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.

这项工作将介绍三种新颖效应引起的动力学的数学描述，该动力学与兰巴达配置中光学介质的相互作用产生了三种新型效应。 第一个是通过lambda-configuration介质传播的光脉冲的随机极化切换，其描述引起了同时完全可以整合和随机的偏微分方程的罕见组合。 第二个是“光停止”现象，它需要为Maxwell-Bloch方程开发新的反向散射转换技术和孤子理论，该方程在无穷大的边界条件下。第三个是通过合并的兰伯达 - 配置的超材料来传播的，这需要通过精确的解决方案，渐近性和数值技术的结合来衍生新模型，并可能导致对新型现象的描述，例如同时的颜色和方向交换和相关的元素，以及相关的元素质量以及相关的元素质量以及同时的定位，以及同时的元素效果，以及同时的定位。 从更广泛的角度来看，这项工作将推进完全综合系统的理论，尤其是对超材料中损失补偿的成功描述，可能会对实用的非线性光学器件产生影响。将向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。光和主动光学介质之间的相互作用（这些是这种相互作用特别强的媒体）是应用物理学中最富有成果的领域之一，并提供了诸如激光器和光学放大器等基本机制。 它一直是新的物理现象的丰富来源，其中最新的是“灯”，在此期间，专门准备的光脉冲被放慢到光速的一小部分，并且可以用于设计光学内存。 此外，这种相互作用也可用于减少光学超材料（具有先前无法实现的光学特性（如完美镜头聚焦）的人工纳米复合材料）中的损失，从而有助于将其从当前的概念验证实验到最终实用的光学设备提高。 由于它表现出的各种物理现象种类繁多，与活动介质的光相互作用也引起了对其动力学的广泛数学描述。 这项工作将在这项工作的过程中制定三个新颖的数学描述，包括“停止光”的数学描述，这是超材料中某种潜在的损失补偿类型，最后是对光线通过高度无序介质传播的罕见确切描述。