Elliptic Vortices in Composite Mathieu Lattices

TL;DR

This paper investigates elliptic vortex solitons in defocusing nonlinear media with composite Mathieu lattices, revealing their formation, bifurcation from dipole modes, and stabilization mechanisms, expanding understanding of symmetry breaking in optical systems.

Contribution

It presents the first example of elliptic vortex bifurcation from dipole modes in optics, highlighting their unique formation and stabilization in Mathieu lattice potentials.

Findings

Elliptic vortices exist above a certain energy threshold.

Single-charged elliptic vortices bifurcate from dipole modes.

Higher-order vortices can have spatially separated phase singularities.

Abstract

We address the elliptically shaped vortex solitons in defocusing nonlinear media imprinted with a composite Mathieu lattice. Elliptic vortices feature anisotropic patterns both in intensity and phase, and can only exist when their energy flow exceed some certain threshold. Single-charged elliptic vortices are found to arise via bifurcation from dipole modes, which, to the best of our knowledge is the first example in the context of optics studies of symmetry breaking bifurcations for the phase dislocations of different dimensionalities. Higher-order elliptic vortices with topological charge could exhibit spatially separated single-charged phase singularities, leading to their stabilization. The salient features of reported elliptic vortices qualitatively hold for other elliptic shaped confining potentials.