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A "genuinely" paraxial version of Miyamoto-Wolf's theory aimed at dealingwith sharp-edge diffraction under Gaussian beam illumination is presented. Thetheoretical analysis is carried out in such a way the well knownYoung-Maggi-Rubinowicz boundary diffraction wave theory can be extended to dealwith Gaussian beams in an apparently straightforward way. The key for achievingsuch an extension is the introduction of suitable "complex angles" within theintegral representations of the geometrical and BDW components of the totaldiffracted wavefield. Surprisingly enough, such a simple (although notrigorously justified) mathematical generalization seems to work well within thecomplex Gaussian realm. The resulting integrals provide meaningful quantitiesthat, once suitably combined, give rise to predictions which are in perfectagreement with results already obtained in the past. An interesting and stillopen theoretical question about how to evaluate "Gaussian geometrical shadows"for arbitrarily shaped apertures is also discussed.

Gaussian sharp-edge diffraction: a paraxial revisitation of Miyamoto-Wolf's theory