Time-Dispersive Behavior as a Feature of Critical-Contrast Media
Kirill Cherednichenko, Yulia Yu. Ershova, Alexander V. Kiselev · SIAM Journal on Applied Mathematics · 2019
Motivated by the need to attribute a rigorous mathematical meaning to the term “metamaterial,” we propose a novel approach to the homogenization of critical-contrast composites. This is based on the asymptotic analysis of the Dirichlet-to-Neumann map on the interface between different components (``stiff” and “soft'') of the medium, which leads to an asymptotic approximation of eigenmodes. This allows us to see that the presence of the soft component makes the stiff one behave as a class of time-dispersive media. By an inversion of this argument, we also offer a recipe for the construction of such media with prescribed dispersive properties from periodic composites.