EAGER: Modes in Random Media and Tissue Characterization

非技术性摘要：了解随机系统中的波传播是一个具有无数应用的基本问题。这项工作的目的是表明，所有的波现象可以减少到简单的共振特性。共振在波传播中的作用将在实验中的空间和时间，以及在数值模拟和分析理论中进行探索。它将表明，波在复杂系统中的关键方面可以描述在一个简单的总和。这些发现将被用来表征新系统，如光子拓扑绝缘体中的传输。该项目包括开发一种新的，希望非常有效的医学成像技术，用于基于传输时间的空间图的薄切片。这些研究对医学成像、电信、资源勘探和光子器件都有意义。技术摘要：本项目旨在提供对随机系统中模式统计及其在波传播中的作用的简单而全面的理解。维格纳和戴森早期对共振态统计的研究主要集中在核散射中能级间距和宽度的概率分布上，共振态被称为能级、本征态、准简正模或简单地称为模。但在开放的非厄米特系统中，模式不是正交的，正是它们之间的相关性对随机系统内部的波输运和能量沉积产生了最大的影响。模式在波传播中的作用将在微波和光学实验中的空间和时间以及数值模拟和分析理论中进行探索。模式之间的相关性导致模式之间的相消干涉，并极大地抑制传输，同时导致无序介质内能量密度的空间和光谱相关性。虽然模式之间的干扰是至关重要的，它是最近发现，关键的动力学变量，如传输时间，状态密度和沉积在样品中的能量的总和，单位通量入射在所有通道中可以被描述为一个不相干的总和模式，即使在系统中的耗散和增益。 这些结果将被用来表征强大的传播沿着畴壁之间的拓扑绝缘体的不同陈数的亚晶之间的限制。该项目包括根据传输时间的空间图开发一种新的薄切片医学成像模式，该空间图等于传输场相位的光谱导数。最后，将探讨相位导数的简单函数形式，作为分析场的基本模式的方法。这些研究的结果与经典波和量子波都相关。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值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.