Localized vortex beams in anisotropic Lieb lattices

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 nding localized patterns with symmetric and asymmetric pro les, 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 di erent stability behaviors according to their topological charge. Our ndings might give insight on experimental feasibility to observe these kind of vortex states.