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arXiv · 0811.0156

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

Miguel-Ángel García-March·Albert Ferrando·Mario Zacarés·Sarira Sahu·Daniel E. Ceballos-Herrera
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Abstract

We determine the functional behavior near the discrete rotational symmetry axis of discrete vortices of the nonlinear Schr\"odinger 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.

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Miguel-Ángel García-March, Albert Ferrando, Mario Zacarés, Sarira Sahu, Daniel E. Ceballos-Herrera. 2008-11-02. Symmetry, winding number and topological charge of vortex solitons in discrete-symmetry media. https://doi.org/10.1103/physreva.79.053820

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