Free-space ultrashort pulsed beam propagation beyond the paraxial approximation

Abstract

Applying the temporal and spatial Fourier transform method, we obtain a nonparaxial pulsed beam solution, which is based on the paraxial pulsed beam solution, where the nonparaxiality is evaluated by using a series of expansions. Specifically, the general lowest-order correction field is given in an integral form. Some special examples, such as the lowest-under correction to the paraxial approximation of a fundamental Gaussian pulsed Gaussian-like beam, whose waist plane has a parallel shift from the z = 0 plane, are presented.