  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.
