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Mathematical Analysis of Novel Nonlinear Waves in Dissipative Optical Systems

耗散光学系统中新型非线性波的数学分析

基本信息

批准号：
1910282
负责人：
Jianke Yang
金额：
$ 29.16万
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：
2019
资助国家：
美国
起止时间：
2019-07-01 至 2024-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1910282&HistoricalAwards=false
关键词：
Mathematical Analysis Novel Nonlinear Waves

项目摘要

This project theoretically investigates dissipative nonlinear wave systems in optics, which exhibit novel and counter-intuitive properties such as conservative-like behaviors and unidirectional wave propagation. Examples of such optical systems include certain advanced lasers supporting unidirectional light propagation along the edges of the laser cavity immune to scattering and disorder, which holds promise as an optical diode in the design of optical computers. Other examples include certain dissipative second-harmonic-generation systems featuring soliton families with continuous ranges of powers, which may be exploited for signal processing devices. Properties manifested in such systems are intriguing, and they will be investigated comprehensively in this project. Through advanced mathematical techniques and sophisticated numerical computations, new insight will be gained on the operation of these optical systems, so that their applications for optical diodes and nonlinear data processing can be assessed and optimized. The problems undertaken in this project are at the cutting edge of applied mathematics and optics. Mathematically, this project ventures into the unchartered territory of dissipative systems behaving like conservative systems, which opens new research directions in the study of nonlinear waves. On the physical side, these studies will lead to better understanding of next-generation laser devices, which will have direct applications to many branches of optics and photonics. Educationally, graduate students will be trained, and undergraduate honors thesis and undergraduate summer research will be supervised, so that this project will help train young talents in the STEM fields.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

本计画从理论上探讨光学中的耗散非线性波动系统，其表现出新颖且违反直觉的性质，例如类保守性行为及单向波传播。这样的光学系统的例子包括某些先进的激光器，其支持沿着激光腔的边缘的单向光传播沿着，不受散射和无序的影响，这有望作为光学计算机设计中的光学二极管。其他例子包括某些耗散二次谐波产生系统，其特征在于具有连续功率范围的孤子族，其可以用于信号处理设备。在这样的系统中表现出的属性是有趣的，他们将在这个项目中进行全面的调查。通过先进的数学技术和复杂的数值计算，这些光学系统的操作将获得新的见解，使其应用于光学二极管和非线性数据处理可以评估和优化。该项目中研究的问题处于应用数学和光学的前沿。在数学上，该项目冒险进入行为类似保守系统的耗散系统的未知领域，这为非线性波的研究开辟了新的研究方向。在物理方面，这些研究将有助于更好地理解下一代激光器件，这些器件将直接应用于光学和光子学的许多分支。在教育方面，培养研究生，指导本科生荣誉论文和本科生暑期研究，培养STEM领域的年轻人才。该奖项体现了NSF的法定使命，通过基金会的智力价值和更广泛的影响力审查标准进行评估，被认为值得支持。