Gaussian beam summation analysis of half plane diffraction: A full 3D formulation

A Gaussian beam summation (GBS) representation for a three-dimensional half-plane diffraction of a Gaussian beam (GB) that hits arbitrarily close to the edge is presented. The expansion involves an angular spectrum of GB¿s in the plane normal to the edge and a discrete phase-space decomposition along the edge. The field is thus described as a sum of GB¿s emerging from a discrete set of points along the edge, at a discrete set of directions in a polar coordinate system. Expressions for the excitation amplitudes of the diffracted beams are derived and validated numerically.