NSF-BSF: Global Correlation in complex structures

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Non-technical Abstract:Material disorder is pervasive in natural and fabricated materials. It is therefore important to understand the impact of disorder on the flow of different types of waves in diverse fields of endeavor including electronics, telecommunications, environmental sensing, bio-medical imaging, and resource exploration. The research team seeks to discover common principles governing the flow of waves in disordered materials based on wave scattering in the entirety of a material. This research program explores how to create a state in which transmission vanishes and transmission becomes extremely sensitive to changes in a material. The research team also explores extreme scattering of microwave radiation in samples with metallic elements, which may open up new approaches to the extreme trapping of waves. The feasibility of harnessing the transmission of microwave radiation in scattering media for information processing are explored in experiments and theoretical analysis. The diverse research projects provide high school, undergraduate and graduate students the opportunity to engage with theory, simulations, statistical analysis, and experiments of the flow of waves as part of an international team tackling problems of intense fundamental and applied interest. Technical Summary:The research team carries out linked experimental, computational and theoretical studies of fundamental aspects of global correlation of waves in disordered systems with potential applications in excitation engineering, optical computation, imaging, and sensing. Many of the most intriguing, challenging, and potentially useful aspects of waves in complex systems arise from global correlation of the field. Such correlation governs the statistics of the transmission matrix which links the incident and outgoing fields. The research team explores the singularities of the transmission matrix, which are the resonances of the medium and the transmission zeros. This research (1) studies the evolution of transmission zeros in the complex frequency plane as samples are changed, (2) explores the correlation of the axial velocity of transmission eigenchannels across random samples and its impact upon the energy excited within random systems, (3) investigates the characteristics and source of the vanishing of the density of states within certain random systems, (4) explores the nature of propagation in systems with metallic elements, (5) investigates dimensionality reduction in random mappings via the transmission matrix of scattering samples, and, (6) explores random projections of microwave radiation propagating through scattering media in the context of transmission eigenchannels.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.