A curious instability phenomenon for a rounded corner in presence of a negative material

作者：Chesnel Lucas^*; Claeys Xavier; Nazarov Sergey A

来源：Asymptotic Analysis, 2014, 88(1-2): 43-74.

DOI：10.3233/ASY-141214

• negative materials
• corner
• plasmonic
• metamaterial
• sign-changing coefficients

We study a 2D scalar harmonic wave transmission problem between a classical dielectric and a medium with a real-valued negative permittivity/ permeability which models a metal at optical frequency or an ideal negative metamaterial. We highlight an unusual instability phenomenon for this problem when the interface between the two media presents a rounded corner. To establish this result, we provide an asymptotic expansion of the solution, when it is well-defined, in the geometry with a rounded corner. Then, we prove error estimates. Finally, a careful study of the asymptotic expansion allows us to conclude that the solution, when it is well-defined, depends critically on the value of the rounding parameter. We end the paper with a numerical illustration of this instability phenomenon.

• 出版日期2014