The vectorial nonparaxial propagation method of the few-cycle ultrashort pulsed beam in free space
单周期以上超短脉冲光束在自由空间中的矢量非傍轴传输方法

Based on the purterbative method which was developed by Lax et al, and by using of the Fourier transform, we obtain a vectorial nonparaxial correction method to the propagation of the few-cycle pulsed beam in free space. the first-order of the transverse component of the correction is the same as that of Fu's in the frequency domain, and is more convenient to obtain the analytical nonparaxial solution in the temporal domain. It is shown in the examples and the analysis that the vector corrections must be included in any study that wants to go beyond the scalar paraxial solution. From the examples, we find that the spatial distribution of the vectorial nonparaxial correction would be influenced by the temporal distribution of the pulse.