RESUMEN
Herein, an analysis of the optical field emerging from a topological Young's interferometer is conducted. The interferometer consists of two 3D-slit shape curves and is studied by projecting it onto a trihedral reference system. From the projection, Airy, Pearcey, and cusped-type beams emerge. The optical field of these beams is organized around its caustic region. The interference between these types of beams presents interesting physical properties, which can be derived from the interaction between the interference fringes and the caustic regions. One property of the interaction is the irradiance flow, which induces a long-distance interaction between the caustic regions. Another property is the bending of the interference fringes toward the caustic regions, which acts as a sink. Due to the adiabatic features of the caustic regions, the interaction between the fringes-caustic and caustic irradiance is studied using a predator-prey model, which leads to a logistic-type differential equation with nonlinear harvesting. The stability analysis of this equation is in good agreement with the theoretical and experimental results.
RESUMEN
Focusing regions, also known as caustic regions, are the singular solutions to the amplitude function of optical fields. Focusing regions are generated by the envelope curve of a set of critical points, which can be of attractor or repulsor type. The nature of the critical point depends on the refractive index. An important property of the critical points is that they present charge-like features. When a focusing region is generated in media with a random refractive index, current-like effects appear, and the evolution of the focusing regions follows a diffusion behavior. The morphology of the focusing regions may generate vortices or "eternal solutions" of solitonic type in a nonlinear medium. Herein, the condition under which these effects occur is analyzed and experimentally corroborated.