RESUMEN
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. This process models the thermodynamic equilibrium and then it can be related to the evolution and stability of optical systems, in this way, it offers a similitude with partially coherent processes where the coherence degree is now distributed between all the compounds of the resulting random vector. The matrix representation for the stochastic process allows incorporating entropy properties and the calculus of the purity for the optical field. This constitutes the basis to describe the interference between markovian modes. When the set of markovian modes type Ehrenfest reaches a stable configuration they become indistinguishability non-conservative optical field having associated hysteresis features. Computer simulations are presented.
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.
RESUMEN
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. To corroborate the theoretical predictions, we perform an experiment using a linear grating where the noise is approximated by a stochastic Markov chain. Experimental results are shown.
