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

Abstract

We report our recent work on self-trapping of doubly-charged vortices (DCVs) in two-dimensional optically induced photonic lattices. We show that in an ideal isotropic nonlinear periodic medium self-trapping of a DCV can lead to formation of a rotating 'quasi-vortex' soliton with periodic charge-flipping, but the vortex breaks up into multiple singly-charged vortices in an anisotropic nonlinear medium. Such topological transformation of high-order vortices under conventional four-site excitation in a square photonic lattice has been observed in our experiment and corroborated with numerical simulations. With geometrically extended eight-site excitation, however, discrete self-trapping of a DCV into a stable high-order vortex soliton can be realized with both self-focusing and self-defocusing nonlinearities.We are pleased to contribute this article in honor to and memory of Lorenzo Narducci who remains a source of personal and professional inspiration. Ever clear in his explanations as a teacher and colleague, he was also exemplary in his inclusion of each new student, post-doc, and faculty colleague. Though not an experimentalist, he dedicated himself to understanding experiments and experimental results and matching many of them in his theoretical and computational analyses. He reached out to share his passion for laser physics and quantum optics to colleagues around the world where he was welcomed with warmth which he reciprocated. We treasure his legacy of incisive questions, derivations from first principles, and dedication to physical understanding. We regret that we will not benefit from his questions and critiques in this and future work.

Observation of self-trapping and rotation of higher-band gap solitons in two-dimensional photonic lattices

“…6(a) as an example. Our numerical analysis not only suggests that the quadruple-like soliton will experience rotation similar to dipole solitons but also reveals that the localized quadruple state becomes a rotating doubly-charged vortex (DCV) during rotation and undergoes charge-flipping when the rotating direction is reversed [23,24]. Typical results are shown in Fig.…”