Second-order spatial characterization of hard-edge diffracted beams

Second-order characteristic beam parameters, including beamwidth and far-field divergence, are generalized for hard-edge diffracted fields. On the basis of, the so-called moments formalism these parameters are shown to propagate through ABCD optical systems according to laws similar to those applied to systems with no hard-edge openings. The power–content ratio of any diffracted beam within a certain region is evaluated in terms of such generalized parameters. An alternative analytical expression of such generalized far-field divergence is also provided that is suitable for experimental measurements. Application to Gaussian beams diffracted by slits is included.