GIG: Applied Mathematics of Nonlinear Optics

小科尔9510728 该奖项将为一个跨学科团队提供基础设施支持，该团队致力于非线性光学中广泛的理论和应用问题。该小组由应用数学家、物理学家和工业科学家组成，所研究的问题与激光技术、光纤通信、全光数据传输系统和复合非线性光学材料等应用密切相关。基础设施支持将为研究生研究助理、博士后研究员和长期访问者提供一系列关于非线性光学的密集研讨会、迷你课程和讲习班。 拟议的项目涵盖了广泛的问题，如气体激光器和光纤激光器的动力学和操作，标准和掺铒光纤中脉冲的非线性光学，二次谐波产生介质中的光动力学，复合材料的光学特性，在这些问题的公式化和分析中使用的工具包括渐近展开和微扰理论，精确的数值计算，孤子和逆散射技术，非线性分析估计，和动力系统方法。其成员的不同专业知识将使该小组能够成功完成拟议项目的调查，并从只有来自这种独特的跨学科联系的新角度阐明非线性光学问题。

9510728 Cole This award will provide requests infrastructure support for an interdisciplinary team working on a broad array of theoretical and applied problems in nonlinear optics. The group consists of applied mathematicians, physicists, and industrial scientists, and the problems being researched are closely connected with applications such as laser technology, fiber-optics communications, all-optical data transmission systems, and composite nonlinear optical materials. The infrastructure support will provide for an intensive series of seminars, mini courses, and workshops on nonlinear optics, for graduate research assistants, postdoctoral fellows, and long-term visitors. The proposed projects cover a wide range of problems, such as dynamics and operation of gas lasers and fiber lasers, nonlinear optics of pulses in standard and erbium-doped fibers, dynamics of light in second-harmonia generating media, optical properties of composite materials, and light propagation in periodic media The tools to be used in the formulation and analysis of these problems include asymptotic expansions and perturbation theory, accurate numerical computations, soliton and inverse-scattering techniques, nonlinear analytical estimates, and dynamical systems methods. The diverse expertise of its members will enable the group to successfully complete the investigations of the proposed projects, and shed light on nonlinear optical problems from new angles that could only come from such unique interdisciplinary connections.