It is well-known that classical optical cavities can exhibit localized phenomena associated to scattering resonances (using the Black Box Scattering Theory), leading to numerical instabilities in approximating the solution. Those localized phenomena concentrate at the inner boundary of the cavity and are called whispering gallery modes. In this paper we investigate scattering resonances for unbounded transmission problems with sign-changing coefficient (corresponding to optical cavities with negative optical propertie(s), for example made of metamaterials). Due to the change of sign of optical properties, previous results cannot be applied directly, and interface phenomena at the metamaterial-dielectric interface (such as the so-called surface plasmons) emerge. We establish the existence of scattering resonances for arbitrary two-dimensional smooth metamaterial cavities. The proof relies on an asymptotic characterization of the resonances, and extending the Black Box Scattering Theory to problems with sign-changing coefficient. Our asymptotic analysis reveals that, depending on the metamaterial's properties, scattering resonances situated closed to the real axis are associated to surface plasmons. Examples for several metamaterial cavities are provided.

翻译：众所周知,古典光学洞穴可以展示与分散共振有关的局部现象(使用黑盒散射理论),导致接近溶液时的数值不稳定。这些局部现象集中在洞穴的内部边界,被称为低声道画廊模式。在本文中,我们用符号变化系数(对应负光学正弦(例如以元材料制成的)对准光学正弦(s)的光学正弦(sometive-formation volutions))来调查散射传输问题的共振现象。由于光学特性的改变,先前的结果无法直接应用,而元材料-二电界面(如所谓的表面颗粒子)的界面现象出现。我们建立了任意的两维光滑的元材料孔的散射共振现象。证据依赖于对共振的微调定性,将黑盒散射理论扩大到信号变化系数的问题。我们的合成分析显示,取决于元材料的表面特性,将一些封闭的图像与地轴相联起来。