Numerical Modeling for Liquid Crystal Devices

数值模拟工具已经在液晶领域应用了好几年。它们通常用于交互式地探索效果和优化设备的性能，相对于可控的材料和设备参数。直到最近，使用一维（1-D）模型可以获得令人满意的结果，该模型将结构的横向尺寸视为无限和均匀的。当前的发展（更小的特征尺寸，新技术）正在推动更现实的2-D和3-D建模。当前建模工具中使用的数值算法在现代平台上需要几分钟来分析二维设备；而3d则需要几个小时。要在这些高维环境中产生可接受的性能，需要对数值方法进行重大改进。首席研究员将与器件建模物理学家以及应用数学和数值分析领域的专家合作，以适应和开发基于液晶材料的实际光学器件建模所需的先进数值方法。现代数值算法有望在与当前一代一维工具（秒）相当的时间内实现三维建模。这些工具有望对液晶光学技术的发展产生重大影响。本项目关注基于液晶材料的器件的数值模拟工具的开发和分析。液晶在技术上很重要，因为它们可以用来控制光。已有许多应用（例如，笔记本电脑和平板显示器），新的应用正在开发中，包括平板文件阅读器（电子书、电子报纸）和波束导向装置（用于通信和交换中的软、可编程、非机械应用）。现代数值算法有希望在几秒钟内实现液晶器件的完整建模。这些工具将具有巨大的实际效用，可以预期对这一领域和有关领域的技术发展产生重大影响。

Numerical modeling tools have been used in the liquid crystal arena for several years. They are typically used interactively to explore effects and to optimize the performance of devices with respect to controllable material and device parameters. Until recently, satisfactory results could be achieved by using one-dimensional (1-D) models, which treat the transverse dimensions of the structures as infinite and uniform. Current developments (smaller feature sizes, new technologies) are forcing more realistic 2-D and 3-D modeling. The numerical algorithms utilized in current modeling tools require several minutes on contemporary platforms to analyze a 2-D device; for 3-D, they take several hours. Significant improvements in the numerical approaches are needed to produce acceptable performance in these higher dimensional settings. The principal investigator will work with device-modeling physicists and experts in the applied mathematics and numerical analysis communities to adapt and develop the advanced numerical methods necessary to model realistic optical devices based upon liquid crystal materials. Modern numerical algorithms hold the promise of enabling 3-D modeling in times that are comparable to the current generation of 1-D tools (seconds). These tools are expected to have a significant impact on the development of liquid crystal optics technologies.This project is concerned with the development and analysis of numerical modeling tools for devices based on liquid crystal materials. Liquid crystals are important in technology because they can be used to control light. Numerous applications exist (e.g., lap-top and flat-panel displays), and new ones are being developed, including tablet document readers (e-books, electronic newspapers) and beam-steering devices (for soft, programmable, non-mechanical applications in communications and switching). Modern numerical algorithms hold the promise of enabling full modeling of liquid crystal devices in a matter of seconds. Such tools will be of immense practical utility and can be expected to have a big impact in the development of technologies in this and related areas.