Solitons and vortices formation in deformed photonic graphene

We investigate the formation and evolution of two-dimensional solitons and vortices in deformed photonic graphene, encompassing fundamental solitons, multipole solitons, and vortex solitons. Using the plane-wave expansion method, we analyze the bandgap structure of photonic graphene, revealing Dirac cones whose characteristics are influenced by deformation. Soliton generation results from lattice potential deformation, linear energy gap modulation, and nonlinear effects. Specifically, fundamental and dipole solitons, exhibiting out-of-phase behavior, propagate robustly within photonic graphene, maintaining structural integrity over extended distances, while other soliton solutions are unstable. Furthermore, we explore the realization and propagation characteristics of vortex solitons with unit topological charge within photonic graphene.