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

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.

References in corpus (4)

• Families of Vortex Solitons in Periodic Media
• Stable higher-charge discrete vortices in hexagonal optical lattices
• Discrete solitons and vortices in hexagonal and honeycomb lattices: Existence, stability, and dynamics
• Stability of Quantized Vortices in a Bose-Einstein Condensate Confined in an Optical Lattice

Cited by in corpus (4)

• Composite vortices in nonlinear circular waveguide arrays
• Stable structures with high topological charge in nonlinear photonic quasicrystals
• The Drastic Role of Beyond Nearest-Neighbor Interactions on Two-Dimensional Dynamical Lattices: A Case Example
• Wavepacket spreading dynamics under a non-instantaneous nonlinearity: Self-trapping, defocusing and focusing