Vortex solitons in quasi-phase-matched photonic crystals with competing quadratic and cubic nonlinearity

We introduce a methodology for investigating vortex solitons (VSs) within quasi-phase-matched (QPM) photonic crystals, featuring competing quadratic and cubic nonlinearities. The photonic crystal is introduced with a checkerboard structure, which is feasible through contemporary technological advancements. The VS family is constructed as quadrupole and 8-pole configurations, with the quadrupole solitons displaying rhombus and square modes depending on different phase-matching conditions. Notably, an intriguing transformation from the quadrupole to the 8-pole configuration can be achieved by modulating the cubic nonlinear coefficient. Additionally, the square-shaped VSs would transfer to rhombus patterns by adjusting the power and size of the checkerboard cell in the framework of cubic nonlinearity. This work presents a versatile and powerful tool for exploring and manipulating vortex solitons in QPM photonic structures, with potential applications in optical signal processing, optical communications, and nonlinear optics research.