RESEARCH INITIATION AWARD: Nonlinear Hybrid Vector Finite Element Method for Analyzing Nonlinear Optical Devices

9309587 Lee这项研究的目标是：(I)将目前最先进的数值方法从二维发展到三维；以及(Ii)探索使用有限元方法比传统有限差分方法的潜在优势。本文提出的非线性混合矢量有限元方法是边缘单元和有限差分方法的结合：前者用于波导截面，后者用于传播方向。在目前的公式中，我们考虑了电场的三个分量，并包括了非线性克尔介质的完整张量描述。此外，我们还计划将NL高压有限元与图形前后处理相结合，并在大规模并行计算机上实现它。这些努力将把我们带到一个强大而通用的模拟工具，用于研究许多有趣和复杂的物理现象，这些现象目前无法分析。人们认为，所提出的研究不仅具有科学价值，而且对实现所有光学、集成光学器件也是有用的。***

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. ***