Abstract
By using a Fourier transform technique and applying the paraxial approximation in the frequency domain, we derive an integral solution for the transverse and longitudinal components of the light field of an ultrashort pulsed beam propagating in free space. In particular, on the basis of the theory of complex analytical signals, the solutions for the components of a pulsed Gaussian-like beam, in rectangular coordinates, are derived and compared with those derived from slowly varying envelope approximation (SVEA). The corresponding numerical investigations are carried out and show that for sub-cycle pulses, the SVEA will cause spatial singularity for both transverse and longitudinal components of the light field.
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