Vortex solutions of vector nonlinear amplitude equations in optics

Different kind of vortex structures of laser beam can be created by optical holograms and different optical masks. In the theory these vortices are solutions of the 2D scalar Leontovich equations. These solutions admit amplitude and phase singularities. The main tack of this work is to investigate the possibility of formation of vortex structures for narrow-band optical pulses, propagating in Kerr-type media. The evolution of such type of laser pulses is governed by nonlinear vector system of amplitude equations in second approximation of the linear dispersion. We found new class of analytical solutions with vortex structures. The nonlinear dispersion relations obtained by these vortex solutions show that their stability is due not only to balance between diffraction and nonlinearity, but also to a balance between non-linearity and angular distribution.