Direct and Inverse Electromagnetic Scattering Problems for Complex Periodic Media

Kansas State University, Manhattan KS

Investigators

Abstract

The interaction and scattering of light by periodic structures at the nanoscale is a topic of great significance in the area of nanophotonics and metamaterials technology. With the current rapid development of this enabling technology, there is a high demand on new mathematical theories and computational algorithms for both direct and inverse problems of the light scattering by periodic complex media or periodic metamaterials. This project aims to develop such theories and algorithms. Results from this project will advance knowledge, understanding and imaging techniques in the technology of nanophotonics and metamaterials. For instance, the mathematical theories and the computational algorithms developed for the direct problems are extremely useful for the simulation, fabrication and maintaining of optical devices. The imaging techniques developed for the inverse problems can be potentially of practical use for non-destructive tests, which help to detect and characterize discrete flaws in optical components and devices. The project contains two main areas of study: the mathematical and numerical analysis for direct scattering problems, and the development of efficient inversion algorithms for inverse scattering problems. More precisely, for the direct problem, the PI and his colleagues will work on the following topics: 1) develop volume integral equation formulations for direct scattering problems for periodic complex media; 2) develop fast integral equation-based numerical solvers for the direct scattering problems; 3) study interior transmission eigenvalues for periodic complex media; 4) study well-posedness of the scattering by chiral metamaterials. The proposed research for the inverse problem includes the topics: 1) develop sampling methods for imaging of periodic complex media; 2) develop sampling methods for the detection of local defects in photonic crystals; 3) develop globally convergent methods for the identification of material parameters for photonic crystals. 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.