Study of the interference fringes-caustic region interaction in a topological Young's interferometer

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.