9309587 Lee The objectives of this research are: (i) To advance the current state of art numerical methods for modeling optical beam propagation in a nonlinear waveguide from two to three spatial dimensions; and, (ii) To explore the potential advantages of using the finite element method over the conventional finite difference methods. The new nonlinear hybrid vector finite element method (NL HVFEM) proposed herein is a combination of edge elements and finite difference methods: The former is applied to the waveguide cross section and the latter to the propagation direction. In the current formulation, we consider three components of the electric field and also include the complete tensor description of the nonlinear Kerr medium. Furthermore, we plan to combine the NL HVFEM with graphical pre and post processings and to implement it on massively parallel computers. These efforts will lead us to a powerful and versatile simulation tool for studying many interesting and complex physical phenomena that are not possible to analyze presently. It is believed that the proposed research is not only of scientific interests but is also useful for realizing all optical, integrated optics devices. ***
