Spatial attributes of the diffraction field

Optical diffraction fields have in general a spatial complex structure and some times can generate focusing regions, in this work we describe the focusing region associated with highly symmetric transmittances, analyzing its associated phase function. We show that generic features can be studied from a differential equation for a focusing geometry, which is obtained through angular representation for diffraction fields, according to the choice of the parameters involved, the diffraction field presents a new focusing region whose geometry and spatial evolution can be described with the only analysis of the phase singularities avoiding the integral representation.