Geometric stabilization of extendedS=2vortices 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.

Self-trapping and stabilization of doubly-charged optical vortices in two-dimensional photonic lattices

“…We emphasize again that such solitons are generated under the eight-site excitation, and they are quite different from the four-site excitation which leads to dynamical charge flipping and topological transformation as discussed above. Thus, in an optically induced square lattice, the DCVs can be geometrically stabilized and self-trapped, in good agreement with our theoretical and numerical results [44].…”

“…Our theoretically studies of a continuum model with periodic potentials show that the DCV solitons have large stability regions under both self-focusing and self-defocusing nonlinearities. Details will be reported elsewhere [44]. In our experiment, the same setup of Figure 1 is used.…”

“…It has been suggested that the doubly-charged vortices (DCVs) can be stabilized by introducing a defect site in the square lattices [42], but such defect-stabilized vortex solitons have not been found in experiments. Very recently, however, self-trapping of DCVs into stable higher-order vortex solitons has been observed in experiments with different lattice configurations/excitations under a self-focusing nonlinearity [43,44].…”

Experiments on Linear and Nonlinear Localization of Optical Vortices in Optically Induced Photonic Lattices

“…We want to mention that the DCV beams can also stably self-trap into solitons in the semi-infinite gap under self-focusing nonlinearity with 8-site excitation. Such geometrical extended stabilization mechanism has also been confirmed by theoretical analysis [31].…”

The drastic role of beyond-nearest-neighbor interactions on discrete two-dimensional dynamical lattices: a case example

“…More specifically, we will demonstrate that solutions (such as the discrete vortices of topological charge S = 1), which are robust enough that they can be observed in photonic crystal experiments [26], can be destabilized even by arbitrarily 2 small beyond-nearest-neighbor interaction (of suitable sign). Moreover, we will show that other states which are unstable in the standard case (such as the vortices of topological charge S = 2; see for theory [10,27] and for recent experiments [28]) will be stabilized when the next-nearest neighbor effect is sufficiently strong. Moreover, we will identify special limits (such as the degenerate unit diagonal neighbor limit) whereby even solitary wave (non-vortex) solutions will change (or exchange) their stability.…”