The production and elimination of the spatial singularity for ultrashort chirp ed pulse-beam propagation in free space

Abstract

We study the propagation of ultrashort chirped pulsed beams in free space. We find that the slowly-varying envelope approximation and complex amplitude envelope are not suitable for ultrashort chirped pulsed beams anymore, because they lead to the spatial singularity that is inconsistent with the physical significanc e of the beam propagation. And the chirp influences the spatial singularity mor e seriously than the width of the pulsed beam does. The spatial singularity can be eliminated by using the complex analytical signal theory. In this paper, we g ive the simulations of spatial singularity about ultrashort chirped pulsed Gauss ian beams with a series of parameters, and the conditions that lead to the spati al singularity etc. We think that the broad spectrum of the ultrashort pulsed be am is the original reason for the spatial singularity.