  A "genuinely" paraxial version of Miyamoto-Wolf's theory aimed at dealing
with sharp-edge diffraction under Gaussian beam illumination is presented. The
theoretical analysis is carried out in such a way the well known
Young-Maggi-Rubinowicz boundary diffraction wave theory can be extended to deal
with Gaussian beams in an apparently straightforward way. The key for achieving
such an extension is the introduction of suitable "complex angles" within the
integral representations of the geometrical and BDW components of the total
diffracted wavefield. Surprisingly enough, such a simple (although not
rigorously justified) mathematical generalization seems to work well within the
complex Gaussian realm. The resulting integrals provide meaningful quantities
that, once suitably combined, give rise to predictions which are in perfect
agreement with results already obtained in the past. An interesting and still
open theoretical question about how to evaluate "Gaussian geometrical shadows"
for arbitrarily shaped apertures is also discussed.
