Topological properties of the interaction between focusing regions kind cusped.

We study here the cusped-cusped interaction between two kinds of Pearcey optical fields by analyzing its topological structure. We do it in two steps; the first one is an irradiance interaction that allows us to identify organization regions. The second one is an amplitude interaction, where it is shown that the interference fringes are organized around the irradiance distribution. The topological behavior of the optical field is analyzed identifying regions with different phase functions, one of them, corresponds with a catastrophe function which has associated a focusing region, the other region can be approximated by a quadratic function. The main consequence heritage from the phase structure is interference fringes emerge from focusing regions having similar features like a topological charges. We show computational and experimental results which are in very well agreement with the theoretical model.

Diffraction by three-dimensional slit-shape curves: decomposition in terms of Airy and Pearcey functions.

We analyze the diffraction field generated by coherent illumination of a three-dimensional transmittance characterized by a slit-shape curve. Generic features are obtained using the Frenet-Serret equations, which allow a decomposition of the optical field. The analysis is performed by describing the influence of the curvature and torsion on osculating, normal, and rectifying planes. We show that the diffracted field has a decomposition in three optical fields propagating along three optical axes that are mutually perpendicular. The decomposition is in terms of the Pearcey and Airy functions, and the generalized Airy function. Experimental results are shown.