Within the limits of the paraxial approximation used in treating gaussian beams, the ordinary boundary-diffraction-wave theory is also applicable to diffraction problems that involve gaussian incident beams. The total field diffracted by an aperture is thus given by the interference of two component waves: a boundary-diffraction wave and, if allowed by geometrical considerations, the unperturbed wave that would propagate freely to the observation point in the absence of the diffracting aperture. To this end, the gaussian field distribution must be described by properly defined complex amplitude and phase functions. Examples are calculated for gaussian beams with cylindrical symmetry. The general equation for the ray paths associated with the gaussian beams is also derived; it is used to show that the shadow boundarybehind the diffracting screen follows a hyperbola.
Gabriel Otis, "Application of the boundary-diffraction-wave theory to gaussian beams," J. Opt. Soc. Am. 64, 1545-1550 (1974)