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.