Analytical and computational methods for femtosecond lasers

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One of the most important recent advances in nonlinear optics has been the development of a new generation of very stable short-pulse lasers, with typical pulse durations of just a few femtoseconds. Such lasers have numerous applications. Among others, they provide precise sources for spectroscopy and frequency metrology, and are an essential component in optical atomic clocks. Because of the many physical effects present and the vastly different timescales involved, however, making quantitative predictions about the behavior of these systems and their fundamental performance limits is a challenging task. This project will address these challenges by developing new mathematical models aimed at describing these lasers' behavior and an accompanying set of analytical and computational tools. The new models, which will explicitly take into account the inherent complexity of these systems and the multiple time scales present, will then be used to analyze the mode-locking and nonlinear dynamics of pulses in the laser cavity. Moreover, these new models will guide the development of statistical computational algorithms that can accurately quantify the impact of noise and calculate the probability of the rare events that limit the accuracy and ultimate reliability of these systems.Femtosecond lasers have a wide range of applicability. Beyond metrology and atomic clocks, already mentioned, important applications are a new generation of global positioning systems, the probing of transients occurring during chemical reactions and the ablation of tumors. Thus, this project will impact not only the scientific community, but also society at large. The new mathematical models and computational methods that will be derived as part of this project will substantially advance the theory of femtosecond lasers, and they will make it possible to accurately and efficiently predict the performance of these lasers. As a result, they will provide useful tools for the scientists and engineers who design and build these systems. An important part of the project will also be the training of students and junior researchers: through this interdisciplinary effort, students will be trained to use concepts, methods and techniques outside their main discipline, thus greatly enriching their educational and professional experience.