Optical vortices in waveguides with spatial dependence of the nonlinear refractive index

In the present work, the formation of optical vortex in waveguides, with spatial dependence of the nonlinear refractive index, is studied. The propagation of such type of laser pulses is governed by a system of amplitude equations for x and y components of the electrical field in which the effects of second-order dispersion and self-phase modulation are taken into account. The corresponding system of equations is solved analytically. New class of exact solutions, describing the generation of vortex structures in the optical fibers with spatial dependence of the nonlinear refractive index and anomalous dispersion, are found. These optical vortices admit only amplitude type singularities. Their stability is a result of the delicate balance between diffraction and nonlinearity, as well as nonlinearity and angular distribution. This kind of singularities can be observed as a depolarization of the vector field in the laser spot.