Multiple-scale mathematical models of ultra-short-pulse modelocked lasers

本项目的目标是开发锁模激光器的新数学模型。模型将考虑光学和电子元件的描述，以及它们之间在多个时间尺度上的耦合。不同的时间尺度将被利用来提供分析方法和计算工具，通过这些方法和计算工具可以分析激光的非线性动力学。这些数学技术将允许仔细研究控制脉冲解的存在和稳定性的基本因素，包括确定噪声如何影响这些激光器的精度。最近的进展已经迎来了一个非常稳定的超短模型锁定激光器的新时代，典型的脉冲持续时间只有几飞秒。这些先进设备对于紫外和红外光谱（例如，用于痕量气体传感）和光学和微波波形产生（例如，用于低噪声微波源）的精确源非常重要。它们也是光学原子钟的重要组成部分，光学原子钟是下一代计时设备，其精度比目前的微波原子钟好几个数量级。该项目的目标是提供能够预测飞秒激光器性能的结果，这将有助于设计和建造飞秒激光器的科学家和工程师。这个项目的另一个重要组成部分是对学生的培训。作为这一组成部分的一部分，PI将访问特拉华州立大学，协助指导应用数学研究生在非线性光学领域的建议。

The goal of this project is to develop new mathematical models of mode-locked lasers. Models will take into account descriptions of the optical and electronic components, and the coupling between them, on multiple time scales. The different time scales will be exploited to provide analytical methods and computational tools by which the nonlinear dynamics of the laser can be analyzed. These mathematical techniques will allow a careful study of the fundamental factors governing the existence and stability of pulse solutions, including a determination as to how noise affects these lasers' precision. Recent advances have ushered in a new era of extremely stable ultra-short modelocked lasers, with typical pulse durations of just a few femtoseconds. Such advanced devices are important as precise sources for ultraviolet and infrared spectroscopy (e.g., for trace gas sensing) and optical and microwave waveform generation (e.g., for low noise microwave sources). They are also an essential component in optical atomic clocks, next-generation timekeeping devices with accuracies several orders of magnitude better than current microwave atomic clocks. A goal of this project is to provide results capable of predicting the performance of femtosecond lasers and that will assist scientists and engineers who design and build them. Another important component of this project is the training of students. As part of this component, the PI will visit Delaware State University to assist in the mentoring of applied mathematics graduate students being advised in the field of nonlinear optics.