We have investigated the nonlinear amplitude vector equation governing the evolution of optical pulses in optical and UV region. We have normalized this equation for the case of different transverse and longitudinal size of the optical pulses (long pulses), and also for the case of equal transverse and longitudinal size (so called light bullets or LB). This gives us the possibility to reduce the amplitude equation to several kinds of linear and nonlinear evolution equations in the partial cases. One unexpected new result is the relatively stability of LB and the significant decreasing of the diffraction enlargement in respect to the case of long pulses in linear regime of propagation. In the second part of the paper we look for media parameters and characteristics of the LB to obtain conditions for strong negative dispersion and nonlinearity higher but near to critical for self-focusing. We found that the propagation of LB in these special cases is governed by the 3D+1 vector nonlinear Schrodinger equation (VNSE). For the VNSE exact vortex solutions are found. Conditions for experimental observations of these vortices are determined.
L. M. Kovachev,
L. M. Ivanov,
"Vortex solitons in dispersive nonlinear Kerr type media", Proc. SPIE 5949, Nonlinear Optics Applications, 594907 (5 October 2005); doi: 10.1117/12.621852; https://doi.org/10.1117/12.621852