Vortex solitons in disclination quasicrystals

Quasicrystals are ubiquitous in nature. They represent unique aperiodic materials featuring long-range order that occupy an intermediate niche between exactly periodic and disordered materials. These properties are reflected in the unusual evolutionary dynamics of excitations and unique localization properties of linear eigenmodes supported by quasicrystals. In particular, being the structures characterized by discrete rotational symmetryCνof orderν, photonic quasicrystals can support the stable propagation of linear vortex-carrying light beams and vortex solitons. However, the impact of discrete rotational symmetryνof quasicrystals on the properties of vortex light states has not been investigated so far, as only the systems constructed using the simplest Penrose tiling or corresponding optically induced Penrose lattices are 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 novel quasicrystalline structures with any desired order of discrete rotational symmetry from the basic Penrose structure. Such global topological deformation substantially enriches the 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 find two different classes of stable vortex solitons comprising in-phase or out-of-phase pairs of closely located bright spots, with total intensity distribution reflecting a particular discrete rotational symmetry of the quasicrystal with disclination. Remarkably, even low-charge vortex solitons can be stable in quasicrystals with disclinations, whereas stability intervals for them broaden with the decrease of the discrete rotational symmetryCνof quasicrystals. Our results extend the theory of localization in quasicrystals to structures with global topological deformation, highlighting emerging prospects for the robust transmission of power or information arising in these systems.