标题： 二维光子晶格中扩展S=2涡旋的几何稳定化：理论分析、数值计算和实验结果 显示英文标题

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

摘要： 在本工作中，我们专注于研究二维光子晶格中S=2（双电荷）涡旋的非线性离散自 trapping 现象，包括理论分析、数值计算和实验演示。 我们重新审视了关于S=2涡旋的早期发现，并发现S=2涡旋扩展到八个晶格点时，在某些条件下确实可以稳定（或仅弱不稳定），不仅适用于之前使用的立方非线性，也适用于与我们使用偏置光折变非线性晶体实验更相关的饱和非线性。 随后，我们利用离散分析作为指导，在具有周期势的更现实的连续模型中数值地识别出稳定的（和不稳定的）涡旋解。 最后，我们在自聚焦和自散焦非线性下，展示了在光学诱导晶格中此类几何扩展的S=2涡旋孤子的实验观察，并清楚地表明S=2涡旋奇点在非线性传播过程中得以保留。 显示英文摘要

摘要： 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.