Analytical Studies of Nonlinear Optics in Periodic Media

周期性介质中非线性光学的分析研究

• 批准号: 1311730
• 负责人: Jianke Yang
• 金额: $ 19.83万
• 依托单位: University of Vermont & State Agricultural College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-08-15 至 2016-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1311730&HistoricalAwards=false
• 关键词: Analytical; Studies; Nonlinear; Optics; Periodic

The objective of this proposal is to analytically investigate novel phenomena of nonlinear light propagation in new types of periodic media. Specifically, bifurcation and linear stability of solitary waves in combined linear and nonlinear lattices, general parity-time symmetric lattices and general two-dimensional lattices will be analytically determined through the development of a sophisticated exponential asymptotics technique. Both the positions of solitary waves and their linear-stability eigenvalues will be explicitly calculated; hence the existence and linear-stability properties of these solitary waves in periodic media will be analytically obtained. From a broader perspective, nonlinear optics in periodic media is currently at the forefront of research in optics and applied mathematics. With appropriate engineering of microscale periodic structures, light propagation can be controlled and steered in various different ways, which point to promising applications for micro-scale optical data-processing devices, low-distortion image transmission, and potential optical chips for ultrafast computers. The study of these exciting but difficult physical problems calls for advanced mathematical techniques. In this project, we will develop a powerful exponential asymptotics method, which can yield very detailed information on the existence and stability of solitary waves in periodic media. This information will allow us to assess the potential of optical solitons for various physical applications such as data processing on microscopic periodic structures. In addition, this project will facilitate interdisciplinary training of a graduate student in this important area.

本研究的目的是分析研究非线性光在新型周期性介质中传播的新现象。具体而言，孤立波的分支和线性稳定性的组合线性和非线性晶格，一般奇偶时间对称晶格和一般的二维晶格将通过一个复杂的指数渐近技术的发展分析确定。孤立波的位置和它们的线性稳定性特征值都将被明确地计算出来，因此这些孤立波在周期性介质中的存在性和线性稳定性将被解析地得到。从更广泛的角度来看，周期性介质中的非线性光学是目前光学和应用数学研究的前沿。通过对微尺度周期性结构进行适当的工程设计，可以以各种不同的方式控制和引导光的传播，这将为微尺度光学数据处理设备、低失真图像传输和超高速计算机的潜在光学芯片提供有前途的应用。研究这些令人兴奋但困难的物理问题需要先进的数学技术。在这个项目中，我们将开发一个强大的指数渐近方法，它可以产生非常详细的信息，孤立波的存在性和稳定性的周期性介质。这些信息将使我们能够评估光孤子的各种物理应用，如数据处理的微观周期性结构的潜力。此外，该项目将促进对这一重要领域的研究生进行跨学科培训。