Mathematical and Numerical Study of Electromagnetic Waves Interacting with Metamaterials

University Of Nevada Las Vegas, Las Vegas NV

Investigators

Abstract

This project is concerned with the mathematical analysis and design of robust and efficient computational algorithms for modeling wave interactions with negative index metamaterials (NIMs). These negative index metamaterials have some exotic properties (such as near field refocusing) never seen before in those natural electromagnetic materials. The numerical NIM analysis plays an important role for the design of the nano-structures with complicated geometries that establish a NIM. these NIM models are far more complicated than the well-studied Maxwell's equations in free space due to its dispersiveness, and the introduced electric and magnetic polarization currents. Solving them accurately and efficiently is quite challenging and very few work has been done in regards of solid mathematical analysis and modeling. The ultimate goal of this project is to develop an efficient set of time domain finite element methods that are mathematically sound, accurate and fast convergent for simulating wave interactions with metamaterials. Study of metamaterials is one of the hottest topics in many disciplinaries since 2000, with potential revolution in design of antenna, waveguides and radar, nanolithography and imaging at subwavelength resolution (used for better understanding of the images obtained from noninvasive geophysical probing and tumor detection), near field control and manipulation (used for detecting low levels of chemical and biological agents, manipulation of molecules), and invisibility cloak (used for stealth technology). Developing robust and efficient algorithms for negative index metamaterials will benefit broader areas such as electrical engineering, materials, optics, physics, nano-technology, and biomedical technology. Furthermore, the proposed project will help the PI recruit and train graduate students (this project will support a female Ph.D student currently supervised by the PI) to pursue careers in computational mathematics.