Topological phase of optical vortices in few-mode fibers

It has been found that as they propagate, the natural optical vortices of a few-mode parabolic fiber acquire a topological phase in addition to the dynamic phase. The magnitude of this phase is numerically equal to the polarization correction to the propagation constant of the CV and IV vortices. An analysis revealed that this phase is a new type of optical manifestation of the topological Berry phase. The already known Pancharatnam and Rytov-Vladimirski\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}$$ \end{document}. phases are associated with changes in the magnitude and direction of the angular momentum flow of the wave. In the fields of natural vortices of a few-mode fiber all the explicit parameters of the wave remain unchanged during propagation. However, the direction of the momentum density vector of the vortex undergoes cyclic variations along the trajectory of the energy flow line. These cyclic variations of the implicit vortex parameter are responsible for the new type of topological phase. Unlike the study made by van Enk (Ref. 6), where the topological phase was only related to the angular momentum for the lowest-order Gaussian beams (l=±1), this topological phase describes guided vortices with any values l of the topological charge. The results can be used to estimate the stability of CV and IV vortices relative to external perturbing influences on the optical fiber.