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

研究启动奖：用于分析非线性光学器件的非线性混合矢量有限元方法

• 批准号: 9309587
• 负责人: Jin-Fa Lee
• 金额: $ 8.91万
• 依托单位: Worcester Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-09-15 至 1997-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9309587&HistoricalAwards=false
• 关键词: RESEARCH; INITIATION; AWARD; Nonlinear; Hybrid

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. ***

9309587这项研究的目标是：（i）推进当前的最先进的数值方法，用于建模非线性波导中的光束传播从两个到三个空间维度进行建模； （ii）探索使用有限元方法比常规有限差异方法的潜在优势。 本文提出的新的非线性混合矢量有限元法（NL HVFEM）是边缘元素和有限差方法的组合：前者应用于波导横截面，后者将其应用于传播方向。 在目前的配方中，我们考虑了电场的三个组成部分，还包括非线性Kerr介质的完整张量描述。 此外，我们计划将NL HVFEM与图形前和后处理结合，并在大规模并行计算机上实施。 这些努力将使我们获得一种强大而多才多艺的仿真工具，用于研究许多有趣且复杂的物理现象，目前无法进行分析。 人们认为，拟议的研究不仅具有科学利益，而且对于实现所有光学，集成的光学设备也很有用。 ***