Vortex structures in optical fibers with spatial dependence of the refractive index

It is well-known that vortex structures of laser beam can be created by different optical masks and holograms. These vortices are solutions of the 2D scalar Leontovich equations and admit amplitude and phase singularities. The main idea of present work is to investigate the formation of vortex structures for optical pulses, evolving in dispersive Kerr-type nonlinear medium with spatial dependence of the refractive index. The propagation of such type of laser pulses is governed by nonlinear vector system of amplitude equations. We found new class of analytical solutions with vortex structures for concave gradient fibers. Their stability is a result of the balance between diffraction and nonlinearity, as well as the balance between nonlinearity and angular distribution.