Morphological transformation of generalized spirally polarized beams by anisotropic media and its experimental characterization

Generalized naming game and Bayesian naming game as dynamical systems

We study the β model (β-NG) and the Bayesian Naming Game (BNG) as dynamical systems. By applying linear stability analysis to the dynamical system associated with the β model, we demonstrate the existence of a nongeneric bifurcation with a bifurcation point β_{c}=1/3. As β passes through β_{c}, the stability of isolated fixed points changes, giving rise to a one-dimensional manifold of fixed points. Notably, this attracting invariant manifold forms an arc of an ellipse. In the context of the BNG, we propose modeling the Bayesian learning probabilities p_{A} and p_{B} as logistic functions. This modeling approach allows us to establish the existence of fixed points without relying on the overly strong assumption that p_{A}=p_{B}=p, where p is a constant.

Streamlines and topological transformation of modified vector Bessel-Gauss beams

We characterize the streamline patterns of the transverse electric (TE) and transverse magnetic (TM) modes of the vector-modified Bessel-Gauss (BG) beam, which is the Fourier-transformed version of the ordinary BG beam. We derive analytical expressions to approximate the streamline patterns produced by the superposition of TM and TE modes. An analysis of the effect on the streamlines of the vector BG beams produced by some polarization devices, e.g., linear retarders and spiral polarizers, is presented. Additionally, we study the geometrical phase induced by linear retarders into the TM mode of the field. This work contributes to the description and understanding of the vector structure of the focal field of Bessel-Gauss beams.