Mathematical Analysis of Metamaterials and Applications

Electromagnetic metamaterials are artificially structured composite media with unique and exotic properties that are not observed in natural materials. The first metamaterials with both negative permittivity and permeability was successfully constructed in 2000. The success triggered a new wave in study and design of metamaterials and investigation of potential applications in diverse areas. 

Metamaterials give rise to many interesting and challenging mathematical problems. In this workshop, we plan to focus on the following issues, but not limited to: 

1) Metamaterials require the novel incorporation of complex material models into Maxwell’s equations. How to validate those models is challenging: Is the simple averaging technique good enough? Under what scales are those models applicable? 

2) There exist some PDE models proposed by engineers and physics. However, very few results have been stated concerning well-posedness issues: solvability, stability, existence and regularity. We need some pure PDE mathematicians to get involved. 

3) From the computational modeling point view, much more work is needed. Design of a functional metamaterial leads to a PDE constrained optimization problem, which needs sophisticated numerical analysis and scientific computation.