EAGER: Modes in Random Media and Tissue Characterization

非技术摘要：理解随机系统中的波传播是一个具有无数应用的基本问题。这项工作旨在表明，所有的波动现象都可以简化为简单的共振性质。共振在波传播中的作用将在实验、数值模拟和分析理论中探索空间和时间。它将表明，波在复杂系统中的关键方面可以用一个简单的和来描述。这些发现将用于表征新系统中的输运，如光子拓扑绝缘体。该项目包括开发一种新的、希望非常有影响力的薄片医学成像技术，该技术基于传输时间的空间地图。这些研究对医学成像、电信、资源勘探和光子器件具有重要意义。技术摘要：本项目旨在对随机系统中模态的统计及其在波传播中的作用提供简单而全面的理解。维格纳和戴森在共振统计方面的早期工作，主要集中在核散射中能级间隔和宽度的概率分布上，共振被称为能级、本征态、准正态，或者简单地称为模式。但在开放的非厄米系统中，模态不是正交的，它们之间的相关性对随机系统内的波输运和能量沉积影响最大。在微波和光学实验中，以及在数值模拟和分析理论中，将探索模式在波传播中的作用。模间的相关性导致了模间的相消干涉，极大地抑制了传输，同时导致了无序介质内能量密度的空间和频谱相关性。虽然模式之间的干扰是至关重要的，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、态密度和在所有通道中单位通量入射的样品中沉积的能量总和也可以描述为模式的非相干和。这些结果将用于表征拓扑绝缘体中具有不同陈氏数的元晶之间沿畴壁的鲁棒传播极限。该项目包括开发一种新的薄片医学成像模式，该模式基于传输时间的空间图，传输时间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，作为将场分析为底层模态的方法。这些研究结果与经典波和量子波都有关。该奖项反映了美国国家科学基金会的法定使命，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.