Nonscattering Phenomena and Inverse Scattering

Drexel University, Philadelphia PA

Investigators

Abstract

This project focuses on the study of inverse scattering and non-scattering phenomena, which are used for determining the properties of an object or medium using only scattered waves from the exterior, without having to physically probe the object or medium. Inverse scattering has a wide range of applications in fields such as radar and sonar imaging, medical imaging, geophysical exploration, and astrophysics. This project aims to investigate non-scattering features of inhomogeneous media in a homogeneous free space and explore their potential applications to inverse scattering as well as invisibility, or cloaking, which can be used to make objects undetectable or unimpacted by certain waves. In addition, graduate and undergraduate student will be mentored as part of this project, which will add both depth and breadth to their mathematical education. Despite recent progress concerning some special geometries, the existence or nonexistence of nonscattering wavenumbers for general inhomogeneities largely remains an open question. This project aims to explore the non-scattering behavior of inhomogeneous media by addressing several challenges. The specific goals of this work are to (1) characterize necessary conditions for inhomogeneities and waves to be nonscattering, or the opposite, to be nontrivially scattering, (2) mathematically construct nonscattering media and waves, (3) establish quantitative results on nonscattering wavenumbers for a general class of inhomogeneities, and (4) apply results of nonscattering and/or nontrivial scattering to inverse problems for uniquely determining the shape of an unknown medium by one single measurement. This project will shed light on non-scattering phenomena and pave the way for advancements in inverse scattering and related fields. 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.