Vortex and corner solitons in Stampfli-tiling dodecagonal quasiperiodic lattices

Abstract

Quasicrystals are ubiquitous materials that lack translational symmetry but exhibit rotational symmetry. Past studies have demonstrated that quasicrystals offer a promising platform for vortex generation and topological phase transitions. To date, explorations of quasicrystals are diverse, owing to their abundant structures and fascinating properties. Here, we report the existence and stability of thresholdless vortex and corner solitons in Stampfli-tiled dodecagonal quasiperiodic lattices. Theoretical analysis shows that both types of solitons bifurcate from their linear counterparts. Their propagation constants, confined within the bandgap, along with distinct localization characteristics, can be effectively tuned by adjusting the power. According to linear stability analysis and numerical simulations, both vortex and corner solitons exhibit complete stability across their entire existence domains under self-defocusing nonlinearity. By contrast, vortex solitons are stable only at low power levels, while corner solitons display universal instability under self-focusing conditions. These findings provide novel theoretical insights into the behavior of nonlinear waves in quasiperiodic lattices and hold potential for optical information processing and integrated photonic device design.