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arXiv · 0909.4820

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

K. J. H. Law·D. Song·P. G. Kevrekidis·J. Xu·Zhigang Chen
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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.

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K. J. H. Law, D. Song, P. G. Kevrekidis, J. Xu, Zhigang Chen. 2009-09-25. Geometric stabilization of extended S=2 vortices in two-dimensional photonic lattices: theoretical analysis, numerical computation and experimental results. https://doi.org/10.1103/physreva.80.063817

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