International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 18, Pages 949-967

Optical vortices in dispersive nonlinear Kerr-type media

Lubomir M. Kovachev

Institute of Electronics, Bulgarian Academy of Sciences, Tsarigradsko, Chaussee 72, Sofia 1784, Bulgaria

Received 2 January 2003

Copyright © 2004 Lubomir M. Kovachev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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 =1 and finite energy. Dispersion region and medium parameters necessary for experimental observation of these vortices are determined.