EAGER: Modes in Random Media and Tissue Characterization

非技术摘要：了解波在随机系统中的传播是一个具有无数应用的基本问题。这项工作旨在证明所有的波动现象都可以归结为简单的共振性质。共振在波传播中的作用将在空间和时间上通过实验、数值模拟和分析理论来探索。它将表明，复杂系统中波的关键方面可以用一个简单的总和来描述。这些发现将被用来表征新型系统中的传输，例如光子拓扑绝缘体。该项目包括开发一种新的、有望非常有效的基于传输时间空间地图的薄片医学成像技术。这些研究对医学成像、电信、资源勘探和光子设备都有影响。技术摘要：本项目旨在提供对随机系统中模式的统计及其在波传播中的作用的简单而全面的理解。Wigner和Dyson在共振统计方面的早期工作集中在核散射中能级间距和宽度的概率分布上，这些共振被称为能级、本征态、准简正模或简单为模。但在开放的非厄米系统中，模并不是正交的，它们之间的相关性对随机系统中的波传输和能量沉积具有最大的影响。模式在波传播中的作用将在微波和光学实验中从空间和时间上进行探索，并在数值模拟和分析理论中进行探索。模之间的关联导致模之间的相消干涉，极大地抑制了传输，同时导致无序介质内能量密度的空间和谱相关。尽管模式之间的干涉是至关重要的，但最近发现，即使在具有耗散和增益的系统中，关键的动力学变量，如传输时间、态密度和存储在所有通道中的单位磁通入射的样本中的能量之和，也可以描述为模式之间的非相干和。这些结果将被用来表征拓扑绝缘体中具有不同陈氏数的准晶之间沿着磁区壁的稳健传播的极限。该项目包括开发一种新的基于传输时间空间图的薄片医学成像模式，该空间图等于透射场相位的光谱导数。最后，将探索相位导数的简单函数形式，作为一种将场分析为基本模式的方法。这些研究的结果与经典波和量子波都相关。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Nontechnical abstract:Understanding wave propagation in random systems is a fundamental problem with myriad applications. This work aims to show that all wave phenomena can be reduced to simple resonance properties. The role of resonances in wave propagation will be explored in space and time in experiments, and in numerical simulations and analytical theory. It will be shown that key aspects of waves in complex systems can be described in terms of a simple sum. These findings will be utilized to characterize transport in novel systems such as photonic topological insulators. The project includes development of a new and hopefully very impactful medical imaging technique for thin sections based on a spatial map of the transmission time. These studies have implications for medical imaging, telecommunications, resource exploration, and photonic devices.Technical abstract: This projects seeks to provide a simple and comprehensive understanding of the statistics of modes and their role in wave propagation in random systems. Early work by Wigner and Dyson on the statistics of resonances, variously known as energy levels, eigenstates, quasi-normal modes, or simply as modes, focused on the probability distribution of level spacings and widths in nuclear scattering. But in open non-Hermitian systems, modes are not orthogonal, and it is the correlation between them that has the greatest impact on wave transport and energy deposition inside random systems. The role of modes in wave propagation will be explored in space and time in microwave and optical experiments, and in numerical simulations and analytical theory. The correlation between modes leads to destructive interference between modes and greatly suppresses transmission while leading to spatial and spectral correlation of the energy density within disordered media. Though the interference between modes is crucial, it was recently found that key dynamical variables, such as the transmission time, density of states and the sum of energy deposited in the sample for unit flux incident in all channels can be described as an incoherent sum over modes even in systems with dissipation and gain. These results will be utilized to characterize the limits of robust propagation along the domain wall between metacrystals with different Chern numbers in topological insulators. The project includes development of a new medical imaging modality for thin sections based on a spatial map of the transmission time, which is equal to the spectral derivative of the phase of the transmitted field. Finally, the simple functional form for the derivative of the phase will be explored as an approach to analyzing the field into the underlying modes. The results of these studies are relevant to both classical and quantum waves.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.