Dynamics of Light Interacting with Active Media

光与活性介质相互作用的动力学

• 批准号: 1009453
• 负责人: Gregor Kovacic
• 金额: $ 20.28万
• 依托单位: Rensselaer Polytechnic Institute
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-07-01 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1009453&HistoricalAwards=false
• 关键词: Dynamics; Light; Interacting; Active; Media

This work will address mathematical descriptions of the dynamics arising in three novel effects generated by the interaction of light with an optical medium in the lambda- configuration. The first is random polarization switching of light pulses propagating through a lambda-configuration medium, whose description gives rise to the rare combination of a simultaneously completely integrable and stochastic partial differential equation. The second is the "light stopping" phenomenon, which requires the development of a new inverse-scattering-transform technique and soliton theory for the Maxwell-Bloch equations with nonvanishing boundary conditions at infinity. The third is light propagating through a combined, lambda-configuration metamaterial, which requires the derivation of a new model to be studied through a combination of exact solutions, asymptotic, and numerical techniques, and may give rise to descriptions of novel phenomena such as simultaneous color and direction switching and a related nonlinear version of Anderson localization, as well as mechanisms for loss compensation in metamaterials. More broadly, the work will advance the theory of completely-integrable systems, and especially a successful description of loss compensation in metamaterials, may have impact on practical nonlinear optics. Interdisciplinary training in applied mathematics and nonlinear optics will be provided to graduate and undergraduate students.Interaction between light and active optical media (these are media for which such interaction is particularly strong) is one of the most fruitful areas in applied physics and provides the basic mechanism underlying devices such as lasers and optical amplifiers. It has continued to be a rich source of new physical phenomena, among the latest being "light stopping," during which specially prepared optical pulses are slowed down to a fraction of the light speed, and which could be used in designing optical memory. In addition, this interaction could also be used to reduce losses in optical metamaterials (artificial nano-composites with previously unattainable optical properties such as perfect lens focusing) and thus help advance their development from the current proof-of-concept experiments to eventual practical optical devices. Due to the great variety of physical phenomena it exhibits, light interaction with active media has also given rise to a broad range of mathematical descriptions of their dynamics. Three novel such mathematical descriptions will be developed in the course of this work, including those of "stopped light," a certain potential type of loss compensation in a metamaterial, and finally a rare exact description of light propagating through a highly disordered medium.

这项工作将解决光与 lambda 配置中的光学介质相互作用产生的三种新颖效应的动力学数学描述。 第一个是通过 lambda 配置介质传播的光脉冲的随机偏振切换，其描述产生了同时完全可积和随机偏微分方程的罕见组合。 第二个是“光停止”现象，这需要开发一种新的逆散射变换技术和孤子理论，用于无穷远边界条件不为零的麦克斯韦-布洛赫方程。第三种是通过组合的 lambda 配置超材料传播的光，这需要通过精确解、渐近和数值技术的组合来研究推导新模型，并可能产生对新现象的描述，例如同时颜色和方向切换和安德森定位的相关非线性版本，以及超材料中的损耗补偿机制。 更广泛地说，这项工作将推进完全可积系统的理论，特别是对超材料损耗补偿的成功描述，可能会对实际的非线性光学产生影响。将为研究生和本科生提供应用数学和非线性光学的跨学科培训。光和有源光学介质（这些介质的相互作用特别强）之间的相互作用是应用物理学中最富有成果的领域之一，并提供了激光器和光放大器等器件的基本机制。 它仍然是新物理现象的丰富来源，其中最新的现象是“光停止”，在此过程中，专门准备的光脉冲被减慢到光速的一小部分，并且可以用于设计光存储器。 此外，这种相互作用还可用于减少光学超材料（具有以前无法实现的光学特性（例如完美透镜聚焦）的人造纳米复合材料）的损耗，从而有助于推动其从当前的概念验证实验到最终实用光学设备的发展。 由于其表现出多种多样的物理现象，光与活性介质的相互作用也引发了对其动力学的广泛数学描述。 在这项工作的过程中将开发出三种新颖的数学描述，包括“停止光”的描述、超材料中某种潜在的损失补偿类型，以及最后对通过高度无序介质传播的光的罕见精确描述。