APPLICATION OF THE BOUNDARY-DIFFRACTION-WAVE THEORY TO GAUSSIAN BEAMS

摘要

When applied to a plane or spherical incident wave, the boundary-diffraction-wave (BDW) theory expresses the total field diffracted by an aperture as the interference of two component waves, a boundary-diffraction-wave and, if allowed by geometrical considerations, an unperturbed wave originating from the source. Using properly defined complex amplitude and complex phase functions, it is shown here that, under conditions usually satisfied in practical situations, the diffraction problem involving a gaussian incident beam can be interpreted in terms of the BDW theory. Examples of calculations are given for gaussian beams with cylindrical symmetry. The general equation for the ray paths associated with the gaussian beams is also derived, and it is used to show that the shadow boundary behind the diffracting screen follows a hyperbola.