Section: New Results

Instability phenomenon for a rounded corner in presence of a negative material

We studied a 2D transmission problem between a positive material and a negative material. In electromagnetics, this negative material can be a metal at optical frequencies or a negative metamaterial. We highlighted an unusual instability phenomenon in some configurations: when the interface between the two materials presents a rounded corner, it can happen that the solution depends critically on the value of the rounding parameter. To prove this result, we provided an asymptotic expansion of the solution, when it is well-defined, in the geometry with a rounded corner. Then, we demonstrated that the asymptotic expansion is not stable with respect to the rounding parameter. We also conducted obtained numerical experiments with finite element methods to validate these results.