Localized vortex beams in anisotropic Lieb lattices

TL;DR

This paper investigates nonlinear vortex modes in anisotropic Lieb lattice waveguide arrays, analyzing their existence, stability, and potential for experimental observation, with a focus on topological charges from 1 to 3.

Contribution

It provides the first detailed analysis of vortex solutions in anisotropic Lieb lattices, highlighting stability behaviors related to topological charge and anisotropy effects.

Findings

Localized vortex patterns with topological charges 1 to 3 identified.

Stability varies with anisotropy and topological charge.

Insights into experimental realization of vortex states in waveguide arrays.

Abstract

We address the issue of nonlinear modes in a two-dimensional waveguide array, spatially distributed in the Lieb lattice geometry, and modeled by a saturable nonlinear Schr\"odinger equation. In particular, we analyze the existence and stability of vortex-type solutions finding localized patterns with symmetric and asymmetric profiles, ranging from topological charge S=1 to S=3. By taking into account the presence of anisotropy, which is inherent to experimental realization of waveguide arrays, we identify different stability behaviors according to their topological charge. Our findings might give insight on experimental feasibility to observe these kind of vortex states.