Computational analysis of nonlinear electromagnetics in disordered photonic systems

几个世纪以来，物理学家已经知道如何使用麦克斯韦定律来预测光和其他类型的电磁辐射在真空中传播时的行为；然而，当它在无序介质中传播时，比如我们在开发新的工程设备时使用的那些介质，人们一直依赖非常粗略的近似或粗略的估计来预测将会发生什么。这些PI将开发新的计算机模拟系统，以比过去更准确地预测发生的事情。他们的新工具应该在光子学和电光学中有非常广泛的用途，在开发新的设备和技术方面。他们计划将新软件广泛传播，以使世界各地的科学家能够对这一主题进行研究。该项目将专注于开发一种自洽麦克斯韦-布洛赫方程的集成解算器，该解算器准确且计算高效。这将需要开发(1)区域分解框架；(2)用于辐射/散射的瞬变分析的半分析方法；以及(3)可与这些求解器集成的快速势评估器，以实现对无序系统的大规模分析。该框架将提供各种无序系统中光和光激发(激子)动力学的完整图景，首先是具有无序的垂直腔面发射激光器(VCSEL)结构。另一个要作为试验台研究的系统是嵌入在带有和不带有外腔的半导体中的量子点的情况。

Physicists have known for centuries how to predict the behavior of light and other types of electromagnetic radiation when it moves through a vacuum, using Maxwell's Laws; however, when it propagates through disorderly media, like those we use in developing new engineering devices, people have relied on very gross approximations or back-of-the-envelope estimates to predict what will happen. These PIs will develop new computer simulation systems to predict what happens more accurately than has been possible in the past. Their new tools should be of very widespread use, in photonics and electrooptics, in developing new devices and technologies. They plan to disseminate the new software widely to enable scientists worldwide to conduct research on this topic.The project will focus on developing an integrated solver for self-consistent Maxwell-Bloch equations that is accurate and computationally efficient. This will entail the development of (1) a domain decomposition framework; (2) semi-analytical methods for transient analysis of radiation/scattering; and (3) fast potential evaluators that can be integrated with these solvers to enable large-scale analysis of disordered systems. The framework will provide a complete picture of the dynamics of light and optical excitations (excitons) in a variety of disordered systems, starting with Vertical Cavity Surface Emitting Laser (VCSEL) structures with disorder. Another system to be investigated as a testbed is the case of quantum dots embedded in a semiconductor with and without an external cavity.