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

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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.