Gap vortex solitons in periodic media with quadratic nonlinearity

We explore the existence and stability of two-dimensional spatial gap solitons with embedded vorticity in a bulk medium with the quadratic (χ (2)) nonlinearity and a transverse grating represented by periodic modulation of the refractive index. Gap-vortex solitons (GVSs) can be found in total gaps of the underlying spectra of the fundamental-frequency and second-harmonic waves. We demonstrate the existence of a family of stable GVSs, which are built as four-peak complexes, in the lowest total gap. We also consider dynamical effects, such as self-trapping of GVSs from input beams, and delocalization transitions.