Propagation of pulsed beam beyond the paraxial approximation in free space

We study the propagation of ultrashort pulsed beam (down to the limit of single-cycle pulse) beyond the paraxial approximation in free space. By application of the perturbation method, the nonparaxial corrections to an arbitrary paraxial solution are given in a series form. The rigorous nonparaxial results are obtained for comparison by numerical simulation. It shows that the second-order correction can guarantee a good precision in describing the nonparaxial propagation of a single-cycle pulsed beam, whose beam waist width is of the order of the central wavelength. The nonparaxial propagation of isodiffracting pulsed Gaussian beam is given in detail. It shows the temporal distribution inevitably influences the spatial distribution of the correction due to the inherent spatiotemporal coupling in the pulsed beam. (C) 2003 Elsevier B.V. All rights reserved.