Full Wave Vector Maxwell Equation Simulation of Nonlinear Self-Focusing E ects in Three Spatial Dimensions

| In our eeort to meet an increasing demand for more accurate and realistic nonlinear optics simulations, we have developed a nonlinear hybrid vector nite element method (NL-HVFEM) to study different phenomena due to wave propagation in waveg-uides lled 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 elds in nonlinear media. In this paper, we describe the NL-HVFEM approach and apply it to study nonlinear self-focusing eeects 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 .