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

We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schroedinger equation. We show that these solutions present a central phase singularity whose charge is restricted by symmetry arguments. Consequently, we demonstrate that the existe...

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Bibliographic Details
Published in:Physical review. A, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2009-05, Vol.79 (5)
Main Authors: Garcia-March, Miguel-Angel, Zacares, Mario, Ferrando, Albert, Sahu, Sarira, Ceballos-Herrera, Daniel E., Centro de Investigaciones en Optica A.C., Leon, Gto. 37170
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CRYSTALS
FIBERS
MATHEMATICAL SOLUTIONS
NONLINEAR PROBLEMS
ROTATIONAL INVARIANCE
SCHROEDINGER EQUATION
SINGULARITY
SOLITONS
SYMMETRY
TOPOLOGY
VORTICES
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Summary:We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schroedinger 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.
ISSN:1050-2947
1094-1622
DOI:10.1103/PHYSREVA.79.053820