International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 18, Pages 949-967
doi:10.1155/S0161171204301018
Optical vortices in dispersive nonlinear Kerr-type media
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.
Abstract
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.