By using a different initial value from the previous treatments, we reveal that the pulsed Gaussian beam in free space can be expressed as a simple wave packet along with the complex time, which gives all the information about the spatial and temporal behaviors of the pulse. Then the space-time profiles of a space-time Gaussian pulse are studied. It is shown that even when the pulse propagates in free space, there exist couplings among the beam parameters in space and time. The spot-size-related couplings enlarge the temporal domain (TD) spatial size of the pulse and lessen the carrier frequency of the pulse of the paraxial points, and the wavefront-related couplings bend the transverse spatial shape of the pulse with the wavefront.
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Wang et al. (1997) studied this question.
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