Collaborative Research: Mathematical and computational methods for stochastic systems in nonlinear optics

合作研究：非线性光学中随机系统的数学和计算方法

• 批准号: 1108780
• 负责人: Tobias Schaefer
• 金额: $ 14.89万
• 依托单位: CUNY College of Staten Island
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1108780&HistoricalAwards=false
• 关键词: Collaborative; Research; Mathematical; computational; methods

The objective of this collaborative research project is to develop methods for analysis, modeling, and computation for stochastic partial differential equations arising in nonlinear optics. The study of noise in these systems is complicated by several factors. In particular:(i) the complexity due to the interplay of many physical effects,(ii) the presence of multiple length and time scales, and(iii) the fact that the critical events that represent system failures are, by design, extremely rare. We will address these challenges by (a) creating a set of analytical methods to obtain reductions from the stochastic partial differential equations that govern the system's behavior to a set of low-dimensional stochastic differential equations;(b) developing efficient methods for the study of noise across multiple time and space scales; and (c) implementing hybrid analytical-computational methods that can efficiently target the rare events of interest and ultimately estimate the reliability of these systems.Lightwave systems have a wide range of applications, in particular as lasers and optical communication lines, and their emergence has had a dramatic impact on our lives over the last fifty years. Lasers are used at low powers in applications related to scanning and communications; at higher powers they are employed in surgical and industrial applications. As noise is a major limiting factor in optical systems, further technological progress will depend critically on understanding the impact of noise and on being able to control noise-induced system failures. This research will provide new analytical and computational tools that support the analysis and design of the next generation of optical devices.

该协作研究项目的目的是开发非线性光学中随机部分微分方程的分析，建模和计算方法。这些系统中噪声的研究因几个因素而变得复杂。特别是：（i）由于许多物理效应的相互作用而引起的复杂性，（ii）存在多个长度和时间尺度，以及（iii）代表系统失败的关键事件的事实极为罕见。 我们将通过（a）创建一组分析方法来解决这些挑战，以从随机偏微分方程中降低，这些方程将系统的行为控制到一组低维生的随机微分方程；（b）开发有效的方法，以研究跨多个时间和空间尺度的噪声研究； （c）实施可以有效地针对罕见的感兴趣事件并最终估算这些系统的可靠性的混合分析计算方法。LightWave系统具有广泛的应用，尤其是激光器和光学通信线，并且它们的出现在过去五十年中对我们的生活产生了巨大影响。在与扫描和通信有关的应用中，在低功率上使用了激光器；在较高的大国中，它们被用于手术和工业应用。由于噪声是光学系统中的主要限制因素，因此进一步的技术进步将取决于理解噪声的影响以及能够控制噪声引起的系统故障的影响。这项研究将提供新的分析和计算工具，以支持下一代光学设备的分析和设计。