Full wave vector Maxwell equation simulation of nonlinear self-focusing effects in three spatial dimensions

In our effort to meet an increasing demand for more accurate and realistic nonlinear optics simulations, we have developed a nonlinear hybrid vector finite element method (NL-HVFEM) to study different phenomena due to wave propagation in waveguides filled with nonlinear Kerr-type media. Contrary to the most existing scalar models, the NL-HVFEM approach is based upon the vector Helmholtz equation and thus can predict the vectorial properties of fields in nonlinear media. We describe the NL-HVFEM approach and apply it to study nonlinear self-focusing effects in nonlinear waveguides. The numerical results of the evolution of the beam self-focusing are also included. Also, we summarized conditions under which electromagnetic beam can produce its own dielectric waveguide and propagate without spreading