论文标题
带有签名系数的无限传输问题中的散射共振
Scattering resonances in unbounded transmission problems with sign-changing coefficient
论文作者
论文摘要
众所周知，经典光腔可以表现出与散射共振相关的局部现象，从而导致近似溶液的数值不稳定性。可以通过黑框散射框架的``quasimodes for ressonances''参数建立此结果。这些局部现象集中在腔体的内部边界上，被称为耳语画廊模式。在本文中，我们研究了带有签名系数的无限传输问题的散射共振（对应于具有负光特性的光腔，例如由超材料制成）。由于光学性质的符号的变化，无法直接应用了先前的结果，并且在超材料 - 射线接口（例如所谓的表面等离子体）处出现了界面现象。我们确定了任意二维光滑超材腔的散射共振的存在。证明依赖于共振的渐近表征，并表明签名系数的问题自然适合黑匣子散射框架。我们的渐近分析表明，根据超材料的特性，位于实际轴的散射共振与表面等离子体有关。提供了几个超材料腔的示例。
It is well-known that classical optical cavities can exhibit localized phenomena associated to scattering resonances, leading to numerical instabilities in approximating the solution. This result can be established via the ``quasimodes to resonances'' argument from the black-box scattering framework. 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 properties, 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 showing that problems with sign-changing coefficient naturally fit the black box scattering framework. 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.
