Laser beam shaping with circular serrated apertures. II. Theory of the beam profile formation

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 II, the equation is solved for uniform and Gaussian beams with a flat wavefront propagating from the spatial filter pinhole to its exit. It is shown that serrations with complex shapes (for instance, cosine or parabolic) have no advantage over a simple triangular shape: practically the same beam profiles can be obtained with triangular serrations of slightly different size.