Optical vortices in dispersive nonlinear Kerr-type media - Lubomir M. Kovachev (International Journal of Mathematics and Mathematical Sciences)
The applied method of slowly varying amplitudes gives us the possibility to reduce the nonlinear vector integrodifferential wave equation of the electrical and magnetic vector fields to the amplitude vector nonlinear differential equations. Using this approximation, different orders of dispersion of the linear and nonlinear susceptibility can be estimated. Critical values of parameters to observe different linear and nonlinear effects are determined. The obtained amplitude equations are a vector version of 3D+1 nonlinear Schrödinger equation (VNSE) describing the evolution of slowly varying amplitudes of electrical and magnetic fields in dispersive nonlinear Kerr-type media. We show that VNSE admits exact vortex solutions with classical orbital momentum ℓ=1 and finite energy. Dispersion region and medium parameters necessary for experimental observation of these vortices are determined.