In the present thesis we perform the study of the optical field generated by diffraction, interpreting the phase function as a catastrophe function. As prototype structure, we use plane transmittances of kind slit shape curve. The coherent illumination of the slit transmittance generates focusing regions as a consequence of the curvature function. We show that the topology of the diffraction field may present regions with different phase values separated by the focusing region. The spatial propagation of the optical field is studied by means of numerical solution to the paraxial Helmholtz equation. The study is extended to describe the diffraction field of 3-D slit transmittances. The mathematical description is implemented using the Frenet-Serret equations. The diffraction field is separated in three optical fields, which they are obtained through the projection on three mutually perpendicular planes known as: osculating, normal and rectifying. The analysis is determined using as parameters the curvature and torsion of the curve. An application of the model performed is used to describe the singularities on surface plasmon fields whose representation is given in terms of Airy and Pearcey functions. Finally, the study of the optical singularities allows us to describe some physical properties such as the bifurcation effects and optical vortexes. The experimental results corroborates the theoretical prediction.