Families of Vortex Solitons in Periodic Media

TL;DR

This paper reports on the existence and properties of various families of charge-one vortex solitons in two-dimensional periodic media, highlighting their unique bifurcation behavior and topological diversity across different nonlinearities.

Contribution

It reveals that vortex families in periodic media do not bifurcate from Bloch bands and can include vortices with diverse topologies within the same family.

Findings

Vortex families exist in both semi-infinite and higher band gaps.

Vortex families do not bifurcate from Bloch bands but turn around before reaching band edges.

Different topological vortex shapes can belong to the same family.

Abstract

Various families of charge-one vortex solitons in two-dimensional periodic media are reported. These vortices reside either in the semi-infinite gap or higher band gaps of the media. For both Kerr and saturable nonlinearities (either focusing or defocusing), infinite vortex families are found. All these families do not bifurcate from Bloch bands; rather, they turn around before reaching edges of Bloch bands. It is further revealed that vortices with drastically different topological shapes can belong to the same vortex family, which is quite surprising.