Numerical Methods for Maxwell Equations in Dispersive and Lossy Inhomogeneous Media

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This project is to develop accurate and efficient state-of-the art numerical algorithms for electromagnetic scattering in dispersive and lossy inhomogeneous media. Electromagnetic scattering, wave scattering in general, is ubiquitous in scientific and engineering applications. Simulation of wave scattering in dispersive and lossy inhomogeneous media poses two major challenges for fast and accurate computations, namely, the resolution requirement by the large wave number of the problems involved, and the accuracy degeneracy of numerical discretizations due to interfaces of material discontinuities. To address these challenges, the investigator proposed two new approaches: (1) In Time domain: A high order Cartesian grid based Upwinding Embedded Boundary Method for time dependent Maxwell equations in dispersive and lossy inhomogeneous media, and (2) In Frequency Domain: A fast integral method for wave scattering in layered media based on fast calculation algorithms of dyadic Green's functions.The investigator will apply the numerical algorithms developed under this project for the designing of microscale photonic devices with significant impact on the development of next generation optical technologies for cost efficient home internet broadband access, and also the design of ground penetrating radars, which will contribute to the development of modern detection devices for underground mines and industrial contaminants. Moreover, Research results from this project, in the area of new physics and numerical methods, will be incorporated into the applied mathematics and optics curriculum, potential technology transfer of the results to the area optics industrial will be explored through the existing partnership between the Center and area optics companies. The investigator shall participate actively in the Center's technology training programs with area high schools during the course of this research.