Abstract
In this paper, a family of integral solutions representing ultrashort pulsed beam propagation in free space is studied by using the comoving frame coordinates and the Fourier transformation for time variable in terms of well-known paraxial approximation. The pulsed Gaussian-like beam solution is obtained as a special case of the integral solution, where the pulsed Gaussian beam solution is included. Further, starting from the nonparaxial pulsed beam propagation equation in the temporal-frequency domain and making use of the spatial Fourier transform, the nonparaxial pulsed beam solution is derived based on the paraxial pulsed beam solution, where the nonparaxiality is evaluated by a series of expansions.
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