Focusing evolution of generalized propagation invariant optical fields

The focusing evolution of apertured propagation invariant optical fields (PIOFs) with arbitrary transverse intensity distribution is analysed in detail. A decomposition of the PIOF into its constituent plane waves is applied to find a simple expression of the normalized intensity along the propagation axis which is valid for any PIOR It is shown that the presence of an apparent focus close to the focal plane is a general property of any focused PIOF and that it is not related to the focal shift due to apertures. By selecting appropriate parameters it is possible to generate a second intense peak beyond the focal plane. Additionally, we define the conditions under which the original PIOF can be reconstructed beyond the focal plane with a desired magnification.