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李本研究的目标是：（一）推进当前的最先进的数值方法，从两个到三个空间维度的非线性波导中的光束传播建模;和，（二）探索使用有限元方法的潜在优势，超过传统的有限差分方法。 本文提出的新的非线性混合矢量有限元法（NL HVFEM）是棱边单元和有限差分法的结合：前者适用于波导截面，后者适用于传播方向。 在目前的提法，我们认为电场的三个组成部分，也包括完整的张量描述的非线性克尔介质。 此外，我们计划将联合收割机的NL HVFEM与图形的前处理和后处理，并实现它在大规模并行计算机上。 这些努力将使我们成为一个强大而通用的模拟工具，用于研究许多有趣而复杂的物理现象，这些现象目前还无法分析。 我们相信，所提出的研究不仅是科学的利益，但也是有用的实现全光学，集成光学器件。 ***