Spatial attributes of diffraction free fields.

Optical diffraction fields have a not easy spatial structure, some times optical diffraction fields can generate a focusing region or caustic region, in this contribution, we describe the focusing region associated with highly symmetric transmittances, we analyze its associated phase function and show that generic features can be studied from a differential equation for a focusing geometry, which is obtained through angular representation for diffraction fields, the diffraction field presents focusing region whose geometry and spatial evolution can be described with the analysis of the phase singularities avoiding the integral representation. We show that in general the diffracted field has a decomposition in optical fields propagating along three optical axis mutually perpendicular. The decomposition is in terms of the Pearcey and Airy functions and generalized Airy function. Experimental results are shown.