Vortex solitons in disclination quasicrystals

Abstract

Being structures characterized by discrete rotational symmetry $\mathcal{C}_ν$ of order $ν$, photonic quasicrystals are capable to support stable propagation of linear vortex-carrying light beams and vortex solitons. However, the impact of discrete rotational symmetry $ν$ of quasicrystals on the properties of vortex light states was not investigated so far, as only the systems constructed using the simplest Penrose tiling or corresponding optically induced Penrose lattices were considered in this context. Here we propose a broad class of quasicrystals with global topological defects -- disclinations -- introduced into their structure that allows to produce new quasicrystalline structures with any desired order of discrete rotational symmetry from basic Penrose structure. Such global topological deformation substantially enriches linear spectrum of quasicrystals, allowing them to support new types of linear vortex states and bifurcating from them families of stable thresholdless vortex solitons with unusual intensity and phase distributions. We found two different classes of stable vortex solitons consisting of in-phase or out-of-phase pairs of closely located bright spots, with total intensity distribution reflecting particular discrete rotational symmetry of the quasicrystal with disclination. Remarkably, even low-charge vortex solitons can be stable in quasicrystals with disclinations, while stability intervals for them broaden with decrease of the discrete rotational symmetry $\mathcal{C}_ν$ of quasicrystal. Our results expand the theory of localization in quasicrystals to structures with global topological deformation, highlighting new prospects for robust transmission of power or information arising in these systems.