This paper presents the results of an investigation on whether or not a Gaussian beam of uniform polarization, which is non-Maxwellian but which can be easily and quickly generated analytically, can be used in place of a rigorously Maxwellian tapered beam for computing numerically the plane wave scattering coefficients of a slab. First, the paper presents a general technique for computing numerically the scattering coefficients of the slab with the incident tapered beam illuminating only the centre portion of the slab to avoid the presence of diffraction fields that would be produced by the edges of the slab. Then, the paper presents results from applying the technique to an infinite size slab for which the plane wave scattering coefficients were known a priori, to assess whether or not the accuracy of the numerically computed scattering coefficients was affected by using the Gaussian beam of perfectly uniform polarization in place of the rigorously Maxwellian tapered beam. Results are shown for lossless slabs, under dominant TMZ or TEZ polarization. Finally, the paper presents a new method for synthesizing a Maxwellian incident tapered beam of dominant polarization.