We predict the existence of spatial-spectral vortex solitons in one-dimensional periodic waveguide arrays with quadratic nonlinear response. In such vortices the energy flow forms a closed loop through the simultaneous effects of phase gradients at t
he fundamental frequency and second-harmonic fields, and the parametric frequency conversion between the spectral components. The linear stability analysis shows that such modes are stable in a broad parameter region.
We analyze the existence and stability of two-component vector solitons in nematic liquid crystals for which one of the components carries angular momentum and describes a vortex beam. We demonstrate that the nonlocal, nonlinear response can dramatic
ally enhance the field coupling leading to the stabilization of the vortex beam when the amplitude of the second beam exceeds some threshold value. We develop a variational approach to describe this effect analytically.
We study the properties of surface solitons generated at the edge of a semi-infinite photonic lattice in nonlinear quadratic media, namely two-color surface lattice solitons. We analyze the impact of phase mismatch on existence and stability of surfa
ce modes, and find novel classes of two-color twisted surface solitons which are stable in a large domain of their existence.
