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.

Entropy, purity and optical hysteresis in markovian optical modes.

We describe the synthesis of optical modes whose axial structure follows a random tandem array of Bessel beams of integer order. The array follows fluctuations of Markov-chain type and the amplitude values for each beam are linked to a sequence of random vectors. As a prototype, we describe the synthesis of optical fields for Markov-chain type Ehrenfest.

Stability of focusing regions and its vortex-solitonic properties.

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.

Invariant correlated optical fields driven by multiplicative noise.

We describe the evolution of a linear transmittance when it is perturbed with multiplicative noise; the evolution is approximated through an ensemble of random transmittances that are used to generate diffraction fields. The randomness induces a competition mechanism between noise and transmittance, and it is identified through the self-correlation function. We show that the geometry of the self-correlation function is a single peak preserved in the diffraction field that can be matched with localization-like effects.