Laser beam shaping with circular serrated apertures I Spatial filtering

Propagation of an axially symmetrical beam through an apodizer comprising a circular serrated aperture and a spatial filter is considered on the basis of the parabolic equation solution. In part I, the equation is solved for uniform and Gaussian beams with a flat wavefront, which propagate from the circular serrated aperture to the spatial filter focal plane. By analyzing the field structure in the focal plane, the diameter of the spatial filter pinhole required for recovering the axial symmetry of the field at the spatial filter exit is determined as a function of the serrated aperture and spatial filter parameters.