# Geometric stabilization of extended S=2 vortices in two-dimensional photonic lattices: theoretical analysis, numerical computation and experimental results

## TL;DR

This paper investigates the stability and experimental realization of extended S=2 vortices in two-dimensional photonic lattices, demonstrating their stability under various nonlinearities through theoretical, numerical, and experimental methods.

## Contribution

It provides the first combined theoretical, numerical, and experimental analysis of stable extended S=2 vortices in photonic lattices with different nonlinearities.

## Key findings

- Extended S=2 vortices can be stable or weakly unstable under certain conditions.
- Stable vortices observed in experiments preserve their singularities during propagation.
- Both self-focusing and self-defocusing nonlinearities support vortex stability.

## Abstract

In this work, we focus our studies on the subject of nonlinear discrete self-trapping of S=2 (doubly-charged) vortices in two-dimensional photonic lattices, including theoretical analysis, numerical computation and experimental demonstration. We revisit earlier findings about S=2 vortices with a discrete model, and find that S=2 vortices extended over eight lattice sites can indeed be stable (or only weakly unstable) under certain conditions, not only for the cubic nonlinearity previously used, but also for a saturable nonlinearity more relevant to our experiment with a biased photorefractive nonlinear crystal. We then use the discrete analysis as a guide towards numerically identifying stable (and unstable) vortex solutions in a more realistic continuum model with a periodic potential. Finally, we present our experimental observation of such geometrically extended S=2 vortex solitons in optically induced lattices under both self-focusing and self-defocusing nonlinearities, and show clearly that the S=2 vortex singularities are preserved during nonlinear propagation.