Symmetry, winding number and topological charge of vortex solitons in discrete-symmetry media

Abstract

We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schrödinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existence of high-charged discrete vortices is related to the presence of other off-axis phase singularities, whose positions and charges are also restricted by symmetry arguments. To illustrate our theoretical results, we offer two numerical examples of high-charged discrete vortices in photonic crystal fibers showing hexagonal discrete rotational invariance.

6 pages, 2 figures

References in corpus (2)

• Cosmology with inhomogeneous magnetic fields
• Families of Vortex Solitons in Periodic Media

Cited by in corpus (11)

• Solitons in nonlinear lattices
• One-dimensional mixtures of several ultracold atoms: a review
• Vortex solitons in twisted circular waveguide arrays
• Vortex solitons of the discrete Ginzburg-Landau Equation
• Discrete multivortex solitons
• A topological charge selection rule for phase singularities
• Discrete-Gauss states and the generation of focussing dark beams
• Symmetry breaking and singularity structure in Bose-Einstein condensates
• Creation of topological states of a Bose-Einstein condensate in a plaquette
• A method for the dynamics of vortices in a Bose-Einstein condensate: analytical equations of the trajectories of phase singularities
• Graded-index optical fiber emulator of an interacting three-atom system: illumination control of particle statistics and classical non-separability