Modeling Light Filamentation Science

由于激光技术的重大进步，人们对光与物质相互作用的研究一直很感兴趣，特别是对在大气层中远距离传播的强激光。超过数百千兆瓦功率的激光脉冲可用于许多应用，包括通过光探测和测距(LIDAR)进行遥感、闪电和天气控制以及自由空间光学通信。目前关于自由空间光通信(FSO)的研究，无论是经典的还是量子的，都旨在促进卫星网络内、地球与卫星之间以及地球与无人机之间的信息交换。这一点和其他有待研究的方面，如衍射控制，与NSF的十大想法之一量子飞跃的主题是一致的。在寻求最佳性能的过程中，寻求更好地了解光与大气中分子相互作用时发生的一系列空间和时间效应是至关重要的。为此，适当的数学和数值建模有助于实验者例如考虑新的传播模式(光学灯丝与涡流灯丝)以及多种颜色(多频率)灯丝的可能共存。在该奖项下进行的研究将与实验小组产生强大的协同作用，丰富项目的跨学科性质，并加强应用数学研究生的学习体验，以接受多方面的培训。在轻物质相互作用的总主题下，PI和学生将研究光在非线性介质中传播的时空动力学。这项研究解决了与三种不同介质中不同类型的高度非线性光学模式(灯丝模、涡旋模及其组合)的特征有关的明确问题：空气(克尔介质)、携带两个频率的非线性晶体(通常是紫外线和红外)、非线性晶体(二次介质)，其中对位相失配时的成丝理论以及具有分数衍射和二次色散的离散/连续非线性介质中的成丝理论知之甚少。前两个主题代表了细丝科学正在进行的研究的重大扩展，无论是基于最近的实验观察，还是基于PI已经并将直接参与的潜在的新实验。根据研究的性质和目标，该奖项支持的努力将受益于与几个实验团队的持续互动。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

Thanks to major advances in laser technology, there is an ongoing interest in the study of light interacting with matter, in particular for intense laser beams propagating long distances in the atmosphere. Laser pulses exceeding tens of gigawatts power can be used in many applications including remote sensing through Light Detection and Ranging (LIDAR), lightning and weather control and free-space optics communication. Current research on free space optical communications (FSO), both classical and quantum, is intended to facilitate exchange of information within a network of satellites, between the Earth and satellites and between the Earth and drones. This and other aspects to be studied, such as diffraction control, are in line with topics within Quantum Leap, one of the NSF's 10 Big Ideas. In searching for optimal performance, it is critical to seek better understanding of a range of spatial and temporal effects that take place while light interacts with molecules in the atmosphere. For this, proper mathematical and numerical modeling assist experimentalists to for example consider novel modes of propagation (optical filaments versus vortex filaments) and the possible coexistence of multi- color (multi-frequency) filaments. Research performed under this award will have a strong synergy with experimental groups, enriching the interdisciplinary nature of the project and enhancing the learning experience of applied mathematics graduate students to be trained in a multifaceted approach.Under the general theme of light matter interactions, the PI and students will investigate spatiotemporal dynamics of light propagation in nonlinear media. The research addresses well defined questions related to the characterization of highly nonlinear optical modes of different types (filament modes, vortex modes and combinations) in three different media: air (Kerr media), carrying two frequencies (typically ultraviolet and infrared), nonlinear crystals (quadratic media) where little is known on the theory of filament formation at phase mismatch and on the formation of filaments in discrete/continuum nonlinear media with fractional diffraction and quadratic dispersion. The first two topics represent significant extensions of ongoing research in filament science, based either on recent experimental observations or potential new experiments on which the PI has been and will be directly involved. By the nature and objectives of the research, the effort supported by this award will benefit from continuing interactions with several experimental teams.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.