Optical vortices in dispersive nonlinear Kerr type media

The applied method of slowly varying amplitudes of the electrical and magnet vector fields give us the possibility to reduce the nonlinear vector integro-differential wave equation to the amplitude vector nonlinear differential equations. It can be estimated different orders of dispersion of the linear and nonlinear susceptibility using this approximation. The critical values of parameters to observe different linear and nonlinear effects are determinate. The obtained amplitude equation is a vector version of 3D+1 Nonlinear Schredinger Equation (VNSE) describing the evolution of slowly varying amplitudes of electrical and magnet fields in dispersive nonlinear Kerr type media. We show that VNSE admit exact vortex solutions with classical orbital momentum $\mathrm{\ell }=1$ and finite energy. Dispersion region and medium parameters necessary for experimental observation of these vortices, are determinate. PACS 42.81.Dp;05.45.Yv;42.65.Tg