表示式．由数值计算得出了选择脉冲光束研究方法的条件，并从所得公式对复振幅包络解出现奇异性的现象进行了解释．

By using complex amplitude envelope representation and complex analytic signal representation, propagation expressions of Lorentz pulsed beams are derived. Propagation properties of them with different bandwidths are illustrated by numerical calculations. It is found that they are the same in the neighbourhood of z-axis for narrowband pulses, but in the case of broadband pulses, singularities emerge near z-axis for pulsed beams obtained by using complex amplitude envelope representation and only complex analytic signal representation is applicable. The conditions to decide what representation should be chosen to study pulsed beams are given. And the origin that results in the emergence of singularity is given.