  An approximation is elaborated for the paraxial propagation of diffracted
beams, with both one- and two-dimensional cross sections, which are released
from apertures with sharp boundaries. The approximation applies to any beam
under the condition that the thickness of its edges is much smaller than any
other length scale in the beam's initial profile. The approximation can be
easily generalized for any beam whose initial profile has several sharp
features. Therefore, this method can be used as a tool to investigate the
diffraction of beams on complex obstacles. The analytical results are compared
to numerical solutions and experimental findings, which demonstrates high
accuracy of the approximation. For an initially uniform field confined by sharp
boundaries, this solution becomes exact for any propagation distance and any
sharpness of the edges. Thus, it can be used as an efficient tool to represent
the beams, produced by series of slits with a complex structure, by a simple
but exact analytical solution.
