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We study a 2D scalar harmonic wave transmission problem between a classicaldielectric and a medium with a real-valued negative permittivity/permeabilitywhich models a metal at optical frequency or an ideal negative metamaterial. Wehighlight an unusual instability phenomenon for this problem when the interfacebetween the two media presents a rounded corner. To establish this result, weprovide an asymptotic expansion of the solution, when it is well-defined, inthe geometry with a rounded corner. Then, we prove error estimates. Finally, acareful study of the asymptotic expansion allows us to conclude that thesolution, when it is well-defined, depends critically on the value of therounding parameter. We end the paper with a numerical illustration of thisinstability phenomenon.

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