Elimination of the spatial singularity of ultrashort pulsed beams in dispersive media

Under the condition that the propagation constant k in dispersive media should be larger than zero, a simple method is proposed to eliminate the spatial singularity of ultrashort pulsed beams propagating in dispersive media. Taking the pulsed Gaussian beam (PGB) as a typical example, the analytical propagation equation in the space-time domain is derived and the spatiotemporal propagation properties of PGBs in normal and anomalous dispersive media are discussed both analytically and numerically. The physical explanation of the results is presented.