Paraxial sharp-edge diffraction: a general approach

A general reformulation of classical sharp-edge diffraction theory is proposed within paraxial approximation. The, not so much known, Poincaré vector potential construction is employed directly inside Fresnel's 2D integral in order for it to be converted into a single 1D contour integral over the aperture boundary. Differently from the recently developed paraxial revisitation of BDW's theory, such approach should be applicable, in principle, to arbitrary wavefield distributions impinging onto arbitrarily shaped sharp-edge planar apertures. However, in those cases where such a conversion were not analytically achievable, our approach allows Fresnel's integral to be easily converted, irrespective of the shape and the regularity features of the aperture geometry, into a double integral defined onto a square domain. A couple of interesting examples of application of the proposed method is presented.