EAGER: Modes in Random Media and Tissue Characterization

Cuny Queens College, Flushing NY

Investigators

Abstract

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.