Transformation Optics and Acoustic and Electromagnetic Cloaking

The project aims to study analytically and numerically some central problems arising in the study of invisibility cloaking for acoustic and electromagnetic waves. There has been significant attention in the scientific community in the last few years on invisibility for electromagnetic and other types of waves. The main goal of this project is to develop and analyze practical cloaking schemes under various circumstances, and to understand the cloaking phenomena. The main tools used are analysis and computation. Specifically, the proposed research will be devoted to the following four problems. The first one is to study the regularized approximate cloaking for the full system of Maxwell's equations via the transformation optics approach. Sharp estimates will be derived in assessing cloaking performances under various practical circumstances. The second problem is on the design and analysis of novel cloaking schemes including partial cloaking and on the implementation of isotropic cloaking medium obtained by inverse-homogenization theory. The third problem is to understand the invisibility cloaking from an optimization viewpoint by minimizing the scattering of the waves. This will also gives clues to what is the borderline between visibility and invisibility. The final problem is to develop effective and efficient numerical methods to numerically study cloaking. These problems present interesting challenges from both the analytical and computational points of view.

Research on invisibility cloaking has the potential for many civil and industrial applications, such as in medical surgery, wireless communications, air flight and space exploration etc. However, it presents many challenges both theoretically and in practical implementation due to the singular and unstable structures of the suggested blueprints for cloaking. The solution of the proposed problems would provide theoretical recipes for the construction of practical cloaking devices. Moreover, the mathematical understanding of invisibility cloaking will on the one hand offer a different way than the transformation-optics approach to achieve cloaking, and on the other hand provide important implications for inverse problems involving reconstructing electromagnetic objects. The analytical and computational techniques developed in this project are widely applicable to other electromagnetic phenomena. Some of the ideas developed in this project will be included into a graduate level class. The proposer also plans to advice and train graduate students in this challenging field.