Stabilization of vortex-soliton beams in nematic liquid crystals

We study the interaction of two optical beams of different wavelengths (colors) in a nematic liquid crystal. We consider the case for which one component carries an optical vortex and the other component describes a localized beam. It is shown that a beam in one color can stabilize a vortex in the other color, the vortex being unstable in the absence of the second beam. We also show that the bright vortex can guide the beam in a stable manner, provided that the nonlocality is large enough. In this context we find that a different type of solitary wave (nematicon) instability can arise, one for which a ring structure develops at its peak. The results of approximate modulation solutions for the interaction between the vortex and the beam are found to be in good quantitative agreement with direct numerical simulations.